{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "view-in-github",
"colab_type": "text"
},
"source": [
"![\"Open](\"https://colab.research.google.com/assets/colab-badge.svg\")
"
]
},
{
"cell_type": "markdown",
"id": "a36752ae-c66c-4937-a4b6-d3cdc2628d5c",
"metadata": {
"id": "a36752ae-c66c-4937-a4b6-d3cdc2628d5c"
},
"source": [
"**Programm für die Berechnung der Veformungen und Schnittgrößen von 2D Stabmodellen mittels FE**\n",
"\n",
"Das kleine 2D FE Programm setzt sich aus folgenden Teilen zusammen:\n",
"\n",
"1.) Modellierung und Diskretisierung: Das physische Objekt wird in kleinere Einheiten, sogenannte Elemente, unterteilt. Jeder Knotenpunkt eines Elements hat gewisse Freiheitsgrade, die die Bewegung in diesem Punkt beschreiben.\n",
"\n",
"2.) Defintion der Randbedingungen - Auflager.\n",
"\n",
"3.) Definition der Lasten: Externe Kräfte und Momente, die auf die Struktur wirken, werden als Lastvektor definiert. Dies kann sowohl Punktlasten als auch Linienlasten umfassen.\n",
"\n",
"4.) Berechnung der Elementmatrizen: Für jedes Element wird eine Steifigkeitsmatrix aufgestellt, die die Beziehung zwischen den Verschiebungen und den Kräften an den Knotenpunkten beschreibt.\n",
"\n",
"5.) Zusammenbau der globalen Steifigkeitsmatrix: Die Elementmatrizen werden in eine globale Steifigkeitsmatrix integriert, die das gesamte System beschreibt.\n",
"\n",
"6.) Anwendung von Randbedingungen: Hier werden die Bedingungen für Verschiebungen und Kräfte an den Rändern des Modells festgelegt.\n",
"\n",
"7.) Lösung des Gleichungssystems: Mit der globalen Steifigkeitsmatrix, den Randbedingungen und dem Lastvektor wird das Gleichungssystem gelöst, um die unbekannten Verschiebungen an jedem Knotenpunkt zu bestimmen.\n",
"\n",
"8.) Ermittlung der Auflagerreaktionen: Basierend auf den ermittelten Verschiebungen und der globalen Steifigkeitsmatrix werden die Reaktionen an den Auflagern berechnet.\n",
"\n",
"9.) Berechnung der inneren Kräfte: Basierend auf den ermittelten Verschiebungen werden die inneren Kräfte in jedem Element berechnet.\n",
"\n",
"10.) Visualisierung: Die ermittelten Verschiebungen, inneren Kräfte und Auflagerreaktionen werden visualisiert, um eine Vorstellung von der Beanspruchung und Verformung des Modells zu erhalten."
]
},
{
"cell_type": "markdown",
"id": "d9546489-e8ad-4a8d-bdc5-c780f1e9e3a9",
"metadata": {
"id": "d9546489-e8ad-4a8d-bdc5-c780f1e9e3a9"
},
"source": [
"**Importieren der erforderlichen Libraries**"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "6d4dc1ad-9c99-47f5-99e3-095a41f5af62",
"metadata": {
"id": "6d4dc1ad-9c99-47f5-99e3-095a41f5af62"
},
"outputs": [],
"source": [
"# Importieren von libraries\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import sympy as sp\n"
]
},
{
"cell_type": "markdown",
"id": "beccdc9e-4dc0-4a0f-ab95-4fbf9fb8b343",
"metadata": {
"id": "beccdc9e-4dc0-4a0f-ab95-4fbf9fb8b343"
},
"source": [
"**1.) Eingabe der Knoten und Stabelemente**"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "06483981-4a3e-4ee9-9395-4d1daeabbb7d",
"metadata": {
"tags": [],
"colab": {
"base_uri": "https://localhost:8080/",
"height": 71
},
"id": "06483981-4a3e-4ee9-9395-4d1daeabbb7d",
"outputId": "032e9f8e-03c3-499b-8226-376a843b097b"
},
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"[1, 2, 32837000.0, 0.25, 0.001302]"
]
},
"metadata": {}
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"[2, 3, 32837000.0, 0.3, 0.00225]"
]
},
"metadata": {}
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"[3, 4, 32837000.0, 0.3, 0.00225]"
]
},
"metadata": {}
}
],
"source": [
"# Knoten definition\n",
"# Nodes (node number: [x, y])\n",
"l = 6.00 # length\n",
"h = 3.15 # Height\n",
"nodes = {1: [0, 0],\n",
" 2: [0, h*1],\n",
" 3: [l*0.5, h*1],\n",
" 4: [l*1, h*1]}\n",
"\n",
"# Elements (element number: [node1, node2, E, A, I])\n",
"elements = {1: [1, 2, 32837e03, 0.25, 1.302e-03],\n",
" 2: [2, 3, 32837e03, 0.30, 2.250e-03],\n",
" 3: [3, 4, 32837e03, 0.30, 2.250e-03]}\n",
"display(elements[1])\n",
"display(elements[2])\n",
"display(elements[3])"
]
},
{
"cell_type": "markdown",
"id": "9dccd0ac-dd44-450f-aa9b-05a20fcb874a",
"metadata": {
"id": "9dccd0ac-dd44-450f-aa9b-05a20fcb874a"
},
"source": [
"**2.) Eingabe der Auflager**"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "9aa8260b-9f8f-49b0-a15d-eaf297597a7c",
"metadata": {
"tags": [],
"id": "9aa8260b-9f8f-49b0-a15d-eaf297597a7c"
},
"outputs": [],
"source": [
"# Supports (node number: [x_support, y_support, rot_support])\n",
"# If = -1 => fixed\n",
"# If > 0 => Spring stiffness\n",
"supports = {1: [-1, -1, -1],\n",
" 2: [0, 0, 0],\n",
" 3: [0, 0, 0],\n",
" 4: [0, -1, 0]}\n"
]
},
{
"cell_type": "markdown",
"id": "e68c3d2c-e647-4786-bbfa-ef8d6743eb1c",
"metadata": {
"id": "e68c3d2c-e647-4786-bbfa-ef8d6743eb1c"
},
"source": [
"**3.) Eingabe der Lasten**"
]
},
{
"cell_type": "markdown",
"id": "fbb525b4-6cf4-48f1-8cb0-4e42a89c774d",
"metadata": {
"id": "fbb525b4-6cf4-48f1-8cb0-4e42a89c774d"
},
"source": [
"Knotenlasten"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "83cd48b1-6a55-419e-a905-95bf34364067",
"metadata": {
"tags": [],
"id": "83cd48b1-6a55-419e-a905-95bf34364067"
},
"outputs": [],
"source": [
"# Loads (node number: [Fx, Fy, Mz])\n",
"loads = {1: [0, 0, 0],\n",
" 2: [0, 0, 0],\n",
" 3: [0, 0, 0],\n",
" 4: [0, 0, 0]}\n"
]
},
{
"cell_type": "markdown",
"id": "804b9fbf-479a-4ae9-9f0d-b5112a9d5fa4",
"metadata": {
"id": "804b9fbf-479a-4ae9-9f0d-b5112a9d5fa4"
},
"source": [
"Linienlast (Konstant):\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "1bdcb2e2-befc-4125-8d65-85fa452380de",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 106
},
"id": "1bdcb2e2-befc-4125-8d65-85fa452380de",
"outputId": "381a8819-a0d5-44fe-f696-fb80b116628c"
},
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"Knotenlasten (Punktlasten + Linienlast):\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"{1: [0.0, -9.84375, -5.16796875],\n",
" 2: [0.0, -21.09375, -0.45703125],\n",
" 3: [0.0, -22.5, 0.0],\n",
" 4: [0.0, -11.25, 5.625]}"
]
},
"metadata": {}
}
],
"source": [
"# Line loads (element number: (wx, wy))\n",
"line_loads = {1: (0, -0.25*25), 2: (0, -0.3*25), 3: (0, -0.3*25)} # Line loads on elements 1 and 2 in global coordinate system\n",
"\n",
"def calculate_equivalent_nodal_loads(wx, wy, L):\n",
" \"\"\"Calculate equivalent nodal loads for line loads in x and y directions.\"\"\"\n",
" Wx = wx * L # Total load in x direction\n",
" Wy = wy * L # Total load in y direction\n",
" Fx = Wx / 2 # Equivalent point load in x direction\n",
" Fy = Wy / 2 # Equivalent point load in y direction\n",
" M = Wy * L / 12 # Equivalent moment due to y direction load\n",
" return [Fx, Fy, M, -M] # Return forces and moments for start and end nodes\n",
"\n",
"# Calculate equivalent nodal loads and add to a new dictionary\n",
"udl_loads = {}\n",
"for e, (wx, wy) in line_loads.items():\n",
" node1, node2 = elements[e][:2]\n",
" L = np.sqrt((nodes[node2][0] - nodes[node1][0])**2 + (nodes[node2][1] - nodes[node1][1])**2)\n",
" Fx1, Fy1, M1, M2 = calculate_equivalent_nodal_loads(wx, wy, L)\n",
" if node1 in udl_loads:\n",
" udl_loads[node1][0] += Fx1\n",
" udl_loads[node1][1] += Fy1\n",
" udl_loads[node1][2] += M1\n",
" else:\n",
" udl_loads[node1] = [Fx1, Fy1, M1]\n",
" if node2 in udl_loads:\n",
" udl_loads[node2][0] += Fx1\n",
" udl_loads[node2][1] += Fy1\n",
" udl_loads[node2][2] += M2\n",
" else:\n",
" udl_loads[node2] = [Fx1, Fy1, M2]\n",
"\n",
"# Combine the udl_loads with the loads dictionary\n",
"for node, load in udl_loads.items():\n",
" if node in loads:\n",
" loads[node] = [sum(x) for x in zip(loads[node], load)]\n",
" else:\n",
" loads[node] = load\n",
"\n",
"print(f\"Knotenlasten (Punktlasten + Linienlast):\")\n",
"display(loads)"
]
},
{
"cell_type": "markdown",
"id": "26160da5-37ff-4f4f-8936-a7fd9453b314",
"metadata": {
"id": "26160da5-37ff-4f4f-8936-a7fd9453b314"
},
"source": [
"**4.) Erstellen der lokalen Steifigkeitsmatrix**\n",
"\n",
"Die lokale Steifigkeitsmatrix eines Elements in einem Strukturmodell repräsentiert die Beziehung zwischen den Verschiebungen und den Kräften innerhalb dieses Elements. Sie wird berechnet, indem die physikalischen Eigenschaften des Elements (wie die Elastizitätsmodul E, der Querschnittsfläche A und das Flächenträgheitsmoment I) sowie die Geometrie des Elements (die Länge L und die Ausrichtung) berücksichtigt werden.\n",
"\n",
"In unserem Python-Code definieren wir eine Funktion namens local_beam_element_stiffness, die die lokale Steifigkeitsmatrix für ein gegebenes Element berechnet. Diese Funktion nimmt die Knoten und die Elementinformationen als Eingabe und gibt die lokale Steifigkeitsmatrix als Ausgabe zurück.\n",
"\n",
"Die Funktion berechnet zuerst die Länge des Elements und dann die lokale Steifigkeitsmatrix unter Berücksichtigung der Biegesteifigkeit und der axialen Steifigkeit des Elements. Die resultierende 6x6-Matrix repräsentiert die lokale Steifigkeitsmatrix des Elements in seinem eigenen lokalen Koordinatensystem.\n",
"\n",
"Diese Matrizen sind ein wichtiger Bestandteil der Finite-Elemente-Analyse, da sie verwendet werden, um die globale Steifigkeitsmatrix der gesamten Struktur zu erstellen."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "b8a33181-c1f5-44a2-8221-bb4a295e3a14",
"metadata": {
"tags": [],
"id": "b8a33181-c1f5-44a2-8221-bb4a295e3a14"
},
"outputs": [],
"source": [
"# Lokale Steifigkeits Matrix\n",
"def local_beam_element_stiffness(nodes, element):\n",
" \"\"\"Calculate local element stiffness matrix for a beam element.\"\"\"\n",
" node1, node2, E, A, I = element\n",
" x1, y1 = nodes[node1]\n",
" x2, y2 = nodes[node2]\n",
" L = np.sqrt((x2 - x1)**2 + (y2 - y1)**2)\n",
" k_local = E * np.array([[A/L, 0, 0, -A/L, 0, 0],\n",
" [0, 12*I/L**3, 6*I/L**2, 0, -12*I/L**3, 6*I/L**2],\n",
" [0, 6*I/L**2, 4*I/L, 0, -6*I/L**2, 2*I/L],\n",
" [-A/L, 0, 0, A/L, 0, 0],\n",
" [0, -12*I/L**3, -6*I/L**2, 0, 12*I/L**3, -6*I/L**2],\n",
" [0, 6*I/L**2, 2*I/L, 0, -6*I/L**2, 4*I/L]])\n",
" return k_local"
]
},
{
"cell_type": "markdown",
"id": "857a7b5a-23c0-46e3-9664-858e1ba1dac5",
"metadata": {
"id": "857a7b5a-23c0-46e3-9664-858e1ba1dac5"
},
"source": [
"Durch Iteration über alle Elemente in unserem Modell können wir die lokale Steifigkeitsmatrix für jedes Element berechnen und anzeigen."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "a4f92471-0090-453b-b50b-8fd7d4609a98",
"metadata": {
"tags": [],
"colab": {
"base_uri": "https://localhost:8080/",
"height": 437
},
"id": "a4f92471-0090-453b-b50b-8fd7d4609a98",
"outputId": "73918db2-50b8-4959-e9a0-0779c36d1396"
},
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"Local stiffness matrix for element 1:\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"Matrix([\n",
"[ 2.61e+6, 0, 0, -2.61e+6, 0, 0],\n",
"[ 0, 1.64e+4, 2.59e+4, 0, -1.64e+4, 2.59e+4],\n",
"[ 0, 2.59e+4, 5.43e+4, 0, -2.59e+4, 2.71e+4],\n",
"[-2.61e+6, 0, 0, 2.61e+6, 0, 0],\n",
"[ 0, -1.64e+4, -2.59e+4, 0, 1.64e+4, -2.59e+4],\n",
"[ 0, 2.59e+4, 2.71e+4, 0, -2.59e+4, 5.43e+4]])"
],
"text/latex": "$\\displaystyle \\left[\\begin{matrix}2.61 \\cdot 10^{6} & 0 & 0 & -2.61 \\cdot 10^{6} & 0 & 0\\\\0 & 1.64 \\cdot 10^{4} & 2.59 \\cdot 10^{4} & 0 & -1.64 \\cdot 10^{4} & 2.59 \\cdot 10^{4}\\\\0 & 2.59 \\cdot 10^{4} & 5.43 \\cdot 10^{4} & 0 & -2.59 \\cdot 10^{4} & 2.71 \\cdot 10^{4}\\\\-2.61 \\cdot 10^{6} & 0 & 0 & 2.61 \\cdot 10^{6} & 0 & 0\\\\0 & -1.64 \\cdot 10^{4} & -2.59 \\cdot 10^{4} & 0 & 1.64 \\cdot 10^{4} & -2.59 \\cdot 10^{4}\\\\0 & 2.59 \\cdot 10^{4} & 2.71 \\cdot 10^{4} & 0 & -2.59 \\cdot 10^{4} & 5.43 \\cdot 10^{4}\\end{matrix}\\right]$"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"Local stiffness matrix for element 2:\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"Matrix([\n",
"[ 3.28e+6, 0, 0, -3.28e+6, 0, 0],\n",
"[ 0, 3.28e+4, 4.93e+4, 0, -3.28e+4, 4.93e+4],\n",
"[ 0, 4.93e+4, 9.85e+4, 0, -4.93e+4, 4.93e+4],\n",
"[-3.28e+6, 0, 0, 3.28e+6, 0, 0],\n",
"[ 0, -3.28e+4, -4.93e+4, 0, 3.28e+4, -4.93e+4],\n",
"[ 0, 4.93e+4, 4.93e+4, 0, -4.93e+4, 9.85e+4]])"
],
"text/latex": "$\\displaystyle \\left[\\begin{matrix}3.28 \\cdot 10^{6} & 0 & 0 & -3.28 \\cdot 10^{6} & 0 & 0\\\\0 & 3.28 \\cdot 10^{4} & 4.93 \\cdot 10^{4} & 0 & -3.28 \\cdot 10^{4} & 4.93 \\cdot 10^{4}\\\\0 & 4.93 \\cdot 10^{4} & 9.85 \\cdot 10^{4} & 0 & -4.93 \\cdot 10^{4} & 4.93 \\cdot 10^{4}\\\\-3.28 \\cdot 10^{6} & 0 & 0 & 3.28 \\cdot 10^{6} & 0 & 0\\\\0 & -3.28 \\cdot 10^{4} & -4.93 \\cdot 10^{4} & 0 & 3.28 \\cdot 10^{4} & -4.93 \\cdot 10^{4}\\\\0 & 4.93 \\cdot 10^{4} & 4.93 \\cdot 10^{4} & 0 & -4.93 \\cdot 10^{4} & 9.85 \\cdot 10^{4}\\end{matrix}\\right]$"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"Local stiffness matrix for element 3:\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"Matrix([\n",
"[ 3.28e+6, 0, 0, -3.28e+6, 0, 0],\n",
"[ 0, 3.28e+4, 4.93e+4, 0, -3.28e+4, 4.93e+4],\n",
"[ 0, 4.93e+4, 9.85e+4, 0, -4.93e+4, 4.93e+4],\n",
"[-3.28e+6, 0, 0, 3.28e+6, 0, 0],\n",
"[ 0, -3.28e+4, -4.93e+4, 0, 3.28e+4, -4.93e+4],\n",
"[ 0, 4.93e+4, 4.93e+4, 0, -4.93e+4, 9.85e+4]])"
],
"text/latex": "$\\displaystyle \\left[\\begin{matrix}3.28 \\cdot 10^{6} & 0 & 0 & -3.28 \\cdot 10^{6} & 0 & 0\\\\0 & 3.28 \\cdot 10^{4} & 4.93 \\cdot 10^{4} & 0 & -3.28 \\cdot 10^{4} & 4.93 \\cdot 10^{4}\\\\0 & 4.93 \\cdot 10^{4} & 9.85 \\cdot 10^{4} & 0 & -4.93 \\cdot 10^{4} & 4.93 \\cdot 10^{4}\\\\-3.28 \\cdot 10^{6} & 0 & 0 & 3.28 \\cdot 10^{6} & 0 & 0\\\\0 & -3.28 \\cdot 10^{4} & -4.93 \\cdot 10^{4} & 0 & 3.28 \\cdot 10^{4} & -4.93 \\cdot 10^{4}\\\\0 & 4.93 \\cdot 10^{4} & 4.93 \\cdot 10^{4} & 0 & -4.93 \\cdot 10^{4} & 9.85 \\cdot 10^{4}\\end{matrix}\\right]$"
},
"metadata": {}
}
],
"source": [
"# Calculate local stiffness matrices for all elements and display them\n",
"for element_number, element in elements.items():\n",
" K_local = local_beam_element_stiffness(nodes, element)\n",
" # nice plot of matrix\n",
" K_local_sp = sp.Matrix(K_local).applyfunc(lambda x: sp.N(x, 3))\n",
" print(f\"Local stiffness matrix for element {element_number}:\")\n",
" display(K_local_sp)"
]
},
{
"cell_type": "markdown",
"id": "6a90e992-75e2-47ed-b729-8a31b7f1f26d",
"metadata": {
"id": "6a90e992-75e2-47ed-b729-8a31b7f1f26d"
},
"source": [
"**Erstellen der Transformationsmatrix**\n",
"\n",
"Die Transformationsmatrix wird in der Strukturanalyse verwendet, um die lokalen Steifigkeitsmatrizen der einzelnen Elemente in das globale Koordinatensystem zu übertragen. Dies ist notwendig, weil die lokalen Steifigkeitsmatrizen in den lokalen Koordinatensystemen der einzelnen Elemente definiert sind, während die globale Steifigkeitsmatrix, die das gesamte Strukturmodell repräsentiert, im globalen Koordinatensystem definiert ist.\n",
"\n",
"In unserem Python-Code definieren wir eine Funktion namens calculate_transformation_matrix, die die Transformationsmatrix für ein gegebenes Element berechnet. Diese Funktion nimmt die Knoten und die Elementinformationen als Eingabe und gibt die Transformationsmatrix als Ausgabe zurück.\n",
"\n",
"Die Funktion berechnet zuerst die Länge des Elements und dann die Winkel zwischen der x-Achse des globalen Koordinatensystems und der Linie, die die beiden Knoten des Elements verbindet. Diese Winkel werden dann verwendet, um die Transformationsmatrix zu berechnen.\n",
"\n",
"Die resultierende 6x6-Matrix ist die Transformationsmatrix des Elements. Sie wird verwendet, um die lokale Steifigkeitsmatrix des Elements in das globale Koordinatensystem zu transformieren, indem sie von links und von rechts auf die lokale Steifigkeitsmatrix angewendet wird.\n",
"\n",
"Diese Matrizen sind ein weiterer wichtiger Bestandteil der Finite-Elemente-Analyse, da sie verwendet werden, um die lokalen Steifigkeitsmatrizen in das globale Koordinatensystem zu übertragen."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "f3530760-1a3f-40a6-b402-c7c8cf15ff39",
"metadata": {
"tags": [],
"id": "f3530760-1a3f-40a6-b402-c7c8cf15ff39"
},
"outputs": [],
"source": [
"def calculate_transformation_matrix(nodes, element):\n",
" \"\"\"Calculate the transformation matrix for an element.\"\"\"\n",
" node1, node2 = element[0:2]\n",
" x1, y1 = nodes[node1]\n",
" x2, y2 = nodes[node2]\n",
" L = np.sqrt((x2 - x1)**2 + (y2 - y1)**2)\n",
" cos = (x2 - x1) / L\n",
" sin = (y2 - y1) / L\n",
" T = np.zeros((6, 6))\n",
" T[:2, :2] = T[3:5, 3:5] = np.array([[cos, sin], [-sin, cos]])\n",
" T[2, 2] = T[5, 5] = 1\n",
" return T\n"
]
},
{
"cell_type": "markdown",
"id": "e8c9f69d-1b36-4685-9035-1096c7816558",
"metadata": {
"id": "e8c9f69d-1b36-4685-9035-1096c7816558"
},
"source": [
"Durch Iteration über alle Elemente in unserem Modell können wir die Transformationsmatrix für jedes Element berechnen und anzeigen."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "3742e37e-481d-4ae2-a269-9dc8137a416e",
"metadata": {
"tags": [],
"colab": {
"base_uri": "https://localhost:8080/",
"height": 437
},
"id": "3742e37e-481d-4ae2-a269-9dc8137a416e",
"outputId": "9609673b-82a6-4b20-b453-2927f67b0ca4"
},
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"Transformation matrix for element 1:\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"Matrix([\n",
"[ 0, 1.0, 0, 0, 0, 0],\n",
"[-1.0, 0, 0, 0, 0, 0],\n",
"[ 0, 0, 1.0, 0, 0, 0],\n",
"[ 0, 0, 0, 0, 1.0, 0],\n",
"[ 0, 0, 0, -1.0, 0, 0],\n",
"[ 0, 0, 0, 0, 0, 1.0]])"
],
"text/latex": "$\\displaystyle \\left[\\begin{matrix}0 & 1.0 & 0 & 0 & 0 & 0\\\\-1.0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 1.0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 1.0 & 0\\\\0 & 0 & 0 & -1.0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 1.0\\end{matrix}\\right]$"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"Transformation matrix for element 2:\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"Matrix([\n",
"[1.0, 0, 0, 0, 0, 0],\n",
"[ 0, 1.0, 0, 0, 0, 0],\n",
"[ 0, 0, 1.0, 0, 0, 0],\n",
"[ 0, 0, 0, 1.0, 0, 0],\n",
"[ 0, 0, 0, 0, 1.0, 0],\n",
"[ 0, 0, 0, 0, 0, 1.0]])"
],
"text/latex": "$\\displaystyle \\left[\\begin{matrix}1.0 & 0 & 0 & 0 & 0 & 0\\\\0 & 1.0 & 0 & 0 & 0 & 0\\\\0 & 0 & 1.0 & 0 & 0 & 0\\\\0 & 0 & 0 & 1.0 & 0 & 0\\\\0 & 0 & 0 & 0 & 1.0 & 0\\\\0 & 0 & 0 & 0 & 0 & 1.0\\end{matrix}\\right]$"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"Transformation matrix for element 3:\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"Matrix([\n",
"[1.0, 0, 0, 0, 0, 0],\n",
"[ 0, 1.0, 0, 0, 0, 0],\n",
"[ 0, 0, 1.0, 0, 0, 0],\n",
"[ 0, 0, 0, 1.0, 0, 0],\n",
"[ 0, 0, 0, 0, 1.0, 0],\n",
"[ 0, 0, 0, 0, 0, 1.0]])"
],
"text/latex": "$\\displaystyle \\left[\\begin{matrix}1.0 & 0 & 0 & 0 & 0 & 0\\\\0 & 1.0 & 0 & 0 & 0 & 0\\\\0 & 0 & 1.0 & 0 & 0 & 0\\\\0 & 0 & 0 & 1.0 & 0 & 0\\\\0 & 0 & 0 & 0 & 1.0 & 0\\\\0 & 0 & 0 & 0 & 0 & 1.0\\end{matrix}\\right]$"
},
"metadata": {}
}
],
"source": [
"# Calculate transformation matrices for all elements and display them\n",
"for element_number, element in elements.items():\n",
" T = calculate_transformation_matrix(nodes, element)\n",
" # nice plot of matrix\n",
" T_sp = sp.Matrix(T).applyfunc(lambda x: sp.N(x, 3))\n",
" print(f\"Transformation matrix for element {element_number}:\")\n",
" display(T_sp)\n"
]
},
{
"cell_type": "markdown",
"id": "ae2ed96b-2a9a-4eae-97a7-6824b9199e05",
"metadata": {
"id": "ae2ed96b-2a9a-4eae-97a7-6824b9199e05"
},
"source": [
"**5.) Globale Steifigkeitsmatrix der Stabelemente**\n",
"\n",
"Die Funktion global_beam_element_stiffness berechnet die globale Steifigkeitsmatrix für ein gegebenes Element in einem Strukturmodell. Die globale Steifigkeitsmatrix repräsentiert die Beziehung zwischen den Verschiebungen und den Kräften innerhalb dieses Elements im globalen Koordinatensystem der gesamten Struktur.\n",
"\n",
"Die Funktion nimmt die Knoten und die Elementinformationen als Eingabe und gibt die globale Steifigkeitsmatrix als Ausgabe zurück. Sie tut dies, indem sie zuerst die lokale Steifigkeitsmatrix des Elements mit der Funktion local_beam_element_stiffness berechnet und dann die Transformationsmatrix des Elements mit der Funktion calculate_transformation_matrix berechnet.\n",
"\n",
"Die lokale Steifigkeitsmatrix wird dann in das globale Koordinatensystem transformiert, indem sie mit der transponierten Transformationsmatrix von links und der Transformationsmatrix von rechts multipliziert wird. Das Ergebnis dieser Operation ist die globale Steifigkeitsmatrix des Elements.\n",
"\n",
"Diese Matrizen sind ein entscheidender Bestandteil der Finite-Elemente-Analyse, da sie verwendet werden, um die globale Steifigkeitsmatrix der gesamten Struktur zu erstellen."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "0cc971a1-5c51-4293-952f-45d22506f0d1",
"metadata": {
"tags": [],
"id": "0cc971a1-5c51-4293-952f-45d22506f0d1"
},
"outputs": [],
"source": [
"def global_beam_element_stiffness(nodes, element):\n",
" \"\"\"Calculate global element stiffness matrix for a beam element.\"\"\"\n",
" k_local = local_beam_element_stiffness(nodes, element)\n",
" T = calculate_transformation_matrix(nodes, element)\n",
" k_global = T.T @ k_local @ T\n",
" return k_global\n"
]
},
{
"cell_type": "markdown",
"id": "185d2a22-7290-41c7-bbf4-89755a062ef4",
"metadata": {
"id": "185d2a22-7290-41c7-bbf4-89755a062ef4"
},
"source": [
"Durch Iteration über alle Elemente in unserem Modell können wir die globale Steifigkeitsmatrix für jedes Element berechnen und anzeigen."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "00b36732-6d13-406f-9923-06f965d68a42",
"metadata": {
"tags": [],
"colab": {
"base_uri": "https://localhost:8080/",
"height": 437
},
"id": "00b36732-6d13-406f-9923-06f965d68a42",
"outputId": "d8fbbb29-2520-41aa-c118-a5eaa3a23783"
},
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"Global stiffness matrix for element1:\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"Matrix([\n",
"[ 1.64e+4, 0, -2.59e+4, -1.64e+4, 0, -2.59e+4],\n",
"[ 0, 2.61e+6, 0, 0, -2.61e+6, 0],\n",
"[-2.59e+4, 0, 5.43e+4, 2.59e+4, 0, 2.71e+4],\n",
"[-1.64e+4, 0, 2.59e+4, 1.64e+4, 0, 2.59e+4],\n",
"[ 0, -2.61e+6, 0, 0, 2.61e+6, 0],\n",
"[-2.59e+4, 0, 2.71e+4, 2.59e+4, 0, 5.43e+4]])"
],
"text/latex": "$\\displaystyle \\left[\\begin{matrix}1.64 \\cdot 10^{4} & 0 & -2.59 \\cdot 10^{4} & -1.64 \\cdot 10^{4} & 0 & -2.59 \\cdot 10^{4}\\\\0 & 2.61 \\cdot 10^{6} & 0 & 0 & -2.61 \\cdot 10^{6} & 0\\\\-2.59 \\cdot 10^{4} & 0 & 5.43 \\cdot 10^{4} & 2.59 \\cdot 10^{4} & 0 & 2.71 \\cdot 10^{4}\\\\-1.64 \\cdot 10^{4} & 0 & 2.59 \\cdot 10^{4} & 1.64 \\cdot 10^{4} & 0 & 2.59 \\cdot 10^{4}\\\\0 & -2.61 \\cdot 10^{6} & 0 & 0 & 2.61 \\cdot 10^{6} & 0\\\\-2.59 \\cdot 10^{4} & 0 & 2.71 \\cdot 10^{4} & 2.59 \\cdot 10^{4} & 0 & 5.43 \\cdot 10^{4}\\end{matrix}\\right]$"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"Global stiffness matrix for element2:\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"Matrix([\n",
"[ 3.28e+6, 0, 0, -3.28e+6, 0, 0],\n",
"[ 0, 3.28e+4, 4.93e+4, 0, -3.28e+4, 4.93e+4],\n",
"[ 0, 4.93e+4, 9.85e+4, 0, -4.93e+4, 4.93e+4],\n",
"[-3.28e+6, 0, 0, 3.28e+6, 0, 0],\n",
"[ 0, -3.28e+4, -4.93e+4, 0, 3.28e+4, -4.93e+4],\n",
"[ 0, 4.93e+4, 4.93e+4, 0, -4.93e+4, 9.85e+4]])"
],
"text/latex": "$\\displaystyle \\left[\\begin{matrix}3.28 \\cdot 10^{6} & 0 & 0 & -3.28 \\cdot 10^{6} & 0 & 0\\\\0 & 3.28 \\cdot 10^{4} & 4.93 \\cdot 10^{4} & 0 & -3.28 \\cdot 10^{4} & 4.93 \\cdot 10^{4}\\\\0 & 4.93 \\cdot 10^{4} & 9.85 \\cdot 10^{4} & 0 & -4.93 \\cdot 10^{4} & 4.93 \\cdot 10^{4}\\\\-3.28 \\cdot 10^{6} & 0 & 0 & 3.28 \\cdot 10^{6} & 0 & 0\\\\0 & -3.28 \\cdot 10^{4} & -4.93 \\cdot 10^{4} & 0 & 3.28 \\cdot 10^{4} & -4.93 \\cdot 10^{4}\\\\0 & 4.93 \\cdot 10^{4} & 4.93 \\cdot 10^{4} & 0 & -4.93 \\cdot 10^{4} & 9.85 \\cdot 10^{4}\\end{matrix}\\right]$"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"Global stiffness matrix for element3:\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"Matrix([\n",
"[ 3.28e+6, 0, 0, -3.28e+6, 0, 0],\n",
"[ 0, 3.28e+4, 4.93e+4, 0, -3.28e+4, 4.93e+4],\n",
"[ 0, 4.93e+4, 9.85e+4, 0, -4.93e+4, 4.93e+4],\n",
"[-3.28e+6, 0, 0, 3.28e+6, 0, 0],\n",
"[ 0, -3.28e+4, -4.93e+4, 0, 3.28e+4, -4.93e+4],\n",
"[ 0, 4.93e+4, 4.93e+4, 0, -4.93e+4, 9.85e+4]])"
],
"text/latex": "$\\displaystyle \\left[\\begin{matrix}3.28 \\cdot 10^{6} & 0 & 0 & -3.28 \\cdot 10^{6} & 0 & 0\\\\0 & 3.28 \\cdot 10^{4} & 4.93 \\cdot 10^{4} & 0 & -3.28 \\cdot 10^{4} & 4.93 \\cdot 10^{4}\\\\0 & 4.93 \\cdot 10^{4} & 9.85 \\cdot 10^{4} & 0 & -4.93 \\cdot 10^{4} & 4.93 \\cdot 10^{4}\\\\-3.28 \\cdot 10^{6} & 0 & 0 & 3.28 \\cdot 10^{6} & 0 & 0\\\\0 & -3.28 \\cdot 10^{4} & -4.93 \\cdot 10^{4} & 0 & 3.28 \\cdot 10^{4} & -4.93 \\cdot 10^{4}\\\\0 & 4.93 \\cdot 10^{4} & 4.93 \\cdot 10^{4} & 0 & -4.93 \\cdot 10^{4} & 9.85 \\cdot 10^{4}\\end{matrix}\\right]$"
},
"metadata": {}
}
],
"source": [
"# Calculate global stiffness matrices for all elements and display them\n",
"for element_number, element in elements.items():\n",
" K_global = global_beam_element_stiffness(nodes, element)\n",
" # nice plot of matrix\n",
" K_global_sp = sp.Matrix(K_global).applyfunc(lambda x: sp.N(x, 3))\n",
" print(f\"Global stiffness matrix for element{element_number}:\")\n",
" display(K_global_sp)"
]
},
{
"cell_type": "markdown",
"id": "deefb4ed-c509-4f45-ba17-6735161ab178",
"metadata": {
"id": "deefb4ed-c509-4f45-ba17-6735161ab178"
},
"source": [
"Die Funktion assemble_global_stiffness erstellt die globale Steifigkeitsmatrix für die gesamte Struktur aus den globalen Steifigkeitsmatrizen der einzelnen Elemente.\n",
"\n",
"Zuerst berechnet die Funktion die Anzahl der Freiheitsgrade der gesamten Struktur, die gleich der Anzahl der Knoten multipliziert mit 3 ist (da es in einem 2D-Balkenproblem 3 Freiheitsgrade pro Knoten gibt). Dann initialisiert sie die globale Steifigkeitsmatrix als Nullmatrix der entsprechenden Größe.\n",
"\n",
"Die Funktion iteriert dann über alle Elemente in der Struktur. Für jedes Element berechnet sie die globale Steifigkeitsmatrix mit der Funktion global_beam_element_stiffness und zeigt diese an. Dann bestimmt sie die Freiheitsgrade, die mit den beiden Knoten des Elements verbunden sind.\n",
"\n",
"In einer verschachtelten Schleife fügt die Funktion dann die Einträge der globalen Steifigkeitsmatrix des Elements zur entsprechenden Position in der globalen Steifigkeitsmatrix der gesamten Struktur hinzu. Nach dem Hinzufügen jedes Elements zeigt die Funktion die aktualisierte globale Steifigkeitsmatrix an.\n",
"\n",
"Am Ende gibt die Funktion die zusammengesetzte globale Steifigkeitsmatrix zurück. Diese Matrix repräsentiert die Beziehung zwischen den Verschiebungen und den Kräften in der gesamten Struktur und ist ein zentraler Bestandteil der Finite-Elemente-Analyse."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "2f320248-8914-4eb4-a5ca-5b7ed9ed2774",
"metadata": {
"tags": [],
"id": "2f320248-8914-4eb4-a5ca-5b7ed9ed2774"
},
"outputs": [],
"source": [
"def assemble_global_stiffness(nodes, elements):\n",
" \"\"\"Assemble the global stiffness matrix from the element stiffness matrices.\"\"\"\n",
" dof = len(nodes) * 3 # Degrees of freedom (3 per node for 2D beam)\n",
" K = np.zeros((dof, dof))\n",
" for element, properties in elements.items():\n",
" k_global = global_beam_element_stiffness(nodes, properties)\n",
" # nice plot of matrix\n",
" k_global_sp = sp.Matrix(k_global).applyfunc(lambda x: sp.N(x, 3))\n",
" print(f\"Global stiffness matrix for element {element}:\")\n",
" display(k_global_sp)\n",
" node1, node2 = properties[:2]\n",
" # DOFs related to the element (6 for each beam element)\n",
" dofs = [node1*3-3, node1*3-2, node1*3-1, node2*3-3, node2*3-2, node2*3-1]\n",
" for i in range(6):\n",
" for j in range(6):\n",
" K[dofs[i], dofs[j]] += k_global[i, j]\n",
" K_sp = sp.Matrix(K).applyfunc(lambda x: sp.N(x, 3))\n",
" print(f\"Global stiffness matrix after adding element {element}:\")\n",
" display(K_sp)\n",
" return K\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "2b77a7cd-3ec2-49fb-8f55-438e6fc82acf",
"metadata": {
"tags": [],
"colab": {
"base_uri": "https://localhost:8080/",
"height": 1000
},
"id": "2b77a7cd-3ec2-49fb-8f55-438e6fc82acf",
"outputId": "1eceb911-8781-4ac6-e22f-d18826d765fc"
},
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"Global stiffness matrix for element 1:\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"Matrix([\n",
"[ 1.64e+4, 0, -2.59e+4, -1.64e+4, 0, -2.59e+4],\n",
"[ 0, 2.61e+6, 0, 0, -2.61e+6, 0],\n",
"[-2.59e+4, 0, 5.43e+4, 2.59e+4, 0, 2.71e+4],\n",
"[-1.64e+4, 0, 2.59e+4, 1.64e+4, 0, 2.59e+4],\n",
"[ 0, -2.61e+6, 0, 0, 2.61e+6, 0],\n",
"[-2.59e+4, 0, 2.71e+4, 2.59e+4, 0, 5.43e+4]])"
],
"text/latex": "$\\displaystyle \\left[\\begin{matrix}1.64 \\cdot 10^{4} & 0 & -2.59 \\cdot 10^{4} & -1.64 \\cdot 10^{4} & 0 & -2.59 \\cdot 10^{4}\\\\0 & 2.61 \\cdot 10^{6} & 0 & 0 & -2.61 \\cdot 10^{6} & 0\\\\-2.59 \\cdot 10^{4} & 0 & 5.43 \\cdot 10^{4} & 2.59 \\cdot 10^{4} & 0 & 2.71 \\cdot 10^{4}\\\\-1.64 \\cdot 10^{4} & 0 & 2.59 \\cdot 10^{4} & 1.64 \\cdot 10^{4} & 0 & 2.59 \\cdot 10^{4}\\\\0 & -2.61 \\cdot 10^{6} & 0 & 0 & 2.61 \\cdot 10^{6} & 0\\\\-2.59 \\cdot 10^{4} & 0 & 2.71 \\cdot 10^{4} & 2.59 \\cdot 10^{4} & 0 & 5.43 \\cdot 10^{4}\\end{matrix}\\right]$"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"Global stiffness matrix after adding element 1:\n"
]
},
{
"output_type": "display_data",
"data": {
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"Matrix([\n",
"[ 1.64e+4, 0, -2.59e+4, -1.64e+4, 0, -2.59e+4, 0, 0, 0, 0, 0, 0],\n",
"[ 0, 2.61e+6, 0, 0, -2.61e+6, 0, 0, 0, 0, 0, 0, 0],\n",
"[-2.59e+4, 0, 5.43e+4, 2.59e+4, 0, 2.71e+4, 0, 0, 0, 0, 0, 0],\n",
"[-1.64e+4, 0, 2.59e+4, 1.64e+4, 0, 2.59e+4, 0, 0, 0, 0, 0, 0],\n",
"[ 0, -2.61e+6, 0, 0, 2.61e+6, 0, 0, 0, 0, 0, 0, 0],\n",
"[-2.59e+4, 0, 2.71e+4, 2.59e+4, 0, 5.43e+4, 0, 0, 0, 0, 0, 0],\n",
"[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
"[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
"[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
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"[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])"
],
"text/latex": "$\\displaystyle \\left[\\begin{array}{cccccccccccc}1.64 \\cdot 10^{4} & 0 & -2.59 \\cdot 10^{4} & -1.64 \\cdot 10^{4} & 0 & -2.59 \\cdot 10^{4} & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 2.61 \\cdot 10^{6} & 0 & 0 & -2.61 \\cdot 10^{6} & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\-2.59 \\cdot 10^{4} & 0 & 5.43 \\cdot 10^{4} & 2.59 \\cdot 10^{4} & 0 & 2.71 \\cdot 10^{4} & 0 & 0 & 0 & 0 & 0 & 0\\\\-1.64 \\cdot 10^{4} & 0 & 2.59 \\cdot 10^{4} & 1.64 \\cdot 10^{4} & 0 & 2.59 \\cdot 10^{4} & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & -2.61 \\cdot 10^{6} & 0 & 0 & 2.61 \\cdot 10^{6} & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\-2.59 \\cdot 10^{4} & 0 & 2.71 \\cdot 10^{4} & 2.59 \\cdot 10^{4} & 0 & 5.43 \\cdot 10^{4} & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\end{array}\\right]$"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"Global stiffness matrix for element 2:\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"Matrix([\n",
"[ 3.28e+6, 0, 0, -3.28e+6, 0, 0],\n",
"[ 0, 3.28e+4, 4.93e+4, 0, -3.28e+4, 4.93e+4],\n",
"[ 0, 4.93e+4, 9.85e+4, 0, -4.93e+4, 4.93e+4],\n",
"[-3.28e+6, 0, 0, 3.28e+6, 0, 0],\n",
"[ 0, -3.28e+4, -4.93e+4, 0, 3.28e+4, -4.93e+4],\n",
"[ 0, 4.93e+4, 4.93e+4, 0, -4.93e+4, 9.85e+4]])"
],
"text/latex": "$\\displaystyle \\left[\\begin{matrix}3.28 \\cdot 10^{6} & 0 & 0 & -3.28 \\cdot 10^{6} & 0 & 0\\\\0 & 3.28 \\cdot 10^{4} & 4.93 \\cdot 10^{4} & 0 & -3.28 \\cdot 10^{4} & 4.93 \\cdot 10^{4}\\\\0 & 4.93 \\cdot 10^{4} & 9.85 \\cdot 10^{4} & 0 & -4.93 \\cdot 10^{4} & 4.93 \\cdot 10^{4}\\\\-3.28 \\cdot 10^{6} & 0 & 0 & 3.28 \\cdot 10^{6} & 0 & 0\\\\0 & -3.28 \\cdot 10^{4} & -4.93 \\cdot 10^{4} & 0 & 3.28 \\cdot 10^{4} & -4.93 \\cdot 10^{4}\\\\0 & 4.93 \\cdot 10^{4} & 4.93 \\cdot 10^{4} & 0 & -4.93 \\cdot 10^{4} & 9.85 \\cdot 10^{4}\\end{matrix}\\right]$"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"Global stiffness matrix after adding element 2:\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"Matrix([\n",
"[ 1.64e+4, 0, -2.59e+4, -1.64e+4, 0, -2.59e+4, 0, 0, 0, 0, 0, 0],\n",
"[ 0, 2.61e+6, 0, 0, -2.61e+6, 0, 0, 0, 0, 0, 0, 0],\n",
"[-2.59e+4, 0, 5.43e+4, 2.59e+4, 0, 2.71e+4, 0, 0, 0, 0, 0, 0],\n",
"[-1.64e+4, 0, 2.59e+4, 3.3e+6, 0, 2.59e+4, -3.28e+6, 0, 0, 0, 0, 0],\n",
"[ 0, -2.61e+6, 0, 0, 2.64e+6, 4.93e+4, 0, -3.28e+4, 4.93e+4, 0, 0, 0],\n",
"[-2.59e+4, 0, 2.71e+4, 2.59e+4, 4.93e+4, 1.53e+5, 0, -4.93e+4, 4.93e+4, 0, 0, 0],\n",
"[ 0, 0, 0, -3.28e+6, 0, 0, 3.28e+6, 0, 0, 0, 0, 0],\n",
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"[ 0, 0, 0, 0, 4.93e+4, 4.93e+4, 0, -4.93e+4, 9.85e+4, 0, 0, 0],\n",
"[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
"[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
"[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])"
],
"text/latex": "$\\displaystyle \\left[\\begin{array}{cccccccccccc}1.64 \\cdot 10^{4} & 0 & -2.59 \\cdot 10^{4} & -1.64 \\cdot 10^{4} & 0 & -2.59 \\cdot 10^{4} & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 2.61 \\cdot 10^{6} & 0 & 0 & -2.61 \\cdot 10^{6} & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\-2.59 \\cdot 10^{4} & 0 & 5.43 \\cdot 10^{4} & 2.59 \\cdot 10^{4} & 0 & 2.71 \\cdot 10^{4} & 0 & 0 & 0 & 0 & 0 & 0\\\\-1.64 \\cdot 10^{4} & 0 & 2.59 \\cdot 10^{4} & 3.3 \\cdot 10^{6} & 0 & 2.59 \\cdot 10^{4} & -3.28 \\cdot 10^{6} & 0 & 0 & 0 & 0 & 0\\\\0 & -2.61 \\cdot 10^{6} & 0 & 0 & 2.64 \\cdot 10^{6} & 4.93 \\cdot 10^{4} & 0 & -3.28 \\cdot 10^{4} & 4.93 \\cdot 10^{4} & 0 & 0 & 0\\\\-2.59 \\cdot 10^{4} & 0 & 2.71 \\cdot 10^{4} & 2.59 \\cdot 10^{4} & 4.93 \\cdot 10^{4} & 1.53 \\cdot 10^{5} & 0 & -4.93 \\cdot 10^{4} & 4.93 \\cdot 10^{4} & 0 & 0 & 0\\\\0 & 0 & 0 & -3.28 \\cdot 10^{6} & 0 & 0 & 3.28 \\cdot 10^{6} & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & -3.28 \\cdot 10^{4} & -4.93 \\cdot 10^{4} & 0 & 3.28 \\cdot 10^{4} & -4.93 \\cdot 10^{4} & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 4.93 \\cdot 10^{4} & 4.93 \\cdot 10^{4} & 0 & -4.93 \\cdot 10^{4} & 9.85 \\cdot 10^{4} & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\end{array}\\right]$"
},
"metadata": {}
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{
"output_type": "stream",
"name": "stdout",
"text": [
"Global stiffness matrix for element 3:\n"
]
},
{
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"data": {
"text/plain": [
"Matrix([\n",
"[ 3.28e+6, 0, 0, -3.28e+6, 0, 0],\n",
"[ 0, 3.28e+4, 4.93e+4, 0, -3.28e+4, 4.93e+4],\n",
"[ 0, 4.93e+4, 9.85e+4, 0, -4.93e+4, 4.93e+4],\n",
"[-3.28e+6, 0, 0, 3.28e+6, 0, 0],\n",
"[ 0, -3.28e+4, -4.93e+4, 0, 3.28e+4, -4.93e+4],\n",
"[ 0, 4.93e+4, 4.93e+4, 0, -4.93e+4, 9.85e+4]])"
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"text/latex": "$\\displaystyle \\left[\\begin{matrix}3.28 \\cdot 10^{6} & 0 & 0 & -3.28 \\cdot 10^{6} & 0 & 0\\\\0 & 3.28 \\cdot 10^{4} & 4.93 \\cdot 10^{4} & 0 & -3.28 \\cdot 10^{4} & 4.93 \\cdot 10^{4}\\\\0 & 4.93 \\cdot 10^{4} & 9.85 \\cdot 10^{4} & 0 & -4.93 \\cdot 10^{4} & 4.93 \\cdot 10^{4}\\\\-3.28 \\cdot 10^{6} & 0 & 0 & 3.28 \\cdot 10^{6} & 0 & 0\\\\0 & -3.28 \\cdot 10^{4} & -4.93 \\cdot 10^{4} & 0 & 3.28 \\cdot 10^{4} & -4.93 \\cdot 10^{4}\\\\0 & 4.93 \\cdot 10^{4} & 4.93 \\cdot 10^{4} & 0 & -4.93 \\cdot 10^{4} & 9.85 \\cdot 10^{4}\\end{matrix}\\right]$"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"Global stiffness matrix after adding element 3:\n"
]
},
{
"output_type": "display_data",
"data": {
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"Matrix([\n",
"[ 1.64e+4, 0, -2.59e+4, -1.64e+4, 0, -2.59e+4, 0, 0, 0, 0, 0, 0],\n",
"[ 0, 2.61e+6, 0, 0, -2.61e+6, 0, 0, 0, 0, 0, 0, 0],\n",
"[-2.59e+4, 0, 5.43e+4, 2.59e+4, 0, 2.71e+4, 0, 0, 0, 0, 0, 0],\n",
"[-1.64e+4, 0, 2.59e+4, 3.3e+6, 0, 2.59e+4, -3.28e+6, 0, 0, 0, 0, 0],\n",
"[ 0, -2.61e+6, 0, 0, 2.64e+6, 4.93e+4, 0, -3.28e+4, 4.93e+4, 0, 0, 0],\n",
"[-2.59e+4, 0, 2.71e+4, 2.59e+4, 4.93e+4, 1.53e+5, 0, -4.93e+4, 4.93e+4, 0, 0, 0],\n",
"[ 0, 0, 0, -3.28e+6, 0, 0, 6.57e+6, 0, 0, -3.28e+6, 0, 0],\n",
"[ 0, 0, 0, 0, -3.28e+4, -4.93e+4, 0, 6.57e+4, 0, 0, -3.28e+4, 4.93e+4],\n",
"[ 0, 0, 0, 0, 4.93e+4, 4.93e+4, 0, 0, 1.97e+5, 0, -4.93e+4, 4.93e+4],\n",
"[ 0, 0, 0, 0, 0, 0, -3.28e+6, 0, 0, 3.28e+6, 0, 0],\n",
"[ 0, 0, 0, 0, 0, 0, 0, -3.28e+4, -4.93e+4, 0, 3.28e+4, -4.93e+4],\n",
"[ 0, 0, 0, 0, 0, 0, 0, 4.93e+4, 4.93e+4, 0, -4.93e+4, 9.85e+4]])"
],
"text/latex": "$\\displaystyle \\left[\\begin{array}{cccccccccccc}1.64 \\cdot 10^{4} & 0 & -2.59 \\cdot 10^{4} & -1.64 \\cdot 10^{4} & 0 & -2.59 \\cdot 10^{4} & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 2.61 \\cdot 10^{6} & 0 & 0 & -2.61 \\cdot 10^{6} & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\-2.59 \\cdot 10^{4} & 0 & 5.43 \\cdot 10^{4} & 2.59 \\cdot 10^{4} & 0 & 2.71 \\cdot 10^{4} & 0 & 0 & 0 & 0 & 0 & 0\\\\-1.64 \\cdot 10^{4} & 0 & 2.59 \\cdot 10^{4} & 3.3 \\cdot 10^{6} & 0 & 2.59 \\cdot 10^{4} & -3.28 \\cdot 10^{6} & 0 & 0 & 0 & 0 & 0\\\\0 & -2.61 \\cdot 10^{6} & 0 & 0 & 2.64 \\cdot 10^{6} & 4.93 \\cdot 10^{4} & 0 & -3.28 \\cdot 10^{4} & 4.93 \\cdot 10^{4} & 0 & 0 & 0\\\\-2.59 \\cdot 10^{4} & 0 & 2.71 \\cdot 10^{4} & 2.59 \\cdot 10^{4} & 4.93 \\cdot 10^{4} & 1.53 \\cdot 10^{5} & 0 & -4.93 \\cdot 10^{4} & 4.93 \\cdot 10^{4} & 0 & 0 & 0\\\\0 & 0 & 0 & -3.28 \\cdot 10^{6} & 0 & 0 & 6.57 \\cdot 10^{6} & 0 & 0 & -3.28 \\cdot 10^{6} & 0 & 0\\\\0 & 0 & 0 & 0 & -3.28 \\cdot 10^{4} & -4.93 \\cdot 10^{4} & 0 & 6.57 \\cdot 10^{4} & 0 & 0 & -3.28 \\cdot 10^{4} & 4.93 \\cdot 10^{4}\\\\0 & 0 & 0 & 0 & 4.93 \\cdot 10^{4} & 4.93 \\cdot 10^{4} & 0 & 0 & 1.97 \\cdot 10^{5} & 0 & -4.93 \\cdot 10^{4} & 4.93 \\cdot 10^{4}\\\\0 & 0 & 0 & 0 & 0 & 0 & -3.28 \\cdot 10^{6} & 0 & 0 & 3.28 \\cdot 10^{6} & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & -3.28 \\cdot 10^{4} & -4.93 \\cdot 10^{4} & 0 & 3.28 \\cdot 10^{4} & -4.93 \\cdot 10^{4}\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 4.93 \\cdot 10^{4} & 4.93 \\cdot 10^{4} & 0 & -4.93 \\cdot 10^{4} & 9.85 \\cdot 10^{4}\\end{array}\\right]$"
},
"metadata": {}
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],
"source": [
"# Calculate the global stiffness matrix\n",
"K_global = assemble_global_stiffness(nodes, elements)"
]
},
{
"cell_type": "markdown",
"id": "fdc8d07f-4f6e-4909-a139-d86d12af81c8",
"metadata": {
"id": "fdc8d07f-4f6e-4909-a139-d86d12af81c8"
},
"source": [
"Die Funktion apply_boundary_conditions wendet die Randbedingungen auf die Steifigkeitsmatrix und den Lastvektor an.\n",
"\n",
"Zuerst berechnet die Funktion die Anzahl der Freiheitsgrade der gesamten Struktur, die gleich der Anzahl der Knoten multipliziert mit 3 ist (da es in einem 2D-Balkenproblem 3 Freiheitsgrade pro Knoten gibt). Dann initialisiert sie den Lastvektor als Nullvektor der entsprechenden Größe.\n",
"\n",
"Die Funktion iteriert dann über alle Knoten und Lasten in der Struktur. Für jeden Knoten und jede Last fügt sie die Lastwerte zum entsprechenden Eintrag im Lastvektor hinzu.\n",
"\n",
"Danach iteriert die Funktion über alle Knoten und Stützen in der Struktur. Für jeden Knoten und jede Stütze überprüft sie, ob der Freiheitsgrad fest ist (d.h., ob er den Wert -1 hat). Wenn ja, setzt sie die entsprechende Zeile und Spalte in der Steifigkeitsmatrix auf Null, setzt den Diagonaleintrag auf 1 und setzt den entsprechenden Eintrag im Lastvektor auf Null. Dies stellt sicher, dass die Randbedingung, dass die Verschiebung an diesem Freiheitsgrad Null ist, erfüllt ist.\n",
"\n",
"Wenn der Freiheitsgrad eine Federstütze hat (d.h., wenn er einen Wert größer als Null hat), fügt sie die Federsteifigkeit zum Diagonaleintrag in der Steifigkeitsmatrix hinzu. Dies stellt die zusätzliche Steifigkeit dar, die die Federstütze der Struktur verleiht.\n",
"\n",
"Am Ende gibt die Funktion die modifizierte Steifigkeitsmatrix und den Lastvektor zurück. Diese können dann zur Lösung des Systems von Gleichungen verwendet werden, um die Verschiebungen an jedem Freiheitsgrad zu finden."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "9f32b48d-7b0a-4094-abe2-534d0d57f0b4",
"metadata": {
"tags": [],
"id": "9f32b48d-7b0a-4094-abe2-534d0d57f0b4"
},
"outputs": [],
"source": [
"def apply_boundary_conditions(K, supports, loads):\n",
" \"\"\"Apply boundary conditions to the stiffness matrix and load vector.\"\"\"\n",
" dof = len(nodes) * 3 # Degrees of freedom (3 per node for 2D beam)\n",
" F = np.zeros(dof)\n",
" for node, load in loads.items():\n",
" F[node*3-3:node*3] = load # Apply loads\n",
" for node, support in supports.items():\n",
" for i in range(3):\n",
" if support[i] == -1: # If the DOF is fixed\n",
" K[node*3-3+i, :] = K[:, node*3-3+i] = 0 # Zero out the corresponding row and column in K\n",
" K[node*3-3+i, node*3-3+i] = 1 # Set the diagonal to 1\n",
" F[node*3-3+i] = 0 # Zero out the corresponding entry in F\n",
" elif support[i] > 0: # If there is a spring support\n",
" K[node*3-3+i, node*3-3+i] += support[i] # Add spring stiffness to the diagonal\n",
" return K, F\n"
]
},
{
"cell_type": "markdown",
"id": "41862db2-427d-461e-8d85-e73737f1b1e4",
"metadata": {
"id": "41862db2-427d-461e-8d85-e73737f1b1e4"
},
"source": [
"**6.) Ermittlung der Verschiebungen**\n",
"Die Funktion calculate_displacements löst das Gleichungssystem K * d = F, um die Verschiebungen d zu finden. Es wird die Funktion np.linalg.solve von NumPy, die eine lineare Matrixgleichung löst, verwendet."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "3d43ddcf-52c4-4330-af71-24349dca6281",
"metadata": {
"tags": [],
"id": "3d43ddcf-52c4-4330-af71-24349dca6281"
},
"outputs": [],
"source": [
"def calculate_displacements(K, F):\n",
" \"\"\"Solve the system of equations to find the displacements.\"\"\"\n",
" d = np.linalg.solve(K, F)\n",
" return d"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "dff8ec93-5c4f-4f32-9d0a-73b70d627188",
"metadata": {
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"colab": {
"base_uri": "https://localhost:8080/",
"height": 1000
},
"id": "dff8ec93-5c4f-4f32-9d0a-73b70d627188",
"outputId": "b950ed46-6eda-4cf8-c1e6-bc2f15e91e7a"
},
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"Global stiffness matrix for element 1:\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"Matrix([\n",
"[ 1.64e+4, 0, -2.59e+4, -1.64e+4, 0, -2.59e+4],\n",
"[ 0, 2.61e+6, 0, 0, -2.61e+6, 0],\n",
"[-2.59e+4, 0, 5.43e+4, 2.59e+4, 0, 2.71e+4],\n",
"[-1.64e+4, 0, 2.59e+4, 1.64e+4, 0, 2.59e+4],\n",
"[ 0, -2.61e+6, 0, 0, 2.61e+6, 0],\n",
"[-2.59e+4, 0, 2.71e+4, 2.59e+4, 0, 5.43e+4]])"
],
"text/latex": "$\\displaystyle \\left[\\begin{matrix}1.64 \\cdot 10^{4} & 0 & -2.59 \\cdot 10^{4} & -1.64 \\cdot 10^{4} & 0 & -2.59 \\cdot 10^{4}\\\\0 & 2.61 \\cdot 10^{6} & 0 & 0 & -2.61 \\cdot 10^{6} & 0\\\\-2.59 \\cdot 10^{4} & 0 & 5.43 \\cdot 10^{4} & 2.59 \\cdot 10^{4} & 0 & 2.71 \\cdot 10^{4}\\\\-1.64 \\cdot 10^{4} & 0 & 2.59 \\cdot 10^{4} & 1.64 \\cdot 10^{4} & 0 & 2.59 \\cdot 10^{4}\\\\0 & -2.61 \\cdot 10^{6} & 0 & 0 & 2.61 \\cdot 10^{6} & 0\\\\-2.59 \\cdot 10^{4} & 0 & 2.71 \\cdot 10^{4} & 2.59 \\cdot 10^{4} & 0 & 5.43 \\cdot 10^{4}\\end{matrix}\\right]$"
},
"metadata": {}
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{
"output_type": "stream",
"name": "stdout",
"text": [
"Global stiffness matrix after adding element 1:\n"
]
},
{
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"data": {
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"Matrix([\n",
"[ 1.64e+4, 0, -2.59e+4, -1.64e+4, 0, -2.59e+4, 0, 0, 0, 0, 0, 0],\n",
"[ 0, 2.61e+6, 0, 0, -2.61e+6, 0, 0, 0, 0, 0, 0, 0],\n",
"[-2.59e+4, 0, 5.43e+4, 2.59e+4, 0, 2.71e+4, 0, 0, 0, 0, 0, 0],\n",
"[-1.64e+4, 0, 2.59e+4, 1.64e+4, 0, 2.59e+4, 0, 0, 0, 0, 0, 0],\n",
"[ 0, -2.61e+6, 0, 0, 2.61e+6, 0, 0, 0, 0, 0, 0, 0],\n",
"[-2.59e+4, 0, 2.71e+4, 2.59e+4, 0, 5.43e+4, 0, 0, 0, 0, 0, 0],\n",
"[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
"[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
"[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
"[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
"[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
"[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])"
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"text/latex": "$\\displaystyle \\left[\\begin{array}{cccccccccccc}1.64 \\cdot 10^{4} & 0 & -2.59 \\cdot 10^{4} & -1.64 \\cdot 10^{4} & 0 & -2.59 \\cdot 10^{4} & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 2.61 \\cdot 10^{6} & 0 & 0 & -2.61 \\cdot 10^{6} & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\-2.59 \\cdot 10^{4} & 0 & 5.43 \\cdot 10^{4} & 2.59 \\cdot 10^{4} & 0 & 2.71 \\cdot 10^{4} & 0 & 0 & 0 & 0 & 0 & 0\\\\-1.64 \\cdot 10^{4} & 0 & 2.59 \\cdot 10^{4} & 1.64 \\cdot 10^{4} & 0 & 2.59 \\cdot 10^{4} & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & -2.61 \\cdot 10^{6} & 0 & 0 & 2.61 \\cdot 10^{6} & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\-2.59 \\cdot 10^{4} & 0 & 2.71 \\cdot 10^{4} & 2.59 \\cdot 10^{4} & 0 & 5.43 \\cdot 10^{4} & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\end{array}\\right]$"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"Global stiffness matrix for element 2:\n"
]
},
{
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"data": {
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"Matrix([\n",
"[ 3.28e+6, 0, 0, -3.28e+6, 0, 0],\n",
"[ 0, 3.28e+4, 4.93e+4, 0, -3.28e+4, 4.93e+4],\n",
"[ 0, 4.93e+4, 9.85e+4, 0, -4.93e+4, 4.93e+4],\n",
"[-3.28e+6, 0, 0, 3.28e+6, 0, 0],\n",
"[ 0, -3.28e+4, -4.93e+4, 0, 3.28e+4, -4.93e+4],\n",
"[ 0, 4.93e+4, 4.93e+4, 0, -4.93e+4, 9.85e+4]])"
],
"text/latex": "$\\displaystyle \\left[\\begin{matrix}3.28 \\cdot 10^{6} & 0 & 0 & -3.28 \\cdot 10^{6} & 0 & 0\\\\0 & 3.28 \\cdot 10^{4} & 4.93 \\cdot 10^{4} & 0 & -3.28 \\cdot 10^{4} & 4.93 \\cdot 10^{4}\\\\0 & 4.93 \\cdot 10^{4} & 9.85 \\cdot 10^{4} & 0 & -4.93 \\cdot 10^{4} & 4.93 \\cdot 10^{4}\\\\-3.28 \\cdot 10^{6} & 0 & 0 & 3.28 \\cdot 10^{6} & 0 & 0\\\\0 & -3.28 \\cdot 10^{4} & -4.93 \\cdot 10^{4} & 0 & 3.28 \\cdot 10^{4} & -4.93 \\cdot 10^{4}\\\\0 & 4.93 \\cdot 10^{4} & 4.93 \\cdot 10^{4} & 0 & -4.93 \\cdot 10^{4} & 9.85 \\cdot 10^{4}\\end{matrix}\\right]$"
},
"metadata": {}
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{
"output_type": "stream",
"name": "stdout",
"text": [
"Global stiffness matrix after adding element 2:\n"
]
},
{
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"data": {
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"Matrix([\n",
"[ 1.64e+4, 0, -2.59e+4, -1.64e+4, 0, -2.59e+4, 0, 0, 0, 0, 0, 0],\n",
"[ 0, 2.61e+6, 0, 0, -2.61e+6, 0, 0, 0, 0, 0, 0, 0],\n",
"[-2.59e+4, 0, 5.43e+4, 2.59e+4, 0, 2.71e+4, 0, 0, 0, 0, 0, 0],\n",
"[-1.64e+4, 0, 2.59e+4, 3.3e+6, 0, 2.59e+4, -3.28e+6, 0, 0, 0, 0, 0],\n",
"[ 0, -2.61e+6, 0, 0, 2.64e+6, 4.93e+4, 0, -3.28e+4, 4.93e+4, 0, 0, 0],\n",
"[-2.59e+4, 0, 2.71e+4, 2.59e+4, 4.93e+4, 1.53e+5, 0, -4.93e+4, 4.93e+4, 0, 0, 0],\n",
"[ 0, 0, 0, -3.28e+6, 0, 0, 3.28e+6, 0, 0, 0, 0, 0],\n",
"[ 0, 0, 0, 0, -3.28e+4, -4.93e+4, 0, 3.28e+4, -4.93e+4, 0, 0, 0],\n",
"[ 0, 0, 0, 0, 4.93e+4, 4.93e+4, 0, -4.93e+4, 9.85e+4, 0, 0, 0],\n",
"[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
"[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
"[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])"
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"text/latex": "$\\displaystyle \\left[\\begin{array}{cccccccccccc}1.64 \\cdot 10^{4} & 0 & -2.59 \\cdot 10^{4} & -1.64 \\cdot 10^{4} & 0 & -2.59 \\cdot 10^{4} & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 2.61 \\cdot 10^{6} & 0 & 0 & -2.61 \\cdot 10^{6} & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\-2.59 \\cdot 10^{4} & 0 & 5.43 \\cdot 10^{4} & 2.59 \\cdot 10^{4} & 0 & 2.71 \\cdot 10^{4} & 0 & 0 & 0 & 0 & 0 & 0\\\\-1.64 \\cdot 10^{4} & 0 & 2.59 \\cdot 10^{4} & 3.3 \\cdot 10^{6} & 0 & 2.59 \\cdot 10^{4} & -3.28 \\cdot 10^{6} & 0 & 0 & 0 & 0 & 0\\\\0 & -2.61 \\cdot 10^{6} & 0 & 0 & 2.64 \\cdot 10^{6} & 4.93 \\cdot 10^{4} & 0 & -3.28 \\cdot 10^{4} & 4.93 \\cdot 10^{4} & 0 & 0 & 0\\\\-2.59 \\cdot 10^{4} & 0 & 2.71 \\cdot 10^{4} & 2.59 \\cdot 10^{4} & 4.93 \\cdot 10^{4} & 1.53 \\cdot 10^{5} & 0 & -4.93 \\cdot 10^{4} & 4.93 \\cdot 10^{4} & 0 & 0 & 0\\\\0 & 0 & 0 & -3.28 \\cdot 10^{6} & 0 & 0 & 3.28 \\cdot 10^{6} & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & -3.28 \\cdot 10^{4} & -4.93 \\cdot 10^{4} & 0 & 3.28 \\cdot 10^{4} & -4.93 \\cdot 10^{4} & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 4.93 \\cdot 10^{4} & 4.93 \\cdot 10^{4} & 0 & -4.93 \\cdot 10^{4} & 9.85 \\cdot 10^{4} & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\end{array}\\right]$"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"Global stiffness matrix for element 3:\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"Matrix([\n",
"[ 3.28e+6, 0, 0, -3.28e+6, 0, 0],\n",
"[ 0, 3.28e+4, 4.93e+4, 0, -3.28e+4, 4.93e+4],\n",
"[ 0, 4.93e+4, 9.85e+4, 0, -4.93e+4, 4.93e+4],\n",
"[-3.28e+6, 0, 0, 3.28e+6, 0, 0],\n",
"[ 0, -3.28e+4, -4.93e+4, 0, 3.28e+4, -4.93e+4],\n",
"[ 0, 4.93e+4, 4.93e+4, 0, -4.93e+4, 9.85e+4]])"
],
"text/latex": "$\\displaystyle \\left[\\begin{matrix}3.28 \\cdot 10^{6} & 0 & 0 & -3.28 \\cdot 10^{6} & 0 & 0\\\\0 & 3.28 \\cdot 10^{4} & 4.93 \\cdot 10^{4} & 0 & -3.28 \\cdot 10^{4} & 4.93 \\cdot 10^{4}\\\\0 & 4.93 \\cdot 10^{4} & 9.85 \\cdot 10^{4} & 0 & -4.93 \\cdot 10^{4} & 4.93 \\cdot 10^{4}\\\\-3.28 \\cdot 10^{6} & 0 & 0 & 3.28 \\cdot 10^{6} & 0 & 0\\\\0 & -3.28 \\cdot 10^{4} & -4.93 \\cdot 10^{4} & 0 & 3.28 \\cdot 10^{4} & -4.93 \\cdot 10^{4}\\\\0 & 4.93 \\cdot 10^{4} & 4.93 \\cdot 10^{4} & 0 & -4.93 \\cdot 10^{4} & 9.85 \\cdot 10^{4}\\end{matrix}\\right]$"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"Global stiffness matrix after adding element 3:\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"Matrix([\n",
"[ 1.64e+4, 0, -2.59e+4, -1.64e+4, 0, -2.59e+4, 0, 0, 0, 0, 0, 0],\n",
"[ 0, 2.61e+6, 0, 0, -2.61e+6, 0, 0, 0, 0, 0, 0, 0],\n",
"[-2.59e+4, 0, 5.43e+4, 2.59e+4, 0, 2.71e+4, 0, 0, 0, 0, 0, 0],\n",
"[-1.64e+4, 0, 2.59e+4, 3.3e+6, 0, 2.59e+4, -3.28e+6, 0, 0, 0, 0, 0],\n",
"[ 0, -2.61e+6, 0, 0, 2.64e+6, 4.93e+4, 0, -3.28e+4, 4.93e+4, 0, 0, 0],\n",
"[-2.59e+4, 0, 2.71e+4, 2.59e+4, 4.93e+4, 1.53e+5, 0, -4.93e+4, 4.93e+4, 0, 0, 0],\n",
"[ 0, 0, 0, -3.28e+6, 0, 0, 6.57e+6, 0, 0, -3.28e+6, 0, 0],\n",
"[ 0, 0, 0, 0, -3.28e+4, -4.93e+4, 0, 6.57e+4, 0, 0, -3.28e+4, 4.93e+4],\n",
"[ 0, 0, 0, 0, 4.93e+4, 4.93e+4, 0, 0, 1.97e+5, 0, -4.93e+4, 4.93e+4],\n",
"[ 0, 0, 0, 0, 0, 0, -3.28e+6, 0, 0, 3.28e+6, 0, 0],\n",
"[ 0, 0, 0, 0, 0, 0, 0, -3.28e+4, -4.93e+4, 0, 3.28e+4, -4.93e+4],\n",
"[ 0, 0, 0, 0, 0, 0, 0, 4.93e+4, 4.93e+4, 0, -4.93e+4, 9.85e+4]])"
],
"text/latex": "$\\displaystyle \\left[\\begin{array}{cccccccccccc}1.64 \\cdot 10^{4} & 0 & -2.59 \\cdot 10^{4} & -1.64 \\cdot 10^{4} & 0 & -2.59 \\cdot 10^{4} & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 2.61 \\cdot 10^{6} & 0 & 0 & -2.61 \\cdot 10^{6} & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\-2.59 \\cdot 10^{4} & 0 & 5.43 \\cdot 10^{4} & 2.59 \\cdot 10^{4} & 0 & 2.71 \\cdot 10^{4} & 0 & 0 & 0 & 0 & 0 & 0\\\\-1.64 \\cdot 10^{4} & 0 & 2.59 \\cdot 10^{4} & 3.3 \\cdot 10^{6} & 0 & 2.59 \\cdot 10^{4} & -3.28 \\cdot 10^{6} & 0 & 0 & 0 & 0 & 0\\\\0 & -2.61 \\cdot 10^{6} & 0 & 0 & 2.64 \\cdot 10^{6} & 4.93 \\cdot 10^{4} & 0 & -3.28 \\cdot 10^{4} & 4.93 \\cdot 10^{4} & 0 & 0 & 0\\\\-2.59 \\cdot 10^{4} & 0 & 2.71 \\cdot 10^{4} & 2.59 \\cdot 10^{4} & 4.93 \\cdot 10^{4} & 1.53 \\cdot 10^{5} & 0 & -4.93 \\cdot 10^{4} & 4.93 \\cdot 10^{4} & 0 & 0 & 0\\\\0 & 0 & 0 & -3.28 \\cdot 10^{6} & 0 & 0 & 6.57 \\cdot 10^{6} & 0 & 0 & -3.28 \\cdot 10^{6} & 0 & 0\\\\0 & 0 & 0 & 0 & -3.28 \\cdot 10^{4} & -4.93 \\cdot 10^{4} & 0 & 6.57 \\cdot 10^{4} & 0 & 0 & -3.28 \\cdot 10^{4} & 4.93 \\cdot 10^{4}\\\\0 & 0 & 0 & 0 & 4.93 \\cdot 10^{4} & 4.93 \\cdot 10^{4} & 0 & 0 & 1.97 \\cdot 10^{5} & 0 & -4.93 \\cdot 10^{4} & 4.93 \\cdot 10^{4}\\\\0 & 0 & 0 & 0 & 0 & 0 & -3.28 \\cdot 10^{6} & 0 & 0 & 3.28 \\cdot 10^{6} & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & -3.28 \\cdot 10^{4} & -4.93 \\cdot 10^{4} & 0 & 3.28 \\cdot 10^{4} & -4.93 \\cdot 10^{4}\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 4.93 \\cdot 10^{4} & 4.93 \\cdot 10^{4} & 0 & -4.93 \\cdot 10^{4} & 9.85 \\cdot 10^{4}\\end{array}\\right]$"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"Global stiffness matrix with boundary conditions considered:\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"Matrix([\n",
"[1.0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
"[ 0, 1.0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
"[ 0, 0, 1.0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
"[ 0, 0, 0, 3.3e+6, 0, 2.59e+4, -3.28e+6, 0, 0, 0, 0, 0],\n",
"[ 0, 0, 0, 0, 2.64e+6, 4.93e+4, 0, -3.28e+4, 4.93e+4, 0, 0, 0],\n",
"[ 0, 0, 0, 2.59e+4, 4.93e+4, 1.53e+5, 0, -4.93e+4, 4.93e+4, 0, 0, 0],\n",
"[ 0, 0, 0, -3.28e+6, 0, 0, 6.57e+6, 0, 0, -3.28e+6, 0, 0],\n",
"[ 0, 0, 0, 0, -3.28e+4, -4.93e+4, 0, 6.57e+4, 0, 0, 0, 4.93e+4],\n",
"[ 0, 0, 0, 0, 4.93e+4, 4.93e+4, 0, 0, 1.97e+5, 0, 0, 4.93e+4],\n",
"[ 0, 0, 0, 0, 0, 0, -3.28e+6, 0, 0, 3.28e+6, 0, 0],\n",
"[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1.0, 0],\n",
"[ 0, 0, 0, 0, 0, 0, 0, 4.93e+4, 4.93e+4, 0, 0, 9.85e+4]])"
],
"text/latex": "$\\displaystyle \\left[\\begin{array}{cccccccccccc}1.0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 1.0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 1.0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 3.3 \\cdot 10^{6} & 0 & 2.59 \\cdot 10^{4} & -3.28 \\cdot 10^{6} & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 2.64 \\cdot 10^{6} & 4.93 \\cdot 10^{4} & 0 & -3.28 \\cdot 10^{4} & 4.93 \\cdot 10^{4} & 0 & 0 & 0\\\\0 & 0 & 0 & 2.59 \\cdot 10^{4} & 4.93 \\cdot 10^{4} & 1.53 \\cdot 10^{5} & 0 & -4.93 \\cdot 10^{4} & 4.93 \\cdot 10^{4} & 0 & 0 & 0\\\\0 & 0 & 0 & -3.28 \\cdot 10^{6} & 0 & 0 & 6.57 \\cdot 10^{6} & 0 & 0 & -3.28 \\cdot 10^{6} & 0 & 0\\\\0 & 0 & 0 & 0 & -3.28 \\cdot 10^{4} & -4.93 \\cdot 10^{4} & 0 & 6.57 \\cdot 10^{4} & 0 & 0 & 0 & 4.93 \\cdot 10^{4}\\\\0 & 0 & 0 & 0 & 4.93 \\cdot 10^{4} & 4.93 \\cdot 10^{4} & 0 & 0 & 1.97 \\cdot 10^{5} & 0 & 0 & 4.93 \\cdot 10^{4}\\\\0 & 0 & 0 & 0 & 0 & 0 & -3.28 \\cdot 10^{6} & 0 & 0 & 3.28 \\cdot 10^{6} & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1.0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 4.93 \\cdot 10^{4} & 4.93 \\cdot 10^{4} & 0 & 0 & 9.85 \\cdot 10^{4}\\end{array}\\right]$"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"Load vector:\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"Matrix([\n",
"[ 0],\n",
"[ 0],\n",
"[ 0],\n",
"[ 0],\n",
"[ -21.1],\n",
"[-0.457],\n",
"[ 0],\n",
"[ -22.5],\n",
"[ 0],\n",
"[ 0],\n",
"[ 0],\n",
"[ 5.63]])"
],
"text/latex": "$\\displaystyle \\left[\\begin{matrix}0\\\\0\\\\0\\\\0\\\\-21.1\\\\-0.457\\\\0\\\\-22.5\\\\0\\\\0\\\\0\\\\5.63\\end{matrix}\\right]$"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"Displacement vector in [m], [rad]:\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"Matrix([\n",
"[ 0],\n",
"[ 0],\n",
"[ 0],\n",
"[ 0.000889],\n",
"[ -1.32e-5],\n",
"[-0.000564],\n",
"[ 0.000889],\n",
"[ -0.00133],\n",
"[ -4.12e-5],\n",
"[ 0.000889],\n",
"[ 0],\n",
"[ 0.000742]])"
],
"text/latex": "$\\displaystyle \\left[\\begin{matrix}0\\\\0\\\\0\\\\0.000889\\\\-1.32 \\cdot 10^{-5}\\\\-0.000564\\\\0.000889\\\\-0.00133\\\\-4.12 \\cdot 10^{-5}\\\\0.000889\\\\0\\\\0.000742\\end{matrix}\\right]$"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"Displacement vector in [mm], [mrad]:\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"Matrix([\n",
"[ 0],\n",
"[ 0],\n",
"[ 0],\n",
"[ 0.889],\n",
"[-0.0132],\n",
"[ -0.564],\n",
"[ 0.889],\n",
"[ -1.33],\n",
"[-0.0412],\n",
"[ 0.889],\n",
"[ 0],\n",
"[ 0.742]])"
],
"text/latex": "$\\displaystyle \\left[\\begin{matrix}0\\\\0\\\\0\\\\0.889\\\\-0.0132\\\\-0.564\\\\0.889\\\\-1.33\\\\-0.0412\\\\0.889\\\\0\\\\0.742\\end{matrix}\\right]$"
},
"metadata": {}
}
],
"source": [
"K = assemble_global_stiffness(nodes, elements)\n",
"K, F = apply_boundary_conditions(K, supports, loads)\n",
"d = calculate_displacements(K, F)\n",
"# nice plot of matrix\n",
"K_sp = sp.Matrix(K).applyfunc(lambda x: sp.N(x, 3))\n",
"print(f\"Global stiffness matrix with boundary conditions considered:\")\n",
"display(K_sp)\n",
"print(f\"Load vector:\")\n",
"display(sp.Matrix([sp.N(x, 3) for x in F])) # plot load vector\n",
"print(f\"Displacement vector in [m], [rad]:\")\n",
"display(sp.Matrix([sp.N(x, 3) for x in d])) # plot calculated displacement vector in [m], [rad]\n",
"print(f\"Displacement vector in [mm], [mrad]:\")\n",
"display(sp.Matrix([sp.N(x, 3) for x in d*1000])) # plot calculated displacement vector in [mm], [mrad]\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "c405feff-9d39-47c4-b352-61e0309f1d8b",
"metadata": {
"id": "c405feff-9d39-47c4-b352-61e0309f1d8b"
},
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"id": "205e2836-be0b-4715-865f-da2bf568bae3",
"metadata": {
"tags": [],
"id": "205e2836-be0b-4715-865f-da2bf568bae3"
},
"outputs": [],
"source": [
"def plot_structure(nodes, elements, displacements=None, factor=1):\n",
" \"\"\"Plot the structure with optional exaggerated displacements.\"\"\"\n",
" fig, ax = plt.subplots()\n",
"\n",
" # If displacements are provided, add them to the node coordinates\n",
" if displacements is not None:\n",
" nodes = nodes.copy() # Don't want to change the original nodes dict\n",
" for node, coords in nodes.items():\n",
" nodes[node] = [coords[0] + factor*displacements[node*3-3],\n",
" coords[1] + factor*displacements[node*3-2]]\n",
"\n",
" # Plot the nodes\n",
" for node, coords in nodes.items():\n",
" ax.plot(coords[0], coords[1], 'ko')\n",
" ax.text(coords[0], coords[1], f'Node {node}')\n",
"\n",
" # Plot the elements\n",
" for element, properties in elements.items():\n",
" node1, node2 = properties[:2]\n",
" ax.plot([nodes[node1][0], nodes[node2][0]],\n",
" [nodes[node1][1], nodes[node2][1]], 'k-')\n",
"\n",
" # Equal aspect ratio and labels\n",
" ax.set_aspect('equal', 'box')\n",
" ax.set_xlabel('X')\n",
" ax.set_ylabel('Y')\n",
" plt.title('Structure Plot')\n",
" plt.grid(True)\n",
" plt.show()\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "51b18232-5c1a-43f6-be8b-ed429ca339af",
"metadata": {
"tags": [],
"colab": {
"base_uri": "https://localhost:8080/",
"height": 705
},
"id": "51b18232-5c1a-43f6-be8b-ed429ca339af",
"outputId": "a1267ab8-840e-44a9-82e0-773084fc097b"
},
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
""
],
"image/png": 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\n"
},
"metadata": {}
},
{
"output_type": "display_data",
"data": {
"text/plain": [
""
],
"image/png": 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\n"
},
"metadata": {}
}
],
"source": [
"plot_structure(nodes, elements)\n",
"plot_structure(nodes, elements, d, factor=100)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "b45725a1-152b-4016-96d2-5cea95d1926a",
"metadata": {
"tags": [],
"colab": {
"base_uri": "https://localhost:8080/",
"height": 856
},
"id": "b45725a1-152b-4016-96d2-5cea95d1926a",
"outputId": "7ca8adff-40f3-4a77-9a48-34128228997b"
},
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"Internal forces for Element 1:\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"Matrix([\n",
"[ 34.5],\n",
"[ 9.38],\n",
"[ 12.3],\n",
"[-34.5],\n",
"[ 9.38],\n",
"[-12.3]])"
],
"text/latex": "$\\displaystyle \\left[\\begin{matrix}34.5\\\\9.38\\\\12.3\\\\-34.5\\\\9.38\\\\-12.3\\end{matrix}\\right]$"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"Internal forces for Element 2:\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"Matrix([\n",
"[ 0],\n",
"[ 24.6],\n",
"[ 12.8],\n",
"[ 0],\n",
"[-2.14],\n",
"[ 27.3]])"
],
"text/latex": "$\\displaystyle \\left[\\begin{matrix}0\\\\24.6\\\\12.8\\\\0\\\\-2.14\\\\27.3\\end{matrix}\\right]$"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"Internal forces for Element 3:\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"Matrix([\n",
"[ 0],\n",
"[ 2.14],\n",
"[ -27.3],\n",
"[ 0],\n",
"[ 20.4],\n",
"[-1.42e-14]])"
],
"text/latex": "$\\displaystyle \\left[\\begin{matrix}0\\\\2.14\\\\-27.3\\\\0\\\\20.4\\\\-1.42 \\cdot 10^{-14}\\end{matrix}\\right]$"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"Internal forces for visualization for Element 1:\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"Matrix([\n",
"[-34.5],\n",
"[-9.38],\n",
"[-12.3],\n",
"[-34.5],\n",
"[ 9.38],\n",
"[-12.3]])"
],
"text/latex": "$\\displaystyle \\left[\\begin{matrix}-34.5\\\\-9.38\\\\-12.3\\\\-34.5\\\\9.38\\\\-12.3\\end{matrix}\\right]$"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"Internal forces for visualization for Element 2:\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"Matrix([\n",
"[ 0],\n",
"[-24.6],\n",
"[-12.8],\n",
"[ 0],\n",
"[-2.14],\n",
"[ 27.3]])"
],
"text/latex": "$\\displaystyle \\left[\\begin{matrix}0\\\\-24.6\\\\-12.8\\\\0\\\\-2.14\\\\27.3\\end{matrix}\\right]$"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"Internal forces for visualization for Element 3:\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"Matrix([\n",
"[ 0],\n",
"[ -2.14],\n",
"[ 27.3],\n",
"[ 0],\n",
"[ 20.4],\n",
"[-1.42e-14]])"
],
"text/latex": "$\\displaystyle \\left[\\begin{matrix}0\\\\-2.14\\\\27.3\\\\0\\\\20.4\\\\-1.42 \\cdot 10^{-14}\\end{matrix}\\right]$"
},
"metadata": {}
}
],
"source": [
"# Calculate local internal forces\n",
"forces = {}\n",
"forces_vis = {} # Dictionary to store modified forces for visualization\n",
"for e, element in elements.items():\n",
" # Get global displacements for this element\n",
" i, j = element[0], element[1]\n",
" d_global = np.concatenate((d[3*i-3:3*i], d[3*j-3:3*j]))\n",
" # Calculate local displacements\n",
" T = calculate_transformation_matrix(nodes, element)\n",
" d_local = T @ d_global\n",
" # Calculate local internal forces\n",
" K_local = local_beam_element_stiffness(nodes, element)\n",
" f_local = K_local @ d_local\n",
" # Adjust for the element loads if they exist\n",
" if e in line_loads:\n",
" wx, wy = line_loads[e]\n",
" L = np.sqrt((nodes[node2][0] - nodes[node1][0])**2 + (nodes[node2][1] - nodes[node1][1])**2)\n",
" Fx1, Fy1, M1, M2 = calculate_equivalent_nodal_loads(wx, wy, L)\n",
" f_local -= np.array([Fx1, Fy1, M1, Fx1, Fy1, M2])\n",
" forces[e] = f_local\n",
" forces_vis[e] = [-f_local[0], -f_local[1], -f_local[2], f_local[3], f_local[4], f_local[5]]\n",
"\n",
"# Display internal forces for each element\n",
"for e, f in forces.items():\n",
" print(f\"Internal forces for Element {e}:\")\n",
" display(sp.Matrix([sp.N(x, 3) for x in f]))\n",
"\n",
"# Display internal forces for each element\n",
"for e, f in forces_vis.items():\n",
" print(f\"Internal forces for visualization for Element {e}:\")\n",
" display(sp.Matrix([sp.N(x, 3) for x in f]))\n"
]
},
{
"cell_type": "markdown",
"id": "36b0fcf8-c248-4a94-a14c-b5d9a0df3896",
"metadata": {
"id": "36b0fcf8-c248-4a94-a14c-b5d9a0df3896"
},
"source": [
"**Graphische Ausgabe der Schnittgrößen pro Element**\n",
"Dieser Code erstellt separate Diagramme für die Axialkraft, Scherkraft und das Biegemoment jedes Elements. Für jedes Element wird ein Satz von drei Diagrammen erstellt. Die x-Achse stellt die Position entlang des Balkenelements dar, während die y-Achse die Größe der jeweiligen internen Kraft darstellt.\n",
"\n",
"Die Funktion linspace wird verwendet, um eine Reihe von x-Koordinaten zu erzeugen, die von 0 bis 1 reichen. Diese repräsentieren die Positionen entlang des Balkenelements, an denen die internen Kräfte berechnet werden.\n",
"\n",
"Die internen Kräfte werden als lineare Variationen entlang des Balkenelements angenommen. Die Funktionen F_axial = np.linspace(f[0], f[3], 100), F_shear = np.linspace(f[1], f[4], 100) und M_bending = np.linspace(f[2], f[5], 100) erzeugen daher eine Reihe von Werten für die Axialkraft, Scherkraft und das Biegemoment, die von den Werten an den Enden des Balkenelements linear variieren.\n",
"\n",
"Die Funktion plt.plot(x, F_axial) zeichnet dann die Axialkraft als Funktion der Position entlang des Balkenelements. Ähnliche Funktionen werden verwendet, um die Scherkraft und das Biegemoment zu zeichnen.\n",
"\n",
"Die Funktion plt.grid(True) wird verwendet, um Gitterlinien zu den Diagrammen hinzuzufügen, was das Ablesen der Diagramme erleichtert.\n",
"\n",
"Schließlich wird die Funktion plt.show() verwendet, um die erstellten Diagramme anzuzeigen."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "5d3e1e57-7a4b-4af8-ae32-6f28417ecfab",
"metadata": {
"tags": [],
"colab": {
"base_uri": "https://localhost:8080/",
"height": 1000
},
"id": "5d3e1e57-7a4b-4af8-ae32-6f28417ecfab",
"outputId": "fc92d9eb-b032-4c31-9374-6017e3c1ba03"
},
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
""
],
"image/png": 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\n"
},
"metadata": {}
},
{
"output_type": "display_data",
"data": {
"text/plain": [
""
],
"image/png": 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\n"
},
"metadata": {}
},
{
"output_type": "display_data",
"data": {
"text/plain": [
""
],
"image/png": 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JJ4qKitKUKVM0derUWp0fGBiob7/9VlOnTtUnn3yi+fPny2Kx6KKLLrL/Q4PZbNaiRYv03HPP6a233tInn3wif39/xcbG6s4776y32xIAAM5nMpyxCwsAAGi0OnfurMsuu0xPPvmkq0sBAMDtsdINAABqrby8XKNHj9aoUaNcXQoAAA0CK90AAAAAADgJu5cDAAAAAOAkhG4AAAAAAJyEe7rrgc1m08GDBxUUFCSTyeTqcgAAAAAATmYYhoqKitSyZUuZzSdfzyZ014ODBw8qOjra1WUAAAAAAM6yffv22R/5WBNCdz0ICgqSVPXDDg4OdnE11VmtVn311VcaMmSIvLy8XF0Omjj6Ee6CXoS7oBfhTuhHuIuG0IuFhYWKjo6258GTIXTXg+OXlAcHB7tt6Pb391dwcLDbNiyaDvoR7oJehLugF+FO6Ee4i4bUi6e7xZiN1AAAAAAAcBJCNwAAAAAATkLoBgAAAADASQjdAAAAAAA4CaEbAAAAAAAnIXQDAAAAAOAkhG4AAAAAAJyE0A0AAAAAgJMQugEAAAAAcBJCNwAAAAAATkLoBgAAAADASQjdAAAAAAA4CaEbAAAAAAAnIXQDAAAAAOAkhG4AAAAAAJyE0A0AAAAAgJMQugEAAAAAcBJCNwAAAAAATkLoBgAAAADASQjdAAAAAAA4CaEbAAAAAAAnIXQDAAAAAOAkhG4AAAAAAJyE0A0AAAAAgJMQugEAAAAAcBJCNwAAAAAATkLoBgAAAADASQjdAAAAAAA4CaEbAAAAAAAnaXChe86cOWrXrp18fX3Vq1cvrVu37pTzP/jgAyUkJMjX11ddu3bVkiVLTjr3lltukclk0uzZs+u5agAAAABAU9SgQvd7772nSZMmaerUqdqwYYPOPfdcDR06VFlZWTXOX7VqlcaMGaPx48dr48aNGjFihEaMGKFff/212txPPvlEa9asUcuWLZ39NQAAAAAATUSDCt3PPvusbrrpJo0bN06dO3fWK6+8In9/f7355ps1zn/++ed18cUX67777lOnTp00c+ZMnX/++XrxxRcd5h04cEC333673n33XXl5eZ2NrwIAAAAAaAI8XV1AbZWXl2v9+vWaMmWK/ZjZbNagQYO0evXqGs9ZvXq1Jk2a5HBs6NChWrRokf21zWbTddddp/vuu0/nnHNOrWopKytTWVmZ/XVhYaEkyWq1ymq11vYrnTXHa3LH2tD00I9wF/Qi3AW9CHdCP8JdNIRerG1tDSZ05+TkqLKyUs2bN3c43rx5c6Wnp9d4TmZmZo3zMzMz7a+feOIJeXp66o477qh1LbNmzdL06dOrHf/qq6/k7+9f6/c525YtW+bqEgA7+hHugl6Eu6AX4U7oR7gLd+7FkpKSWs1rMKHbGdavX6/nn39eGzZskMlkqvV5U6ZMcVhBLywsVHR0tIYMGaLg4GBnlPqXWK1WLVu2TIMHD+byebgc/Qh3QS/CXdCLcCf0I9xFQ+jF41c8n06DCd0RERHy8PDQoUOHHI4fOnRIUVFRNZ4TFRV1yvnffvutsrKy1KZNG/t4ZWWl7rnnHs2ePVu7d++u8X19fHzk4+NT7biXl5fbNoTk/vWhaaEf4S7oRbgLehHuhH6Eu3DnXqxtXQ1mIzVvb28lJibqm2++sR+z2Wz65ptvlJSUVOM5SUlJDvOlqssTjs+/7rrr9PPPP2vTpk32Xy1bttR9992nL7/80nlfBgAAAADQJDSYlW5JmjRpksaOHasePXqoZ8+emj17toqLizVu3DhJ0vXXX69WrVpp1qxZkqQ777xTAwYM0DPPPKNLL71UCxcu1I8//qhXX31VkhQeHq7w8HCHz/Dy8lJUVJTi4+PP7pcDAAAAADQ6DSp0jx49WtnZ2Xr00UeVmZmp7t27a+nSpfbN0vbu3Suz+cTife/evbVgwQI9/PDDevDBB9WhQwctWrRIXbp0cdVXAAAAAAA0IQ0qdEvSxIkTNXHixBrH0tLSqh276qqrdNVVV9X6/U92HzcAAAAAAHXVYO7pBgAAAACgoSF0AwAAAADgJIRuAAAAAACchNANAAAAAICTELoBAAAAAHASQjcAAAAAAE5C6AYAAAAAwEkI3QAAAAAAOAmhGwAAAAAAJyF0AwAAAADgJIRuAAAAAACchNANAAAAAICTELoBAAAAAHASQjcAAAAAAE5C6AYAAAAAwEkI3QAAAAAAOAmhGwAAAAAAJyF0AwAAAADgJIRuAAAAAACchNANAAAAAICTELoBAAAAAHASQjcAAAAAAE5C6AYAAAAAwEkI3QAAAAAAOAmhGwAAAAAAJyF0AwAAAADgJIRuAAAAAACchNANAAAAAICTELoBAAAAAHASQjcAAAAAAE5C6AYAAAAAwEkI3QAAAAAAOAmhGwAAAAAAJyF0AwAAAADgJIRuAAAAAACchNANAAAAAICTELoBAAAAAHCSBhe658yZo3bt2snX11e9evXSunXrTjn/gw8+UEJCgnx9fdW1a1ctWbLEPma1WvXAAw+oa9euCggIUMuWLXX99dfr4MGDzv4aAAAAAIAmoEGF7vfee0+TJk3S1KlTtWHDBp177rkaOnSosrKyapy/atUqjRkzRuPHj9fGjRs1YsQIjRgxQr/++qskqaSkRBs2bNAjjzyiDRs26OOPP1ZGRoaGDx9+Nr8WAAAAAKCR8nR1AXXx7LPP6qabbtK4ceMkSa+88ooWL16sN998U5MnT642//nnn9fFF1+s++67T5I0c+ZMLVu2TC+++KJeeeUVhYSEaNmyZQ7nvPjii+rZs6f27t2rNm3a1FhHWVmZysrK7K8LCwslVa2cW63Wevmu9el4Te5YG5oe+hHugl6Eu6AX4U7oR7iLhtCLta2twYTu8vJyrV+/XlOmTLEfM5vNGjRokFavXl3jOatXr9akSZMcjg0dOlSLFi066ecUFBTIZDIpNDT0pHNmzZql6dOnVzv+1Vdfyd/f/9RfxIX+/A8MgCvRj3AX9CLcBb0Id0I/wl24cy+WlJTUal6DCd05OTmqrKxU8+bNHY43b95c6enpNZ6TmZlZ4/zMzMwa55eWluqBBx7QmDFjFBwcfNJapkyZ4hDmCwsLFR0drSFDhpzyPFexWq1atmyZBg8eLC8vL1eXgyaOfoS7oBfhLuhFuBP6Ee6iIfTi8SueT6fBhG5ns1qtGjVqlAzD0Msvv3zKuT4+PvLx8al23MvLy20bQnL/+tC00I9wF/Qi3AW9CHdCP8JduHMv1rauBhO6IyIi5OHhoUOHDjkcP3TokKKiomo8JyoqqlbzjwfuPXv2aPny5W65Wg0AAAAAaHgazO7l3t7eSkxM1DfffGM/ZrPZ9M033ygpKanGc5KSkhzmS1X3BPxx/vHAvW3bNn399dcKDw93zhcAAAAAADQ5DWalW5ImTZqksWPHqkePHurZs6dmz56t4uJi+27m119/vVq1aqVZs2ZJku68804NGDBAzzzzjC699FItXLhQP/74o1599VVJVYH7yiuv1IYNG/T555+rsrLSfr93WFiYvL29XfNFAQAAAACNQoMK3aNHj1Z2drYeffRRZWZmqnv37lq6dKl9s7S9e/fKbD6xeN+7d28tWLBADz/8sB588EF16NBBixYtUpcuXSRJBw4c0KeffipJ6t69u8NnpaamKjk5+ax8LwAAAABA49SgQrckTZw4URMnTqxxLC0trdqxq666SldddVWN89u1ayfDMOqzPAAAAAAA7BrMPd0AAAAAADQ0hG4AAAAAAJyE0A0AAAAAgJMQugEAAAAAcBJCNwAAAAAATkLoBgAAAADASc4odL/99tvq06ePWrZsqT179kiSZs+erf/973/1WhwAAAAAAA1ZnUP3yy+/rEmTJumSSy5Rfn6+KisrJUmhoaGaPXt2fdcHAAAAAECDVefQ/cILL+i1117TQw89JA8PD/vxHj166JdffqnX4gAAAAAAaMjqHLp37dql8847r9pxHx8fFRcX10tRAAAAAAA0BnUO3TExMdq0aVO140uXLlWnTp3qoyYAAAAAABoFz7qeMGnSJN12220qLS2VYRhat26d/vvf/2rWrFl6/fXXnVEjAAAAAAANUp1D9z//+U/5+fnp4YcfVklJif7xj3+oZcuWev7553X11Vc7o0YAAAAAABqkOoduSbrmmmt0zTXXqKSkREeOHJHFYqnvugAAAAAAaPDqHLp37dqliooKdejQQf7+/vL395ckbdu2TV5eXmrXrl191wgAAAAAQINU543UbrjhBq1atara8bVr1+qGG26oj5oAAAAAAGgU6hy6N27cqD59+lQ7fuGFF9a4qzkAAAAAAE1VnUO3yWRSUVFRteMFBQWqrKysl6IAAAAAAGgM6hy6+/fvr1mzZjkE7MrKSs2aNUt9+/at1+IAAAAAAGjI6ryR2uOPP64BAwYoPj5e/fr1kyR9++23Kiws1PLly+u9QAAAAAAAGqo6r3Sfc845+vnnnzVq1ChlZWWpqKhI119/vdLT09WlSxdn1AgAAAAAQINUp5Vuq9Wqiy++WK+88or+/e9/O6smAAAAAAAahTqtdHt5eennn392Vi0AAAAAADQqdb68/Nprr9Ubb7zhjFoAAAAAAGhU6ryRWkVFhd588019/fXXSkxMVEBAgMP4s88+W2/FAQAAAADQkNU5dP/66686//zzJUlbt251GDOZTPVTFQAAAAAAjUCdQ3dqaqoz6gAAAAAAoNGp8z3df7R//37t37+/vmoBAAAAAKBRqXPottlsmjFjhkJCQtS2bVu1bdtWoaGhmjlzpmw2mzNqBAAAAACgQarz5eUPPfSQ3njjDT3++OPq06ePJOm7777TtGnTVFpaqscee6zeiwQAAAAAoCGqc+ieP3++Xn/9dQ0fPtx+rFu3bmrVqpVuvfVWQjcAAAAAAMfU+fLyvLw8JSQkVDuekJCgvLy8eikKAAAAAIDGoM6h+9xzz9WLL75Y7fiLL76oc889t16KAgAAAACgMajz5eVPPvmkLr30Un399ddKSkqSJK1evVr79u3TkiVL6r1AAAAAAAAaqjqvdA8YMEBbt27V3//+d+Xn5ys/P19XXHGFMjIy1K9fP2fUCAAAAABAg1Srle4rrrhC8+bNU3BwsN566y2NHj2aDdMAAAAAADiNWq10f/755youLpYkjRs3TgUFBU4t6lTmzJmjdu3aydfXV7169dK6detOOf+DDz5QQkKCfH191bVr12qXwBuGoUcffVQtWrSQn5+fBg0apG3btjnzKwAAAAAAmoharXQnJCRoypQpSklJkWEYev/99xUcHFzj3Ouvv75eC/yj9957T5MmTdIrr7yiXr16afbs2Ro6dKgyMjJksViqzV+1apXGjBmjWbNm6bLLLtOCBQs0YsQIbdiwQV26dJFUdY/6//3f/2n+/PmKiYnRI488oqFDh2rz5s3y9fV12ncBAAAAADR+tQrdr7zyiiZNmqTFixfLZDLp4YcflslkqjbPZDI5NXQ/++yzuummmzRu3Dh7XYsXL9abb76pyZMnV5v//PPP6+KLL9Z9990nSZo5c6aWLVumF198Ua+88ooMw9Ds2bP18MMP629/+5sk6a233lLz5s21aNEiXX311U77LmeLYRgqKa9QWaVUUl4hL6P67xtwNlmt9CPcA70Id0Evwp3Qj3AXx3vRMAxXl/KXmYw6fguz2azMzMwaV5adqby8XP7+/vrwww81YsQI+/GxY8cqPz9f//vf/6qd06ZNG02aNEl33XWX/djUqVO1aNEi/fTTT9q5c6fi4uK0ceNGde/e3T5nwIAB6t69u55//vkaaykrK1NZWZn9dWFhoaKjo5WTk3PSKwBcpaS8QufOXO7qMgAAAACgzn6c3F8hAe55BXJhYaEiIiJUUFBwyhxY50eG7dq1S5GRkX+puDORk5OjyspKNW/e3OF48+bNlZ6eXuM5mZmZNc7PzMy0jx8/drI5NZk1a5amT59e7fhXX30lf3//03+Zs6isUjqD32YAAAAAcLnly5fLx8PVVdSspKSkVvPqnMbatm1b52IamylTpmjSpEn218dXuocMGeJ2K92GYWjgwDItX75cAwcOlJcXARyuZbVW0I9wC/Qi3AW9CHdCP8JdHO/FS4cOkre3t6vLqVFhYWGt5jWY/0+KiIiQh4eHDh065HD80KFDioqKqvGcqKioU84//n8PHTqkFi1aOMz54+Xmf+bj4yMfH59qx728vOTl5VWr73M2hZhM8vGQQgJ83bI+NC1Wq5V+hFugF+Eu6EW4E/oR7uJ4L3p7e7ttL9a2rlo9MswdeHt7KzExUd988439mM1m0zfffKOkpKQaz0lKSnKYL0nLli2zz4+JiVFUVJTDnMLCQq1du/ak7wkAAAAAQG01mJVuSZo0aZLGjh2rHj16qGfPnpo9e7aKi4vtu5lff/31atWqlWbNmiVJuvPOOzVgwAA988wzuvTSS7Vw4UL9+OOPevXVVyVV7bZ+11136V//+pc6dOhgf2RYy5YtHTZrAwAAAADgTDSo0D169GhlZ2fr0UcfVWZmprp3766lS5faN0Lbu3evzOYTi/e9e/fWggUL9PDDD+vBBx9Uhw4dtGjRIvszuiXp/vvvV3FxsSZMmKD8/Hz17dtXS5cu5RndAAAAAIC/rFah+7zzzqvxudw12bBhw18q6HQmTpyoiRMn1jiWlpZW7dhVV12lq6666qTvZzKZNGPGDM2YMaO+SgQAAAAAQFItQzeXWgMAAAAAUHe1Ct1Tp051dh0AAAAAADQ6DWb3cgAAAAAAGpo6b6RWWVmp5557Tu+//7727t2r8vJyh/G8vLx6Kw4AAAAAgIaszivd06dP17PPPqvRo0eroKBAkyZN0hVXXCGz2axp06Y5oUQAAAAAABqmOofud999V6+99pruueceeXp6asyYMXr99df16KOPas2aNc6oEQAAAACABqnOoTszM1Ndu3aVJAUGBqqgoECSdNlll2nx4sX1Wx0AAAAAAA1YnUN369at9fvvv0uS4uLi9NVXX0mSfvjhB/n4+NRvdQAAAAAANGB1Dt1///vf9c0330iSbr/9dj3yyCPq0KGDrr/+et144431XiAAAAAAAA1VnXcvf/zxx+3/e/To0WrTpo1Wr16tDh066PLLL6/X4gAAAAAAaMjqHLr/LCkpSUlJSfVRCwAAAAAAjUqtQvenn36qYcOGycvLS59++ukp5w4fPrxeCgMAAAAAoKGrVegeMWKEMjMzZbFYNGLEiJPOM5lMqqysrK/aAAAAAABo0GoVum02W43/GwAAAAAAnFyddy8/lZKSkvp8OwAAAAAAGrQ6h+6LLrpIBw4cqHZ87dq16t69e33UBAAAAABAo1Dn0O3r66tu3brpvffek1R1ufm0adPUr18/XXLJJfVeIAAAAAAADVWdHxm2ePFizZkzRzfeeKP+97//affu3dqzZ48+//xzDRkyxBk1AgAAAADQIJ3Rc7pvu+027d+/X0888YQ8PT2Vlpam3r1713dtAAAAAAA0aHW+vPzw4cMaOXKkXn75Zf3nP//RqFGjNGTIEL300kvOqA8AAAAAgAarzivdXbp0UUxMjDZu3KiYmBjddNNNeu+993Trrbdq8eLFWrx4sTPqBAAAAACgwanzSvctt9yilStXKiYmxn5s9OjR+umnn1ReXl6vxQEAAAAA0JDVeaX7kUceqfF469at9eyzz/7lggAAAAAAaCzqvNL9Z0VFRXr11VfVs2dPntMNAAAAAMAfnHHoXrlypcaOHasWLVro6aef1sCBA7VmzZr6rA0AAAAAgAatTpeXZ2Zmat68eXrjjTdUWFioUaNGqaysTIsWLVLnzp2dVSMAAAAAAA1SrVe6L7/8csXHx+vnn3/W7NmzdfDgQb3wwgvOrA0AAAAAgAat1ivdX3zxhe644w79v//3/9ShQwdn1gQAAAAAQKNQ65Xu7777TkVFRUpMTFSvXr304osvKicnx5m1AQAAAADQoNU6dF944YV67bXX9Pvvv+vmm2/WwoUL1bJlS9lsNi1btkxFRUXOrBMAAAAAgAanzruXBwQE6MYbb9R3332nX375Rffcc48ef/xxWSwWDR8+3Bk1AgAAAADQIP2l53THx8frySef1P79+/Xf//63vmoCAAAAAKBR+Euh+zgPDw+NGDFCn376aX28HQAAAAAAjUK9hG4AAAAAAFAdoRsAAAAAACchdAMAAAAA4CSEbgAAAAAAnKTBhO68vDxdc801Cg4OVmhoqMaPH68jR46c8pzS0lLddtttCg8PV2BgoEaOHKlDhw7Zx3/66SeNGTNG0dHR8vPzU6dOnfT88887+6sAAAAAAJqIBhO6r7nmGv32229atmyZPv/8c61cuVITJkw45Tl33323PvvsM33wwQdasWKFDh48qCuuuMI+vn79elksFr3zzjv67bff9NBDD2nKlCl68cUXnf11AAAAAABNgKerC6iNLVu2aOnSpfrhhx/Uo0cPSdILL7ygSy65RE8//bRatmxZ7ZyCggK98cYbWrBggQYOHChJmjt3rjp16qQ1a9bowgsv1I033uhwTmxsrFavXq2PP/5YEydOPGk9ZWVlKisrs78uLCyUJFmtVlmt1r/8fevb8ZrcsTY0PfQj3AW9CHdBL8Kd0I9wFw2hF2tbW4MI3atXr1ZoaKg9cEvSoEGDZDabtXbtWv3973+vds769etltVo1aNAg+7GEhAS1adNGq1ev1oUXXljjZxUUFCgsLOyU9cyaNUvTp0+vdvyrr76Sv79/bb/WWbds2TJXlwDY0Y9wF/Qi3AW9CHdCP8JduHMvlpSU1GpegwjdmZmZslgsDsc8PT0VFhamzMzMk57j7e2t0NBQh+PNmzc/6TmrVq3Se++9p8WLF5+ynilTpmjSpEn214WFhYqOjtaQIUMUHBxci290dlmtVi1btkyDBw+Wl5eXq8tBE0c/wl3Qi3AX9CLcCf0Id9EQevH4Fc+n49LQPXnyZD3xxBOnnLNly5azUsuvv/6qv/3tb5o6daqGDBlyyrk+Pj7y8fGpdtzLy8ttG0Jy//rQtNCPcBf0ItwFvQh3Qj/CXbhzL9a2LpeG7nvuuUc33HDDKefExsYqKipKWVlZDscrKiqUl5enqKioGs+LiopSeXm58vPzHVa7Dx06VO2czZs366KLLtKECRP08MMPn9F3AQAAAADgz1wauiMjIxUZGXnaeUlJScrPz9f69euVmJgoSVq+fLlsNpt69epV4zmJiYny8vLSN998o5EjR0qSMjIytHfvXiUlJdnn/fbbbxo4cKDGjh2rxx57rB6+FQAAAAAAVRrEI8M6deqkiy++WDfddJPWrVun77//XhMnTtTVV19t37n8wIEDSkhI0Lp16yRJISEhGj9+vCZNmqTU1FStX79e48aNU1JSkn0TtV9//VUpKSkaMmSIJk2apMzMTGVmZio7O9tl3xUAAAAA0Hg0iI3UJOndd9/VxIkTddFFF8lsNmvkyJH6v//7P/u41WpVRkaGww5yzz33nH1uWVmZhg4dqpdeesk+/uGHHyo7O1vvvPOO3nnnHfvxtm3bavfu3WflewEAAAAAGq8GE7rDwsK0YMGCk463a9dOhmE4HPP19dWcOXM0Z86cGs+ZNm2apk2bVp9lAgAAAABg1yAuLwcAAAAAoCEidAMAAAAA4CSEbgAAAAAAnITQDQAAAACAkxC6AQAAAABwEkI3AAAAAABOQugGAAAAAMBJCN0AAAAAADgJoRsAAAAAACchdAMAAAAA4CSEbgAAAAAAnITQDQAAAACAkxC6AQAAAABwEkI3AAAAAABOQugGAAAAAMBJCN0AAAAAADgJoRsAAAAAACchdAMAAAAA4CSEbgAAAAAAnITQDQAAAACAkxC6AQAAAABwEkI3AAAAAABOQugGAAAAAMBJCN0AAAAAADgJoRsAAAAAACchdAMAAAAA4CSEbgAAAAAAnITQDQAAAACAkxC6AQAAAABwEkI3AAAAAABOQugGAAAAAMBJCN0AAAAAADgJoRsAAAAAACchdAMAAAAA4CSEbgAAAAAAnITQDQAAAACAkzSY0J2Xl6drrrlGwcHBCg0N1fjx43XkyJFTnlNaWqrbbrtN4eHhCgwM1MiRI3Xo0KEa5+bm5qp169YymUzKz893wjcAAAAAADQ1DSZ0X3PNNfrtt9+0bNkyff7551q5cqUmTJhwynPuvvtuffbZZ/rggw+0YsUKHTx4UFdccUWNc8ePH69u3bo5o3QAAAAAQBPVIEL3li1btHTpUr3++uvq1auX+vbtqxdeeEELFy7UwYMHazynoKBAb7zxhp599lkNHDhQiYmJmjt3rlatWqU1a9Y4zH355ZeVn5+ve++992x8HQAAAABAE+Hp6gJqY/Xq1QoNDVWPHj3sxwYNGiSz2ay1a9fq73//e7Vz1q9fL6vVqkGDBtmPJSQkqE2bNlq9erUuvPBCSdLmzZs1Y8YMrV27Vjt37qxVPWVlZSorK7O/LiwslCRZrVZZrdYz+o7OdLwmd6wNTQ/9CHdBL8Jd0ItwJ/Qj3EVD6MXa1tYgQndmZqYsFovDMU9PT4WFhSkzM/Ok53h7eys0NNThePPmze3nlJWVacyYMXrqqafUpk2bWofuWbNmafr06dWOf/XVV/L396/Ve7jCsmXLXF0CYEc/wl3Qi3AX9CLcCf0Id+HOvVhSUlKreS4N3ZMnT9YTTzxxyjlbtmxx2udPmTJFnTp10rXXXlvn8yZNmmR/XVhYqOjoaA0ZMkTBwcH1XeZfZrVatWzZMg0ePFheXl6uLgdNHP0Id0Evwl3Qi3An9CPcRUPoxeNXPJ+OS0P3PffcoxtuuOGUc2JjYxUVFaWsrCyH4xUVFcrLy1NUVFSN50VFRam8vFz5+fkOq92HDh2yn7N8+XL98ssv+vDDDyVJhmFIkiIiIvTQQw/VuJotST4+PvLx8al23MvLy20bQnL/+tC00I9wF/Qi3AW9CHdCP8JduHMv1rYul4buyMhIRUZGnnZeUlKS8vPztX79eiUmJkqqCsw2m029evWq8ZzExER5eXnpm2++0ciRIyVJGRkZ2rt3r5KSkiRJH330kY4ePWo/54cfftCNN96ob7/9VnFxcX/16wEAAAAAmrgGcU93p06ddPHFF+umm27SK6+8IqvVqokTJ+rqq69Wy5YtJUkHDhzQRRddpLfeeks9e/ZUSEiIxo8fr0mTJiksLEzBwcG6/fbblZSUZN9E7c/BOicnx/55f74XHAAAAACAumoQoVuS3n33XU2cOFEXXXSRzGazRo4cqf/7v/+zj1utVmVkZDjczP7cc8/Z55aVlWno0KF66aWXXFE+AAAAAKAJajChOywsTAsWLDjpeLt27ez3ZB/n6+urOXPmaM6cObX6jOTk5GrvAQAAAADAmTK7ugAAAAAAABorQjcAAAAAAE5C6AYAAAAAwEkI3QAAAAAAOAmhGwAAAAAAJyF0AwAAAADgJIRuAAAAAACchNANAAAAAICTELoBAAAAAHASQjcAAAAAAE5C6AYAAAAAwEkI3QAAAAAAOAmhGwAAAAAAJyF0AwAAAADgJIRuAAAAAACchNANAAAAAICTELoBAAAAAHASQjcAAAAAAE5C6AYAAAAAwEkI3QAAAAAAOAmhGwAAAAAAJyF0AwAAAADgJIRuAAAAAACchNANAAAAAICTELoBAAAAAHASQjcAAAAAAE5C6AYAAAAAwEk8XV1AY2AYhiSpsLDQxZXUzGq1qqSkRIWFhfLy8nJ1OWji6Ee4C3oR7oJehDuhH+EuGkIvHs9/x/PgyRC660FRUZEkKTo62sWVAAAAAADOpqKiIoWEhJx03GScLpbjtGw2mw4ePKigoCCZTCZXl1NNYWGhoqOjtW/fPgUHB7u6HDRx9CPcBb0Id0Evwp3Qj3AXDaEXDcNQUVGRWrZsKbP55Hdus9JdD8xms1q3bu3qMk4rODjYbRsWTQ/9CHdBL8Jd0ItwJ/Qj3IW79+KpVriPYyM1AAAAAACchNANAAAAAICTELqbAB8fH02dOlU+Pj6uLgWgH+E26EW4C3oR7oR+hLtoTL3IRmoAAAAAADgJK90AAAAAADgJoRsAAAAAACchdAMAAAAA4CSEbgAAAAAAnITQDQAAAACAkxC6G4k5c+aoXbt28vX1Va9evbRu3bpTzv/ggw+UkJAgX19fde3aVUuWLDlLlaIpqEs/vvbaa+rXr5+aNWumZs2aadCgQaftX6C26vpn43ELFy6UyWTSiBEjnFsgmoy69mJ+fr5uu+02tWjRQj4+PurYsSP/rUa9qWs/zp49W/Hx8fLz81N0dLTuvvtulZaWnqVq0VitXLlSl19+uVq2bCmTyaRFixad9py0tDSdf/758vHxUfv27TVv3jyn11kfCN2NwHvvvadJkyZp6tSp2rBhg84991wNHTpUWVlZNc5ftWqVxowZo/Hjx2vjxo0aMWKERowYoV9//fUsV47GqK79mJaWpjFjxig1NVWrV69WdHS0hgwZogMHDpzlytHY1LUXj9u9e7fuvfde9evX7yxVisaurr1YXl6uwYMHa/fu3frwww+VkZGh1157Ta1atTrLlaMxqms/LliwQJMnT9bUqVO1ZcsWvfHGG3rvvff04IMPnuXK0dgUFxfr3HPP1Zw5c2o1f9euXbr00kuVkpKiTZs26a677tI///lPffnll06utB4YaPB69uxp3HbbbfbXlZWVRsuWLY1Zs2bVOH/UqFHGpZde6nCsV69exs033+zUOtE01LUf/6yiosIICgoy5s+f76wS0UScSS9WVFQYvXv3Nl5//XVj7Nixxt/+9rezUCkau7r24ssvv2zExsYa5eXlZ6tENCF17cfbbrvNGDhwoMOxSZMmGX369HFqnWhaJBmffPLJKefcf//9xjnnnONwbPTo0cbQoUOdWFn9YKW7gSsvL9f69es1aNAg+zGz2axBgwZp9erVNZ6zevVqh/mSNHTo0JPOB2rrTPrxz0pKSmS1WhUWFuasMtEEnGkvzpgxQxaLRePHjz8bZaIJOJNe/PTTT5WUlKTbbrtNzZs3V5cuXfTvf/9blZWVZ6tsNFJn0o+9e/fW+vXr7Zeg79y5U0uWLNEll1xyVmoGjmvIGcbT1QXgr8nJyVFlZaWaN2/ucLx58+ZKT0+v8ZzMzMwa52dmZjqtTjQNZ9KPf/bAAw+oZcuW1f5QBeriTHrxu+++0xtvvKFNmzadhQrRVJxJL+7cuVPLly/XNddcoyVLlmj79u269dZbZbVaNXXq1LNRNhqpM+nHf/zjH8rJyVHfvn1lGIYqKip0yy23cHk5zrqTZZjCwkIdPXpUfn5+Lqrs9FjpBuA2Hn/8cS1cuFCffPKJfH19XV0OmpCioiJdd911eu211xQREeHqctDE2Ww2WSwWvfrqq0pMTNTo0aP10EMP6ZVXXnF1aWiC0tLS9O9//1svvfSSNmzYoI8//liLFy/WzJkzXV0a0GCw0t3ARUREyMPDQ4cOHXI4fujQIUVFRdV4TlRUVJ3mA7V1Jv143NNPP63HH39cX3/9tbp16+bMMtEE1LUXd+zYod27d+vyyy+3H7PZbJIkT09PZWRkKC4uzrlFo1E6kz8XW7RoIS8vL3l4eNiPderUSZmZmSovL5e3t7dTa0bjdSb9+Mgjj+i6667TP//5T0lS165dVVxcrAkTJuihhx6S2cwaHs6Ok2WY4OBgt17llljpbvC8vb2VmJiob775xn7MZrPpm2++UVJSUo3nJCUlOcyXpGXLlp10PlBbZ9KPkvTkk09q5syZWrp0qXr06HE2SkUjV9deTEhI0C+//KJNmzbZfw0fPty+Q2p0dPTZLB+NyJn8udinTx9t377d/g8/krR161a1aNGCwI2/5Ez6saSkpFqwPv4PQoZhOK9Y4E8adIZx9U5u+OsWLlxo+Pj4GPPmzTM2b95sTJgwwQgNDTUyMzMNwzCM6667zpg8ebJ9/vfff294enoaTz/9tLFlyxZj6tSphpeXl/HLL7+46iugEalrPz7++OOGt7e38eGHHxq///67/VdRUZGrvgIaibr24p+xeznqS117ce/evUZQUJAxceJEIyMjw/j8888Ni8Vi/Otf/3LVV0AjUtd+nDp1qhEUFGT897//NXbu3Gl89dVXRlxcnDFq1ChXfQU0EkVFRcbGjRuNjRs3GpKMZ5991ti4caOxZ88ewzAMY/LkycZ1111nn79z507D39/fuO+++4wtW7YYc+bMMTw8PIylS5e66ivUGqG7kXjhhReMNm3aGN7e3kbPnj2NNWvW2McGDBhgjB071mH++++/b3Ts2NHw9vY2zjnnHGPx4sVnuWI0ZnXpx7Zt2xqSqv2aOnXq2S8cjU5d/2z8I0I36lNde3HVqlVGr169DB8fHyM2NtZ47LHHjIqKirNcNRqruvSj1Wo1pk2bZsTFxRm+vr5GdHS0ceuttxqHDx8++4WjUUlNTa3x74DH+2/s2LHGgAEDqp3TvXt3w9vb24iNjTXmzp171us+EybD4LoQAAAAAACcgXu6AQAAAABwEkI3AAAAAABOQugGAAAAAMBJCN0AAAAAADgJoRsAAAAAACchdAMAAAAA4CSEbgAAAAAAnITQDQAAAACAkxC6AQAAAABwEkI3AAAAAABOQugGAAAAAMBJCN0AAAAAADgJoRsAAAAAACchdAMAAAAA4CSEbgAAAAAAnITQDQAAAACAkxC6AQAAAABwEkI3AKDJMJlMmjZtmqvLwDFpaWkymUz68MMPXV1KrRw6dEhXXnmlwsPDZTKZNHv2bFeXBABoAAjdAIAGbd68eTKZTCf9tWbNGleX6BQHDx7UtGnTtGnTplrN/+2333TVVVcpNjZW/v7+ioiIUP/+/fXZZ5/V6XMPHz4sT09Pvf/++6ec99lnn2nAgAGyWCzy9/dXbGysRo0apaVLl9bp89zJ3XffrS+//FJTpkzR22+/rYsvvtjVJQEAGgBPVxcAAEB9mDFjhmJiYqodb9++vQuqcb6DBw9q+vTpateunbp3737a+Xv27FFRUZHGjh2rli1bqqSkRB999JGGDx+u//znP5owYUKtPvfLL7+UyWTSkCFDTjrn6aef1n333acBAwZoypQp8vf31/bt2/X1119r4cKFDTasLl++XH/729907733uroUAEADQugGADQKw4YNU48ePVxdhtu65JJLdMkllzgcmzhxohITE/Xss8/WOnQvWbJEffr0UWhoaI3jFRUVmjlzpgYPHqyvvvqq2nhWVladaz9biouLFRAQcNLxrKysk37vM1FaWipvb2+ZzVx4CACNGX/KAwCatAMHDujGG29U8+bN5ePjo3POOUdvvvmmw5zj9x6///77mj59ulq1aqWgoCBdeeWVKigoUFlZme666y5ZLBYFBgZq3LhxKisrq/ZZ77zzjhITE+Xn56ewsDBdffXV2rdvn8Oc5ORkdenSRZs3b1ZKSor8/f3VqlUrPfnkkw71XHDBBZKkcePG2S+lnzdvXp2+u4eHh6Kjo5Wfn1+r+TabTUuXLtWll1560jk5OTkqLCxUnz59ahy3WCw1vu9jjz2m1q1by9fXVxdddJG2b99ebd7atWt18cUXKyQkRP7+/howYIC+//57hzl79uzRrbfeqvj4ePn5+Sk8PFxXXXWVdu/e7TDv+G0JK1as0K233iqLxaLWrVvXWPPxuYZhaM6cOfaf93E7d+7UVVddpbCwMPn7++vCCy/U4sWLHd7jeA8tXLhQDz/8sFq1aiV/f38VFhbav9sll1yiZs2aKSAgQN26ddPzzz/v8B7p6em68sorFRYWJl9fX/Xo0UOffvppjTUDANwHK90AgEahoKBAOTk5DsdMJpPCw8NPes6hQ4d04YUXymQyaeLEiYqMjNQXX3yh8ePHq7CwUHfddZfD/FmzZsnPz0+TJ0/W9u3b9cILL8jLy0tms1mHDx/WtGnTtGbNGs2bN08xMTF69NFH7ec+9thjeuSRRzRq1Cj985//VHZ2tl544QX1799fGzdudFhBPXz4sC6++GJdccUVGjVqlD788EM98MAD6tq1q4YNG6ZOnTppxowZevTRRzVhwgT169dPktS7d+/T/pyKi4t19OhRFRQU6NNPP9UXX3yh0aNH1+InLP3www/Kzs6utmL+RxaLRX5+fvrss890++23Kyws7LTv+/jjj8tsNuvee+9VQUGBnnzySV1zzTVau3atfc7y5cs1bNgwJSYmaurUqTKbzZo7d64GDhyob7/9Vj179rTXuGrVKl199dVq3bq1du/erZdfflnJycnavHmz/P39HT771ltvVWRkpB599FEVFxfXWF///v319ttv67rrrtPgwYN1/fXX28cOHTqk3r17q6SkRHfccYfCw8M1f/58DR8+XB9++KH+/ve/O7zXzJkz5e3trXvvvVdlZWXy9vbWsmXLdNlll6lFixa68847FRUVpS1btujzzz/XnXfeKanqnvw+ffqoVatWmjx5sgICAvT+++9rxIgR+uijj6p9DgDAjRgAADRgc+fONSTV+MvHx8dhriRj6tSp9tfjx483WrRoYeTk5DjMu/rqq42QkBCjpKTEMAzDSE1NNSQZXbp0McrLy+3zxowZY5hMJmPYsGEO5yclJRlt27a1v969e7fh4eFhPPbYYw7zfvnlF8PT09Ph+IABAwxJxltvvWU/VlZWZkRFRRkjR460H/vhhx8MScbcuXNr94M65uabb7b/fMxms3HllVcaeXl5tTr3kUcecfheJ/Poo48akoyAgABj2LBhxmOPPWasX7++2rzjP9dOnToZZWVl9uPPP/+8Icn45ZdfDMMwDJvNZnTo0MEYOnSoYbPZ7PNKSkqMmJgYY/DgwQ7H/mz16tXVfqbH+6Zv375GRUVFrb6/JOO2225zOHbXXXcZkoxvv/3WfqyoqMiIiYkx2rVrZ1RWVjp819jYWIcaKyoqjJiYGKNt27bG4cOHHd77j9/1oosuMrp27WqUlpY6jPfu3dvo0KFDreoHALgGl5cDABqFOXPmaNmyZQ6/vvjii5PONwxDH330kS6//HIZhqGcnBz7r6FDh6qgoEAbNmxwOOf666+Xl5eX/XWvXr1kGIZuvPFGh3m9evXSvn37VFFRIUn6+OOPZbPZNGrUKIfPiYqKUocOHZSamupwfmBgoK699lr7a29vb/Xs2VM7d+4845/PcXfddZeWLVum+fPna9iwYaqsrFR5eXmtzl2yZMkpLy0/bvr06VqwYIHOO+88ffnll3rooYeUmJio888/X1u2bKk2f9y4cfL29ra/Pr5yf/z7btq0Sdu2bdM//vEP5ebm2n9+xcXFuuiii7Ry5UrZbDZJkp+fn/19rFarcnNz1b59e4WGhlb7/ZSkm266SR4eHrX6/jVZsmSJevbsqb59+9qPBQYGasKECdq9e7c2b97sMH/s2LEONW7cuFG7du3SXXfdVe1+8eOXsOfl5Wn58uUaNWqUioqK7N8/NzdXQ4cO1bZt23TgwIEz/g4AAOfi8nIAQKPQs2fPOm2klp2drfz8fL366qt69dVXa5zz502/2rRp4/A6JCREkhQdHV3tuM1mU0FBgcLDw7Vt2zYZhqEOHTrU+Dl/DPKS1Lp1a4d7hiWpWbNm+vnnn0//xU4jISFBCQkJkqr+EWHIkCG6/PLLtXbt2mqf+UeZmZnasGGDZsyYUavPGTNmjMaMGaPCwkKtXbtW8+bN04IFC3T55Zfr119/la+vr33un3+uzZo1k1R1mb0kbdu2TVJVYD2ZgoICNWvWTEePHtWsWbM0d+5cHThwQIZhOMz5s5p2vK+LPXv2qFevXtWOd+rUyT7epUuXk37ejh07JMlhzp9t375dhmHokUce0SOPPFLjnKysLLVq1arO9QMAnI/QDQBoko6vjF577bUnDXPdunVzeH2yFdGTHT8e+Gw2m0wmk7744osa5wYGBtbp/erTlVdeqZtvvllbt25VfHz8Sed98cUX8vX1VUpKSp3ePzg4WIMHD9bgwYPl5eWl+fPna+3atRowYIB9Tm1+fpL01FNPnfTxaMd/hrfffrvmzp2ru+66S0lJSQoJCZHJZNLVV19tf58/+uOq89lwJp93vO57771XQ4cOrXFOY300HgA0BoRuAECTFBkZqaCgIFVWVmrQoEFO/ay4uDgZhqGYmBh17NixXt7zVKvSdXH06FFJNa8C/9HixYuVkpLyl0Jqjx49NH/+fP3+++91Oi8uLk5SVYA/3e/Vhx9+qLFjx+qZZ56xHystLa31Du111bZtW2VkZFQ7np6ebh8/lePf7ddffz3pd4uNjZVUdUWEs3sVAFD/uKcbANAkeXh4aOTIkfroo4/066+/VhvPzs6ut8+64oor5OHhoenTp1dbrTYMQ7m5uXV+z+PPk65tmKzp+dhWq1VvvfWW/Pz81Llz55Oea7VatWzZslrdz11SUqLVq1fXOHb8HvtTrajXJDExUXFxcXr66ad15MiRauN//L3y8PCo9jN+4YUXVFlZWafPrK1LLrlE69atc/jOxcXFevXVV9WuXbtT/lwl6fzzz1dMTIxmz55d7ffy+PewWCxKTk7Wf/7znxr/waI+exUAUP9Y6QYANApffPGFfXXxj3r37m1fKfyzxx9/XKmpqerVq5duuukmde7cWXl5edqwYYO+/vpr5eXl1UttcXFx+te//qUpU6Zo9+7dGjFihIKCgrRr1y598sknmjBhgu699946v2doaKheeeUVBQUFKSAgQL169TrpPco333yzCgsL1b9/f7Vq1UqZmZl69913lZ6ermeeeabaJe5/9N1336mwsLDWobt379668MILdfHFF9ufA75o0SJ9++23GjFihM4777w6fVez2azXX39dw4YN0znnnKNx48apVatWOnDggFJTUxUcHKzPPvtMknTZZZfp7bffVkhIiDp37qzVq1fr66+/PuWj4/6KyZMn67///a+GDRumO+64Q2FhYZo/f7527dqljz76SGbzqdc3zGazXn75ZV1++eXq3r27xo0bpxYtWig9PV2//fabvvzyS0lVGwX27dtXXbt21U033aTY2FgdOnRIq1ev1v79+/XTTz855fsBAP46QjcAoFH44zOx/2ju3LknDd3NmzfXunXrNGPGDH388cd66aWXFB4ernPOOUdPPPFEvdY3efJkdezYUc8995ymT58uqWoDtiFDhmj48OF1fr/j90dPmTJFt9xyiyoqKjR37tyThu7Ro0frjTfe0Msvv6zc3FwFBQUpMTFRTzzxxGk/f8mSJercufNpL5WWpNDQUL322mtavHix5s6dq8zMTHl4eCg+Pl5PPfWU7rjjjjp/V0lKTk7W6tWrNXPmTL344os6cuSIoqKi1KtXL9188832ec8//7w8PDz07rvvqrS0VH369NHXX3990nuh/6rmzZtr1apVeuCBB/TCCy+otLRU3bp102effVarf6SQpKFDhyo1NVXTp0/XM888I5vNpri4ON100032OZ07d9aPP/6o6dOna968ecrNzZXFYtF555130t4HALgHk+GMXVkAAECj0blzZ1122WV68sknXV0KAAANDivdAADgpMrLyzV69GiNGjXK1aUAANAgsdINAAAAAICTsHs5AAAAAABOQugGAAAAAMBJCN0AAAAAADgJG6nVA5vNpoMHDyooKEgmk8nV5QAAAAAAnMwwDBUVFally5Yym0++nk3orgcHDx5UdHS0q8sAAAAAAJxl+/btU+vWrU86TuiuB0FBQZKqftjBwcEurqY6q9Wqr776SkOGDJGXl5ery0ETRz/CXdCLcBf0ItwJ/Qh30RB6sbCwUNHR0fY8eDKE7npw/JLy4OBgtw3d/v7+Cg4OdtuGRdNBP8Jd0ItwF/Qi3An9CHfRkHrxdLcYs5EaAAAAAABOQugGAAAAAMBJCN0AAAAAADgJoRsAAAAAACchdAMAAAAA4CSEbgAAAAAAnITQDQAAAACAkxC6AQAAAABuxTAMHTrq6irqh6erCwAAAAAA4EhZhb7fnqPU9CylpmfpUJGnhg0uVXS4l6tL+0sa9Ur3rFmzdMEFFygoKEgWi0UjRoxQRkaGw5zS0lLddtttCg8PV2BgoEaOHKlDhw65qGIAAAAAaBoMw9CO7CN6/duduub1NTpvxle6+e31WvjDPh0qKpO32dC2Q0dcXeZf1qhXulesWKHbbrtNF1xwgSoqKvTggw9qyJAh2rx5swICAiRJd999txYvXqwPPvhAISEhmjhxoq644gp9//33Lq4eAAAAABqXUmul1uzMrVrNzsjW3rwSh/F24f5KSbCoX/sw5aWvU78OES6qtP406tC9dOlSh9fz5s2TxWLR+vXr1b9/fxUUFOiNN97QggULNHDgQEnS3Llz1alTJ61Zs0YXXnihK8oGAAAAgEZjX16J0jKqQvaqHTkqtdrsY94eZvWKDVNKvEUpCRbFRFQtjlqtVi3Z6qqK61ejDt1/VlBQIEkKCwuTJK1fv15Wq1WDBg2yz0lISFCbNm20evXqk4busrIylZWV2V8XFhZKqmoMq9XqrPLP2PGa3LE2ND30I9wFvQh3QS/CndCPqA/WSps27M1Xaka2VmzN0fbsYofxqGAfJcdHakCHCCXFhinA50Qs/XMPunMv1rY2k2EYhpNrcQs2m03Dhw9Xfn6+vvvuO0nSggULNG7cOIcALUk9e/ZUSkqKnnjiiRrfa9q0aZo+fXq14wsWLJC/v3/9Fw8AAAAAbqygXNqSb9LmwyZlFJhUWmmyj5llKCZI6tzMps6hhlr4SybTKd6sgSgpKdE//vEPFRQUKDg4+KTzmsxK92233aZff/3VHrj/iilTpmjSpEn214WFhYqOjtaQIUNO+cN2FavVqmXLlmnw4MHy8mrYO/+h4aMf4S7oRbgLehHuhH5EbVXaDP18oEBpGTlasS1bvx0schgPC/DSgA4RSu4YqT7twxXiV7d+agi9ePyK59NpEqF74sSJ+vzzz7Vy5Uq1bt3afjwqKkrl5eXKz89XaGio/fihQ4cUFRV10vfz8fGRj49PteNeXl5u2xCS+9eHpoV+hLugF+Eu6EW4E/oRNTlcXK6V27KVmp6lFVuzdbjE8fLqc1uHKCXBopR4i7q2CpHZ/NeXs925F2tbV6MO3YZh6Pbbb9cnn3yitLQ0xcTEOIwnJibKy8tL33zzjUaOHClJysjI0N69e5WUlOSKkgEAAADALRiGod8OFto3Qdu497Bsf7g5OcjXU/07RmpgvEX9O0YqMqj6wiQaeei+7bbbtGDBAv3vf/9TUFCQMjMzJUkhISHy8/NTSEiIxo8fr0mTJiksLEzBwcG6/fbblZSUxM7lAAAAAJqcI2UV+m5bzrFHemUpq8hx/6uEqCAlx1uUEh+pxLbN5OlhdlGlDUejDt0vv/yyJCk5Odnh+Ny5c3XDDTdIkp577jmZzWaNHDlSZWVlGjp0qF566aWzXCkAAAAAnH2GYWhHdrE9ZP+wO0/WyhPL2X5eHurTPkIDEyxKjo9Uy1A/F1bbMDXq0F2bjdl9fX01Z84czZkz5yxUBAAAAACuVWqt1OqdufagvS/vqMN4TESABnSM1MAEi3rFhsnH08NFlTYOjTp0AwAAAACkfXklSs3IUmp6llbtyFVZhc0+5u1hVq/YMKXEW5SSYFFMRIALK218CN0AAAAA0MiUV9j04568Y6vZ2dqedcRhvEWIr32n8T7tw+XvTTR0Fn6yAAAAANAIZBWWKi0jW8vTs/Td9hwdKauwj3mYTUps20wp8RYNTLCoY/NAmUx//ZFeOD1CNwAAAAA0QJU2Q5v25dvvzf7tYKHDeESgtwZ0tCglIVL9OkQqxM89n3fd2BG6AQAAAKCBOFxcrpXbqlazV2zNVn6J1T5mMkndWocq+dgmaF1bhchsZjXb1QjdAAAAAOCmDMPQbwcLlZaRpeXpWdq0L1+2PzykKdjXU/07Riol3qIB8ZGKCPRxXbGoEaEbAAAAANxIUalV32/P0fL0LKVlZCurqMxhPCEqyL4J2vltQuXpYXZRpagNQjcAAAAAuJBhGNqRfUSp6dlKzcjSD7vzZK08sZzt7+2hPu0jlBJvUXJ8pFqG+rmwWtQVoRsAAAAAzrKj5ZVaszNXqccuG99/+KjDeGxEgJLjqzZB6xkTJh9PDxdVir+K0A0AAAAAZ8G+vBKlZmQpNT1Lq3bkqqzCZh/z9jTrwthwpcRX3Z/dLiLAhZWiPhG6AQAAAMAJyits+nF3nn01e0d2scN4yxBf+73ZvduHy9+beNYY8bsKAAAAAPXkUGGp0jKylJqere+25+hIWYV9zMNsUo+2zZQcb9HABIs6Ng+UycQjvRo7QjcAAAAAnKFKm6FN+w7bN0H77WChw3hEoI+Sj10y3rdDhEL8vFxUKVyF0A0AAAAAdZBXXK6VW6tC9oqt2covsdrHTCbp3NahSjm2CVqXliEym1nNbsoI3QAAAABwCoZh6LeDhUpNz1JqRpY27suXceKJXgr29dSAeItS4iPVv2OkIgJ9XFcs3A6hGwAAAAD+pKjUqu+25Sg1I0tpGdnKKipzGO/UIrhqp/EEi86LDpWnh9lFlcLdEboBAAAANHmGYWh71pFjj/TK1g+781RhO7Gc7e/tob7tI+zPzm4R4ufCatGQELoBAAAANElHyyu1emeOfRO0/YePOozHRgZU3Zsdb9EFMc3k4+nhokrRkBG6AQAAADQZe3NLqlazM7K0ekeuyips9jFvT7MujA3XwPhIJcdb1C4iwIWVorEgdAMAAABotMorbPphd559E7Qd2cUO461C/ZSSUPVIr6S4cPl7E5FQv+goAAAAAI1KZkGp0o6tZn+3LUfF5ZX2MQ+zST3aNtPABItSEizqYAmUycQjveA8hG4AAAAADVqlzdDGvYftm6Bt/r3QYTwi0Me+03if9hEK8fNyUaVoigjdAAAAABqcvOJyrdhaFbJXbstWfonVPmYySee2Dq1azY636JyWwTKbWc2GaxC6AQAAALg9m83Q5t8LtfzYvdmb9uXLOPFEL4X4eal/x0gNTIhU/w6RCg/0cV2xwB8QugEAAAC4pcJSq77blqPU9Cylbc1WdlGZw3inFsEaeGwTtO7RofL0MLuoUuDkCN0AAAAA3IJhGNqedcS+mv3j7sOqsJ1Yzvb39lDf9hEamGBRcrxFUSG+LqwWqB1CNwAAAACXOVpeqdU7c6qCdnq2DuQfdRiPjQxQSrxFAxMs6tGumXw8PVxUKXBmCN0AAAAAzqq9uSVann5IqRnZWr0zV+UVNvuYt6dZSbHhx1azI9U2PMCFlQJ/HaEbAAAAgFOVV9j0w+48+2XjO7OLHcZbhfop5di92b3jIuTnzWo2Gg9CNwAAAIB6l1lQqrSMLC1Pz9L323NUXF5pH/M0m9SjXTP7I73aWwJlMvFILzROhG4AAAAAf1lFpU2b9uUfW83O1pbfCx3GI4N8lNwxUgMTLOrTIULBvl4uqhQ4uwjdAAAAAM5I7pEyrdyWreXp2Vq5NVsFR632MZNJ6h4dqoHxFqUkWNS5RbDMZlaz0fQQugEAAADUis1m6LeDhUo9dtn4T/vzZZx4opdC/Lw04Nhqdv+OkQoL8HZdsYCbIHQDAAAAOKnCUqu+25aj1PQspW3NVnZRmcN45xbB9k3QukeHytPD7KJKAfdE6AYAAABgZxjStkNH9O2Oqt3G1+85rArbieXsAG8P9e0QoYEJFg3oaFFUiK8LqwXcH6EbAAAAaOKOlldq1Y4cfbMlU0t/8lDemlUO43GRAUqOt2hggkUXtAuTtyer2UBtEboBAACAJmhPbrFS07O0PCNba3bmqrzCdmzEJB9Ps5LiwpUSX/VIrzbh/i6tFWjICN0AAABAE1BWUakfdh1WakaWUtOztDOn2GG8VaifkjtGKKBwtyZedZGCA7hsHKgPhG4AAACgkfq94KjSMrK1PD1L32/PUUl5pX3M02zSBe3ClJJQtdt4XGSgKioqtGTJLvl5e7iwaqBxIXQDAAAAjURFpU0b9+VXXTaenqX0zCKH8cggH6XEV+003rdDhIJ8vVxUKdB0ELoBAACABiz3SJlWbK1azV65NVuFpRX2MZNJOi86tOre7ASLOrcIltlscmG1QNND6AYAAAAaEJvN0K8HC5Sanq3lGVn6eX++jBNP9FKov5cGdKxaze7fMVJhAd6uKxZA4w/dK1eu1FNPPaX169fr999/1yeffKIRI0bYx2+44QbNnz/f4ZyhQ4dq6dKlZ7lSAAAAoGYFR636bluOUjOylJaRrZwjZQ7jnVsEa2CCRSkJkeoe3UwerGYDbqPRh+7i4mKde+65uvHGG3XFFVfUOOfiiy/W3Llz7a99fHzOVnkAAABANYZhaOuhI/adxn/cc1iVthPL2YE+nurbPkIpCZFKjreoeTA7jQPuqtGH7mHDhmnYsGGnnOPj46OoqKhav2dZWZnKyk7862JhYaEkyWq1ymq1nlmhTnS8JnesDU0P/Qh3QS/CXdCLOK6kvEKrd+ZpxdYcrdiao4MFpQ7jcZEBSu4YoQEdI5TYppm8Pc32sfrqH/oR7qIh9GJtazMZxh/vAGncTCZTjZeXL1q0SN7e3mrWrJkGDhyof/3rXwoPDz/p+0ybNk3Tp0+vdnzBggXy9/d3RukAAABohLKPSpvzTdp82KTthSZVGCcuC/cyGeoQYqhzM0OdQg1FsJgNuJWSkhL94x//UEFBgYKDg086r8mH7oULF8rf318xMTHasWOHHnzwQQUGBmr16tXy8Kj5+YQ1rXRHR0crJyfnlD9sV7FarVq2bJkGDx4sLy8eCwHXoh/hLuhFuAt6sWkpq7Dph92HtWJrtlZszdGu3BKH8dahvkqOj9SAjhHq1S7srD8vm36Eu2gIvVhYWKiIiIjThu5Gf3n56Vx99dX2/921a1d169ZNcXFxSktL00UXXVTjOT4+PjXe9+3l5eW2DSG5f31oWuhHuAt6Ee6CXmy8fi84qtT0bKVmZOn77TkqKa+0j3maTbqgXZhSEiI1MMGiuMhAmUyu3wSNfoS7cOderG1dTT50/1lsbKwiIiK0ffv2k4ZuAAAA4GQqKm3asDffvglaemaRw7glyOfYc7Mj1ad9hIJ83TNQAKgfhO4/2b9/v3Jzc9WiRQtXlwIAAIAGIudImVZkVK1mr9yarcLSCvuYySSdFx2qgQkWJcdbdE7LYLdYzQZwdjT60H3kyBFt377d/nrXrl3atGmTwsLCFBYWpunTp2vkyJGKiorSjh07dP/996t9+/YaOnSoC6sGAACAO7PZDP1yoKBqNTsjWz/vz9cfd0pq5u+lAR0jlZJgUb8OkQoL8HZdsQBcqtGH7h9//FEpKSn215MmTZIkjR07Vi+//LJ+/vlnzZ8/X/n5+WrZsqWGDBmimTNn8qxuAAAAOCg4atW327KVmp6tFVuzlHOk3GG8S6tgpcRXrWZ3jw6Vh5nVbABNIHQnJyfrVBu0f/nll2exGgAAADQUhmFo66EjWp6epdSMLK3fc1iVthN/rwz08VS/DhFKjo9UcrxFzYN5pheA6hp96AYAAABqq6S8Qt9vz1VqRpbS0rN0sKDUYby9JfDYvdmR6tE2TN6eZhdVCqChIHQDAACgSdudU2xfzV67M0/llTb7mI+nWb3jwu2boEWH+buwUgANEaEbAAAATUpZRaXW7crT8vQspWVka1dOscN4dJifBsZblJxgUVJsuHy9PFxUKYDGgNANAACARu9g/tFjz83O1qodOSopr7SPeXmYdEG7MPtqdlxkAI/0AlBvCN0AAABodCoqbdqwN//YanaW0jOLHMYtQT5KibcoJcGiPu3DFeTr5aJKATR2hG4AAAA0CjlHypSWka3UjCx9uzVbhaUV9jGzSTqvTTP7JmidWwSzmg3grCB0AwAAoEGy2Qz9cqDAvpr90/4Ch/Fm/l4a0DFSKQkW9e8QqWYB3i6qFEBTRugGAABAg1FQYtXKbVWr2SsyspVbXO4w3qVVsP2y8XNbh8rDzGo2ANcidAMAAMBtGYahjENFVavZ6dlav/ewKm2GfTzQx1P9OkQoJb7qsnFLsK8LqwWA6gjdAAAAcCvFZRVatSPXftn47wWlDuMdLIFKSbAoJd6ixLbN5O1pdlGlAHB6hG4AAAC43K6cYnvIXrszT+WVNvuYr5dZveMilBIfqeR4i6LD/F1YKQDUDaEbAAAAZ12ptVLrduXZg/bu3BKH8egwPw2Mtyg5waKk2HD5enm4qFIA+GsI3QAAADgrDuQfVVpGllLTs/T99lwdtVbax7w8TOoZE2bfBC02IoBHegFoFAjdAAAAcAprpU0b9hxWaka2UtOzlHGoyGG8ebCPkjtWhey+HSIU6MNfTQE0PvzJBgAAgHqTXVSmFVurQvbKbdkqKq2wj5lN0vltmikloWqn8c4tglnNBtDoEboBAABwxmw2Qz8fKFBqepZSM7L08/4Ch/Fm/l5KPvY4rwEdIxXq7+2iSgHANdw6dJeXl2vXrl2Ki4uTp6dblwoAANBkFJRYtXJbtlIzsrQiI1u5xeUO411bhVTtNJ5g0bmtQ+VhZjUbQNPllkm2pKREt99+u+bPny9J2rp1q2JjY3X77berVatWmjx5sosrBAAAaDoMw1B6ZpFSj22CtmFvvipthn08yMdT/TpGVK1od4yUJdjXhdUCgHtxy9A9ZcoU/fTTT0pLS9PFF19sPz5o0CBNmzaN0A0AAOBkxWUV+n57jlIzspWWkaXfC0odxjs2D1RyvEUp8Rb1aNdMXh5mF1UKAO7NLUP3okWL9N577+nCCy902FzjnHPO0Y4dO1xYGQAAQOO1M/uIPWSv3Zmn8kqbfczXy6w+cRFKTrAoJT5SrZv5u7BSAGg43DJ0Z2dny2KxVDteXFzMDpcAAAD1pNRaqbW78pSanqW0jCztzi1xGG8T5q+Bx3YavzA2XL5eHi6qFAAaLrcM3T169NDixYt1++23S5I9aL/++utKSkpyZWkAAAAN2oH8o/aQ/f32XB21VtrHvDxM6hUTruT4SKUkWBQbEcCCBwD8RW4Zuv/9739r2LBh2rx5syoqKvT8889r8+bNWrVqlVasWOHq8gAAABoMa6VN6/ccVmpGltLSs5VxqMhhPCrYVykJkUqOt6hP+wgF+rjlXw8BoMFyyz9V+/btq02bNunxxx9X165d9dVXX+n888/X6tWr1bVrV1eXBwAA4Nayikq1IiNbaRnZWrktW0WlFfYxs0lKbNvMvglapxZBrGYDgBO5ZeiWpLi4OL322muuLgMAAMDt2WyGftqfb98E7ef9BQ7jYQHeSu5Y9dzs/h0iFOrv7aJKAaDpccvQvWTJEnl4eGjo0KEOx7/88kvZbDYNGzbMRZUBAAC4h4ISq1Zsy1ZaepZWbM1WbnG5w3i31iFK7lh1b3a31qHyMLOaDQCu4Jahe/LkyXr88cerHTcMQ5MnTyZ0AwCAJscwDG35vajq3uyMLK3fc1g248R4kI+n+neMVHJ8pAbER8oS5Ou6YgEAdm4Zurdt26bOnTtXO56QkKDt27e7oCIAAICz70hZhb7fnqO0jCylpmcrs7DUYbxj80ClJFTdm53Ytpm8PMwuqhQAcDJuGbpDQkK0c+dOtWvXzuH49u3bFRAQ4JqiAAAAnMwwDO3MKT72SK9srd2VK2vlieVsPy8P9WkfruT4qmdnt27m78JqAQC14Zah+29/+5vuuusuffLJJ4qLi5NUFbjvueceDR8+3MXVAQAA1J8ya6W2HDbpx8XpWrktR3tySxzG24b7KyXeopQEi3rFhMnXy8NFlQIAzoRbhu4nn3xSF198sRISEtS6dWtJ0v79+9WvXz89/fTTLq4OAADgr9l/uKRqp/H0LH2/I0elVg9JeyVJXh4m9YoJV3J8pAYmWBQTEcAjvQCgAXPL0B0SEqJVq1Zp2bJl+umnn+Tn56du3bqpf//+ri4NAACgzqyVNv24+3DVvdkZWdp66IjDeIi3oYu7ReuiTs3Vp32EAnzc8q9oAIAz4HZ/olutVvn5+WnTpk0aMmSIhgwZ4uqSAAAA6iyrqFRpx56b/e3WHBWVVdjHzCYpsW0zpSRY1C8uTDvWf6tLL+0sLy8vF1YMAHAGtwvdXl5eatOmjSorK11dCgAAQK1V2gz9tD9faelZSs3I1i8HChzGwwK87c/N7t8hUiH+VQHbarVqJ1ePA0Cj5XahW5IeeughPfjgg3r77bcVFhbm6nIAAABqlF9SrhVbs5WWka0VW7OVV1zuMN6tdYiS4y0amGBRt1YhMptJ1wDQ1Lhl6H7xxRe1fft2tWzZUm3btq32mLANGza4qDIAANCUGYahLb8XKTUjS6npWdqw97BsJ57opSBfT/XvcGw1u2OELEG+risWAOAW3DJ0jxgxwtUlAAAASJKOlFXo++05Sk2v2gTtUGGZw3h88yAlJ0RqYLxF57dtJi8Ps4sqBQC4I7cM3VOnTnV1CQAAoIkyDEM7c4rtIXvdrjxZK08sZ/t5eah3XLhSEqqend0q1M+F1QIA3J1bhu7j1q9fry1btkiSzjnnHJ133nkurggAADRGpdZKrd6Za98EbW9eicN423B/pRy7N7tnTJh8vTxcVCkAoKFxy9CdlZWlq6++WmlpaQoNDZUk5efnKyUlRQsXLlRkZKRrCwQAAA3evrySY8/NztaqHTkqtdrsY94eZvWKDbNvghYTEXCKdwIA4OTcMnTffvvtKioq0m+//aZOnTpJkjZv3qyxY8fqjjvu0H//+18XVwgAABoaa6VNP+4+bN8EbVvWEYfxFiG+9pDdOy5cAT5u+dckAEAD45b/NVm6dKm+/vpre+CWpM6dO2vOnDkaMmSICysDAAANSVZhqdIyspWakaXvtuWoqKzCPuZhNimxTbOqTdASLIpvHiSTiUd6AQDql1uGbpvNJi8vr2rHvby8ZLPZajjj5FauXKmnnnpK69ev1++//65PPvnEYXd0wzA0depUvfbaa8rPz1efPn308ssvq0OHDn/1awAAgLOs0mbop/359k3Qfj1Q6DAeHuCtAfGRSom3qH+HSIX4V//7BgAA9cktQ/fAgQN155136r///a9atmwpSTpw4IDuvvtuXXTRRXV6r+LiYp177rm68cYbdcUVV1Qbf/LJJ/V///d/mj9/vmJiYvTII49o6NCh2rx5s3x9ebYmAADu7nBxuVZuy1ZqepZWbM3W4RKrw/i5rUOqdhqPt6hrqxCZzaxmAwDOHrcM3S+++KKGDx+udu3aKTo6WpK0b98+denSRe+8806d3mvYsGEaNmxYjWOGYWj27Nl6+OGH9be//U2S9NZbb6l58+ZatGiRrr766hrPKysrU1nZiWd0FhZW/Su61WqV1Wqt8RxXOl6TO9aGpod+hLugFxsuwzC0JbNIaRk5WrEtR5v25ct24oleCvL1VL/24UruGKl+HcIVEehjH6usrFBlpQuKPgV6Ee6EfoS7aAi9WNvaTIZhGKefdvYZhqGvv/5a6enpkqROnTpp0KBBf+k9TSaTw+XlO3fuVFxcnDZu3Kju3bvb5w0YMEDdu3fX888/X+P7TJs2TdOnT692fMGCBfL39/9LNQIAgOpKK6WMfJO25Ju0+bBJBVbH1eoW/obOCTXUuZlN7YIkDxazAQBOVlJSon/84x8qKChQcHDwSee5zUp3WFiYtm7dqoiICN144416/vnnNXjwYA0ePNhpn5mZmSlJat68ucPx5s2b28dqMmXKFE2aNMn+urCwUNHR0RoyZMgpf9iuYrVatWzZMg0ePLjGe+WBs4l+hLugF92bYRjamVOiFVuzlbY1Rz/uOSxr5Yl1Aj8vs3rHVa1mD+gYoRYhDfeWMHoR7oR+hLtoCL14/Irn03Gb0F1eXq7CwkJFRERo/vz5euKJJxQUFOTqsmrk4+MjHx+fase9vLzctiEk968PTQv9CHdBL7qPUmulVu/MVVp6lpZnZGlf3lGH8ZiIACUf2wStV2yYfDw9XFSpc9CLcCf0I9yFO/dibetym9CdlJSkESNGKDExUYZh6I477pCfn1+Nc9988816+cyoqChJ0qFDh9SiRQv78UOHDjlcbg4AAJxjX16J0jKytDw9S6t25Kqs4sRTSrw9zOoVG6aUeItSEiyKiQhwYaUAAJwZtwnd77zzjp577jnt2LFDJpNJBQUFKi0tdepnxsTEKCoqSt988409ZBcWFmrt2rX6f//v/zn1swEAaIrKK2z6cU+e0jKytTw9S9uzjjiMtwzx1YB4iwYmWNSnfbj8vd3mryoAAJwRt/kvWfPmzfX4449LqgrDb7/9tsLDw//y+x45ckTbt2+3v961a5c2bdqksLAwtWnTRnfddZf+9a9/qUOHDvZHhrVs2dLhWd4AAODMZRWW2kP2d9tzdKSswj7mYTYpsW0zpRwL2h2bB8pkYhc0AEDj4Tah+4927dpVb+/1448/KiUlxf76+AZoY8eO1bx583T//feruLhYEyZMUH5+vvr27aulS5fyjG4AAM5Qpc3Qpn35Sk3PUmpGln476LjRTESgtwZ0tCglIVL9OkQqxM8979UDAKA+uGXork/Jyck61VPRTCaTZsyYoRkzZpzFqgAAaFwOF5dr5bZspaZnacXWbB0uOfHsUpNJ6tY6VCnxkRqYYFGXliEym1nNBgA0DY0+dAMAgPpnGIZ+O1ho3wRt07582f7wb9zBvp7q37Fqp/EB8ZGKCKz+1A8AAJoCQjcAAKiVolKrvt+eo9T0bKVmZCmrqMxhPCEqSCkJFqXEW3R+m1B5ephdVCkAAO7D7UJ3RUWFFixYoKFDh6p58+auLgcAgCbLMAztyD6i5elZSk3P1g+781Txh+Vsf28P9WkfoZR4i5LjI9UytOZHfQIA0JS5Xej29PTULbfcoi1btri6FAAAmpyj5ZVavfPEavb+w0cdxmMiAo49NztSPWPC5OPp4aJKAQBoGNwudEtSz549tWnTJrVt29bVpQAA0OjtzS1RakbVTuOrd+SqrMJmH/P2NOvC2HClxFfdn90uIsCFlQIA0PC4Zei+9dZbNWnSJO3bt0+JiYkKCHD8D3y3bt1cVBkAAA1feYVNP+zOsz/Sa0d2scN4yxBf+73ZvduHy9/bLf+6AABAg+CW/xW9+uqrJUl33HGH/ZjJZJJhGDKZTKqsrHRVaQAANEiZBaVKO7aa/d22HBWXn/hvqYfZpB5tmykloere7PjmQTKZeKQXAAD1wS1D965du1xdAgAADVqlzdDGvYerLhtPz9bm3wsdxiMCvZUcX7Wa3bdDhEL8vFxUKQAAjZtbhm7u5QYAoO7yisu1YmtVyF65LVv5JVb7mMkkdWsdqpT4SA1MsKhLyxCZzaxmAwDgbG4Zuo/bvHmz9u7dq/Lycofjw4cPd1FFAAC4D5vN0G8HC+2boG3aly/jxBO9FOzrqQHxFqXER6p/x0hFBPq4rlgAAJootwzdO3fu1N///nf98ssv9nu5JdnvL+OebgBAU1VYatV323KUmp6ltK3Zyi4qcxhPiArSwASLUhIsOi86VJ4eZhdVCgAAJDcN3XfeeadiYmL0zTffKCYmRuvWrVNubq7uuecePf30064uDwCAs8YwDG3POqLlx3Ya/3H3YVXYTixn+3t7qG/7CPsmaC1C/FxYLQAA+DO3DN2rV6/W8uXLFRERIbPZLLPZrL59+2rWrFm64447tHHjRleXCACA0xwtr9SqHTn2TdAO5B91GI+NDFDKsU3QLohpJh9PDxdVCgAATsctQ3dlZaWCgoIkSRERETp48KDi4+PVtm1bZWRkuLg6AADq397cEi1PP6TUjGyt3pmr8gqbfczb06yk2HAlx0cqJd6idhEBLqwUAADUhVuG7i5duuinn35STEyMevXqpSeffFLe3t569dVXFRsb6+ryAAD4y8orbPphd579svGd2cUO461C/ZSSUBWyk+LC5e/tlv/JBgAAp+GW/wV/+OGHVVxc9ZePGTNm6LLLLlO/fv0UHh6u9957z8XVAQBwZjILSpWWkaXl6Vn6fnuOistPbAzqYTapR9tm9k3QOlgC7RuIAgCAhsstQ/fQoUPt/7t9+/ZKT09XXl6emjVrxl9AAAANRkWlTZv25R9bzc7Wlt8LHcYjAn2UEh+plASL+naIULCvl4sqBQAAzuKWofu47du3a8eOHerfv7/CwsLsjw4DAMBd5R4p04qt2UrNyNbKrdkqOGq1j5lM0rmtQ6tWs+MtOqdlsMxm/jEZAIDGzC1Dd25urkaNGqXU1FSZTCZt27ZNsbGxGj9+vJo1a6ZnnnnG1SUCACBJstkM/Xaw0H5v9k/78/XHfyMO8fNS/46RGpgQqf4dIhUe6OO6YgEAwFnnlqH77rvvlpeXl/bu3atOnTrZj48ePVqTJk0idAMAXKqw1Kpvt1Y90istI1s5R8ocxju1CNbAY5ugdY8OlaeH2UWVAgAAV3PL0P3VV1/pyy+/VOvWrR2Od+jQQXv27HFRVQCApsowDG3LOlK1mp2epfV7DqvCdmI529/bQ33bRyjl2GXjUSG+LqwWAAC4E7cM3cXFxfL39692PC8vTz4+XJYHAHC+kvIKrd6Rq+XpVavZB/KPOozHRgYoJd6igQkW9WjXTD6eHi6qFAAAuDO3DN39+vXTW2+9pZkzZ0qSTCaTbDabnnzySaWkpLi4OgBAY7Unt1ip6VlanpGtNTtzVV5hs495e5qVFBtu3228bXiACysFAAANhVuG7ieffFIXXXSRfvzxR5WXl+v+++/Xb7/9pry8PH3//feuLg8A0EhU2KTvd+Rq5bY8pWVkaWdOscN4q1A/pSREamCCRUmxEfLzZjUbAADUjVuG7i5dumjr1q168cUXFRQUpCNHjuiKK67QbbfdphYtWri6PABAA/Z7wVGlZWTrm82ZWrnVQ+Vr19vHPM0m9WjXzH7ZeHtLoEwmHukFAADOnFuGbkkKCQnRQw895OoyAAANXEWlTRv35VddNp6epfTMoj+MmhQR6K2UeItSEizq2yFCwb5eLqsVAAA0Pm4buvPz87Vu3TplZWXJZrM5jF1//fUuqgoA0BDkHinTiq3ZWp6epZVbs1VYWmEfM5mk7tGh6t8+XF7ZGbrpysHy8fF2YbUAAKAxc8vQ/dlnn+maa67RkSNHFBwc7HBpn8lkInQDABzYbIZ+PVig1PRsLc/I0s/782WceKKXQvy81L9jpAYmRGpAR4vCArxltVq1ZEmGzGYuHwcAAM7jlqH7nnvu0Y033qh///vfNT46DACAgqNWfbctR6kZVY/0yjlS5jDeuUWwUhIilRJvUffoUHl6mF1UKQAAaMrcMnQfOHBAd9xxB4EbAGBnGIa2Hjqi1Iyqe7PX7zmsStuJ5ewAbw/17RChlHiLkuMtigrxdWG1AAAAVdwydA8dOlQ//vijYmNjXV0KAMCFSsortGp7rn01+0D+UYfxuMgA+yZoPdo1k48nj/QCAADuxW1C96effmr/35deeqnuu+8+bd68WV27dpWXl+NOssOHDz/b5QEAzpLdOcVKzchSaka21uzMVXnFic00fTzNSooLrwra8Ra1CeeKKAAA4N7cJnSPGDGi2rEZM2ZUO2YymVRZWXkWKgIAnA1lFZVatytPqenZSsvI0s6cYofxVqF+SkmI1MAEi5JiI+TnzWo2AABoONwmdP/5sWAAgMbrYP5RpWVkKzUjS99vz1FJ+Yl/TPU0m3RBuzB70I6LDHR4igUAAEBD4jahGwDQeFVU2rRhb37VZePpWUrPLHIYjwzyUUp81U7jfTtEKMjX6yTvBAAA0LC4VehevXq1cnNzddlll9mPvfXWW5o6daqKi4s1YsQIvfDCC/Lx8XFhlQCA2sg5UqYVx1azV27NVmFphX3MZJLOiw61b4LWuUUwz8sGAACNkluF7hkzZig5Odkeun/55ReNHz9eN9xwgzp16qSnnnpKLVu21LRp01xbKACgGpvN0C8HCuyboP28P1/GiSd6KdTfSwM6Vq1m9+8YqbAAb9cVCwAAcJa4VejetGmTZs6caX+9cOFC9erVS6+99pokKTo6WlOnTiV0A4CbKDhq1bfbspWanq0VW7OUc6TcYfyclsHHVrMj1T26mTxYzQYAAE2MW4Xuw4cPq3nz5vbXK1as0LBhw+yvL7jgAu3bt88VpQEAJBmGoYxDRUpNr7psfP2ew6q0nVjODvTxVN/2EUpJiFRyvEXNg31dWC0AAIDruVXobt68uXbt2qXo6GiVl5drw4YNmj59un28qKio2jO7AQDOVVxWoVU7cpWakaW09CwdLCh1GG9vCVRyx6qdxnu0C5O3p9lFlQIAALgftwrdl1xyiSZPnqwnnnhCixYtkr+/v/r162cf//nnnxUXF+fCCgGgadiVU6zU9CylZmRp7c48lVeeeKyjj6dZvePClZJgUXJHi9qE+7uwUgAAAPfmVqF75syZuuKKKzRgwAAFBgZq/vz58vY+sdHOm2++qSFDhtTrZ06bNs1hNV2S4uPjlZ6eXq+fAwDurNRaqXW78uyP9NqdW+Iw3rqZnwYmWJQSb9GFseHy8/ZwUaUAAAANi1uF7oiICK1cuVIFBQUKDAyUh4fjX+o++OADBQYG1vvnnnPOOfr666/trz093erHAgBOcSD/qNIyspSanq3vt+foqLXSPuZpNqlnTJhS4i1Kjo9Ue0ugTCY2QQMAAKgrt0yXISEhNR4PCwtzyud5enoqKirKKe8NAO7CWmnThj2HlZqRrdT0LGUcKnIYtwT52Hca79M+QkG+7KEBAADwV7ll6D7btm3bppYtW8rX11dJSUmaNWuW2rRpc9L5ZWVlKisrs78uLCyUJFmtVlmtVqfXW1fHa3LH2tD00I9nV+6RMq3YlqMVW3P07fZcFZVW2MfMJum86FD17xCh5PgIdYoKcljNbuy/R/Qi3AW9CHdCP8JdNIRerG1tJsMwjNNPa7y++OILHTlyRPHx8fr99981ffp0HThwQL/++quCgoJqPKem+8AlacGCBfL3Z0MhAK5jM6R9R6TN+WZtPmzS3mLHS8IDPA11CjXUuZmhhBBDASxmAwAAnJGSkhL94x//UEFBgYKDg086r8mH7j/Lz89X27Zt9eyzz2r8+PE1zqlppTs6Olo5OTmn/GG7itVq1bJlyzR48GAeuQaXox/rX8FRq77bnqsVW7O1YluO8ood/9X1nJZBSu4YqQEdI9StVYg8zNybLdGLcB/0ItwJ/Qh30RB6sbCwUBEREacN3Vxe/iehoaHq2LGjtm/fftI5Pj4+8vHxqXbcy8vLbRtCcv/60LTQj2fOMAylZxYde252ttbvPaxK24l/Pw3y8VS/jhFKjrcouWOkLMG+LqzW/dGLcBf0ItwJ/Qh34c69WNu6CN1/cuTIEe3YsUPXXXedq0sBALvisgp9vz1HqRnZSsvI0u8FpQ7jHSyBGphgUXK8RT3aNZOXh9lFlQIAAOCPmnzovvfee3X55Zerbdu2OnjwoKZOnSoPDw+NGTPG1aUBaOJ25RRreXqW0jKytHZnnsorbfYxXy+zesdFKCWhajU7Ooz9JAAAANxRkw/d+/fv15gxY5Sbm6vIyEj17dtXa9asUWRkpKtLA9DElFortXZXnlKPBe3duSUO49FhfhoYb1FKgkUXxobL18vDRZUCAACgtpp86F64cKGrSwDQhB3IP2oP2d9vz9VRa6V9zMvDpAvahWlgQlXQjo0IcHikFwAAANxfkw/dAHA2WStt2rDnsJYf2wQt41CRw3jzYB+lHFvN7tM+QoE+/DENAADQkPG3OQBwsuyiMqVlZCktI1srt2WrqLTCPmY2See3aaaUBItS4i3q1CKI1WwAAIBGhNANAPXMZjP084ECpaZnKTUjSz/vL3AYDwvw1oCOkUpJsKh/hwiF+nu7qFIAAAA4G6EbAOpBQYlVK7dlKzU9Syu2Ziu3uNxhvGurkGOr2ZHq1jpUHmZWswEAAJoCQjcAnAHDMJSeWaTUjCylpmdp/Z7DshknxoN8PNWvY4SS4y1Kjo+UJcjXdcUCAADAZQjdAFBLxWUV+n57zrGgna3MwlKH8Y7NA+2boCW2bSYvD7OLKgUAAIC7IHQDwEkYhqFdOcVKzai6bHzdrjyVV9rs475eZvWOi7BfNt66mb8LqwUAAIA7InQDwB+UWiu1dleefRO0PbklDuNtwvztz83uFRMmXy8PF1UKAACAhoDQDaDJO5B/tCpkp2dp1Y5cHbVW2se8PEzqFROu5PhIDUywKCYigEd6AQAAoNYI3QCaHGulTev3HLZvgrb10BGH8ahgX6UkRCo53qI+7SMU6MMflQAAADgz/E0SQJOQVVSqFRnZSs3I0rdbc1RUVmEfM5ukxLbNlBxv0cAEixKigljNBgAAQL0gdANolCpthn7en2/fBO2XAwUO42EB3hrQMVIpCRb17xChUH9vF1UKAACAxozQDaDRyC8p18ptOUpNz9KKrdnKKy53GO/WOkTJ8VU7jXdrHSoPM6vZAAAAcC5CN4AGyzAMbfm9yH5v9oa9h2UzTowH+Xiqf8dIJcdX3Z8dGeTjumIBAADQJBG6ATQoR8oq9P32HKVlZCk1PVuZhaUO4/HNg5ScEKmUeIsS2zaTl4fZRZUCAAAAhG4Abs4wDO3MKbY/N3vdrjxZK08sZ/t5eahP+3Alx1uUHB+p1s38XVgtAAAA4IjQDcDtlFortWZnrtIysrU8PUt780ocxtuG+yvlWMi+MDZcvl4eLqoUAAAAODVCNwC3sP9wiVIzspWWnqXvd+So1Gqzj3l7mNUrNsy+CVpsZKALKwUAAABqj9ANwCWslTb9uDdXaRlZWp6epW1ZRxzGo4J9lZJQFbL7tI9QgA9/XAEAAKDh4W+xAM6arKJSfbM5U+9lmPXQhjQdKauwj3mYTUps08y+CVpCVJBMJh7pBQAAgIaN0A3AaSpthn7an6+09CylZmTrlwMFx0bMkioUHuCtAfFVIbt/h0iF+Hu5slwAAACg3hG6AdSr/JJyrdiarbSMbK3Ymq284nKH8a6tgtXKlK/xl1yoxHYRMptZzQYAAEDjRegG8JcYhqHNvxcqLSNbqelZ2rD3sGwnnuilIF9P9e9YtZo9oGOkQn3NWrJkibpHhxK4AQAA0OgRugHU2ZGyCn23LUdpGVXPzj5UWOYwnhAVpAHxkRoYb9H5bZvJy8NsH7NarWe7XAAAAMBlCN0ATsswDO3ILraH7HW78mStPLGc7efloT7tI5SSEKnkeItahfq5sFoAAADAfRC6AdSo1Fqp1Ttz7Zug7c0rcRhvF+5/7JFeFvWMCZOvl4eLKgUAAADcF6EbgN2+vJJjq9nZWrUjR6VWm33M28OsXrFhSom3KCXBopiIABdWCgAAADQMhG6gCbNW2vTD7jz7Jmjbso44jLcI8bWvZveOC1eAD39kAAAAAHXB36CBJiarsFRpW6tC9nfbclRUVmEf8zCblNimmZITIjUwwaL45kEymdhhHAAAADhThG6gkau0Gfppf75S06s2Qfv1QKHDeESgtwZ0tCglIVL92kcqxN/LRZUCAAAAjQ+hG2iE/j97dx7eVJm+D/w+SZN0S9ck3enehB1lLWtbWQRFGfUHisPgis6gM4qOgzoKuIzLOMqMXxW3AWfBfRmVRRFakH1fS9KdFmibpFu6N23O749AZiogFNqe0/b+XFevy5zzJudJeGx79z3nPVX1LdiS657N3pxjQ1VD+9t0DYkORLrRgAyTAYOjAnm/bCIiIiKiLsLQTdQLiKKI7FLHmdlsGw4UV8H13zt6QevthYkp7vtmT0zRQ6/VSFcsEREREVEfwtBN1EPVNbdia64NmWYbMi1WWGub2+03hWs9i6Bd3S8IXkqFRJUSEREREfVdDN1EPYQoisi31Xuuzd5TVAln23+ns31USoxL0iHDZECaUY/IIB8JqyUiIiIiIoChm0jWmpxt2JFfgUyLO2iXVDa22x+v80Oa0b3S+Kj4EGi8lBJVSkRERERE58PQTSQzJZUN7pBttmJ7fgWaW12efWqlAqMTQpBuNCDdZEC8zk/CSomIiIiI6GIYuokk1tLqwt4TlZ5F0PKsde32RwZ6I81kQIbRgLFJofBV839bIiIiIqKegr+9E0nA6mhClsWGTWYrtubZUdfc6tmnVAgYHhvsuaVXSpg/BIG39CIiIiIi6okYuom6QZtLxMGSamRZrNhktuLYaUe7/Tp/NSalGJBu0mNCsh6BPiqJKiUiIiIios7E0E3URarqW7Al1z2bvTnHhuoGp2efIABDooOQfmYRtEGRgVAoOJtNRERERNTbMHQTdRJRFHHstMMzm32wpBqu/97RCwHeXpiYoke60YBJRj10/hrpiiUiIiIiom7B0E10BWqbnNiWZ8cmsxVZFhustc3t9pvCtUg3GZBuNODqfkHwUiokqpSIiIiIiKTA0H3GG2+8gT//+c8oKyvD0KFD8frrr2PUqFFSl0UyI4oi8m11yDS7TxvfU1SJ1v+ZzvZVKzE2UYcMkwFpRj0ig3wkrJaIiIiIiKTG0A3g448/xqJFi7BixQqMHj0ay5cvx7Rp02CxWGAwGKQujyTW2NKGnQUV7ntnW6woqWxstz9B54c0o3sRtFHxIdB4KSWqlIiIiIiI5IahG8Crr76Ke++9F3feeScAYMWKFVizZg3+/ve/Y/HixRJXR1IoqWxwh2yzFdvzK9Dc6vLsU3spMCYhFOlG9/XZcTo/CSslIiIiIiI56/Ohu6WlBfv27cPjjz/u2aZQKDB58mTs2LHjvM9pbm5Gc/N/r911ONy3f3I6nXA6ned9jpTO1iTH2uSipdWFfcVV2JxjR6bFjgJ7fbv9EYHeSEvRYVKKDqkJIfBV//d/HX6uHcN+JLlgL5JcsBdJTtiPJBc9oRcvtTZBFEXx4sN6r9OnTyMqKgrbt29HamqqZ/tjjz2GzZs3Y9euXec8Z+nSpVi2bNk521evXg1fX98urZc6T00LkF0lILtagKVGQHPbf2/ZpYCIhABgQJALA4JFhPu4b/NFREREREQEAA0NDZg7dy5qamoQEBBwwXF9fqb7cjz++ONYtGiR57HD4UBMTAymTp36sx+2VJxOJzZs2IApU6ZApVJJXY5k2lwiDp2sQVaODZtz7MgurW23X+evxoRkHdJTdBiXGIoAn777WXUl9iPJBXuR5IK9SHLCfiS56Am9ePaM54vp86Fbp9NBqVSivLy83fby8nKEh4ef9zkajQYazbn3WFapVLJtCED+9XWFyvoWbMmxIdNixeYcG6ob/nsKiCAAQ6ODkH5mEbRBkYFQKDid3V36Yj+SPLEXSS7YiyQn7EeSCzn34qXW1edDt1qtxvDhw7Fx40bMmjULAOByubBx40Y88MAD0hZHHSaKIo6ddiDT7F5p/EBJNf73AooAby9MMhqQbtRjYooeOv9z/3hCRERERETUWfp86AaARYsWYf78+RgxYgRGjRqF5cuXo76+3rOaOclbbZMTW3PtyLRYkWWxwVrb3G5//4gA90rjJgOuigmCl1IhUaVERERERNTXMHQDmDNnDmw2G55++mmUlZVh2LBhWL9+PcLCwqQujc5DFEXkWevO3NLLhj1FlWh1/Xc621etxPgkHdJNBqQZ9YgI9JGwWiIiIiIi6ssYus944IEHeDq5jDW2tGFHgR2ZZvf12SerGtvtT9D7Id3oDtmj4kOg8VJKVCkREREREdF/MXSTbBVXNLhnsy1W7MivQHOry7NP7aVAakIo0o16pBkNiNP5SVgpERERERHR+TF0k2y0tLqwp6jSswhavq2+3f6oIB+kGfXIMBmQmhgKXzXbl4iIiIiI5I2phSRVVtOErDOz2Vtz7ahvafPsUyoEjIgNRobJgHSTAckGfwgCb+lFREREREQ9B0M3das2l4gDxVWeRdCyS9vfUF7nr/GsND4+WYcAb3nek4+IiIiIiOhSMHRTl6usb8HmHHfI3pJrQ3WD07NPEICh0UHIOLPS+KDIQCgUnM0mIiIiIqLegaGbOp3LJeLYaYdnEbSDJdUQ/3tHLwT6qDAxRY8Mkx4Tk/UI9ddIVywREREREVEXYuimTuFocmJrrh2ZZiuycmyw1Ta3298/IgDpZxZBGxYTBC+lQqJKiYiIiIiIug9DN10WURSRZ63DpjMrje8tqkKr67/T2b5qJcYn6c6cNm5AeKC3hNUSERERERFJg6GbLlljSxu259s9i6Cdqm5stz9B54d0kwEZJgNGxAVD46WUqFIiIiIiIiJ5YOimn1Vc0YBN5nJkWmzYUVCBllaXZ5/aS4HUhFDPImixoX4SVkpERERERCQ/DN3UTkurC3uKKj2njRfY6tvtjwryQbrJfW12aoIOPmrOZhMREREREV0IQzehrKYJWRYrNpmt2JZnR31Lm2efl0LAiLhgpBsNSDcZkGzwhyDwll5ERERERESXgqG7D2ptc+FgSfWZ2Wwbjpc62u3XazVIS3HPZo9L1iHAWyVRpURERERERD0bQ3cfUecEvjp4GlvyKrElx4aaRqdnnyAAQ6ODkHFmEbQBEQFQKDibTUREREREdKUYuvuABz86hO+OKSHuPerZFuSrwqQUPdKNBkxM0SPETy1hhURERERERL0TQ3cfEOyrgggB/cO1uKZ/GNJNegyLCYaSs9lERERERERdiqG7D7hvYjxMbUWY+4tUqFS8PpuIiIiIiKi7KKQugLpeVJAPgjRSV0FERERERNT3MHQTERERERERdRGGbiIiIiIiIqIuwtBNRERERERE1EUYuomIiIiIiIi6CEM3ERERERERURdh6CYiIiIiIiLqIgzdRERERERERF2EoZuIiIiIiIioi3hJXUBvIIoiAMDhcEhcyfk5nU40NDTA4XBApVJJXQ71cexHkgv2IskFe5HkhP1IctETevFs/jubBy+EobsT1NbWAgBiYmIkroSIiIiIiIi6U21tLQIDAy+4XxAvFsvpolwuF06fPg2tVgtBEKQu5xwOhwMxMTEoKSlBQECA1OVQH8d+JLlgL5JcsBdJTtiPJBc9oRdFUURtbS0iIyOhUFz4ym3OdHcChUKB6Ohoqcu4qICAANk2LPU97EeSC/YiyQV7keSE/UhyIfde/LkZ7rO4kBoRERERERFRF2HoJiIiIiIiIuoiDN19gEajwZIlS6DRaKQuhYj9SLLBXiS5YC+SnLAfSS56Uy9yITUiIiIiIiKiLsKZbiIiIiIiIqIuwtBNRERERERE1EUYuomIiIiIiIi6CEM3ERERERERURdh6CYiIiIiIiLqIgzdvcQbb7yBuLg4eHt7Y/To0di9e/fPjv/0009hMpng7e2NwYMHY+3atd1UKfUFHenHd999FxMmTEBwcDCCg4MxefLki/Yv0aXq6PfGsz766CMIgoBZs2Z1bYHUZ3S0F6urq7Fw4UJERERAo9EgJSWFP6up03S0H5cvXw6j0QgfHx/ExMTg4YcfRlNTUzdVS73Vli1bMHPmTERGRkIQBHz11VcXfU5WVhauvvpqaDQaJCUlYdWqVV1eZ2dg6O4FPv74YyxatAhLlizB/v37MXToUEybNg1Wq/W847dv347bbrsNd999Nw4cOIBZs2Zh1qxZOHr0aDdXTr1RR/sxKysLt912GzIzM7Fjxw7ExMRg6tSpOHXqVDdXTr1NR3vxrKKiIjz66KOYMGFCN1VKvV1He7GlpQVTpkxBUVERPvvsM1gsFrz77ruIiorq5sqpN+poP65evRqLFy/GkiVLcPz4cbz//vv4+OOP8cQTT3Rz5dTb1NfXY+jQoXjjjTcuaXxhYSGuu+46pKen4+DBg3jooYdwzz334LvvvuviSjuBSD3eqFGjxIULF3oet7W1iZGRkeILL7xw3vGzZ88Wr7vuunbbRo8eLd53331dWif1DR3tx59qbW0VtVqt+MEHH3RVidRHXE4vtra2imPHjhXfe+89cf78+eKNN97YDZVSb9fRXnzrrbfEhIQEsaWlpbtKpD6ko/24cOFCMSMjo922RYsWiePGjevSOqlvASB++eWXPzvmscceEwcOHNhu25w5c8Rp06Z1YWWdgzPdPVxLSwv27duHyZMne7YpFApMnjwZO3bsOO9zduzY0W48AEybNu2C44ku1eX04081NDTA6XQiJCSkq8qkPuBye/GZZ56BwWDA3Xff3R1lUh9wOb349ddfIzU1FQsXLkRYWBgGDRqEP/3pT2hra+uusqmXupx+HDt2LPbt2+c5Bb2goABr167FjBkzuqVmorN6cobxkroAujJ2ux1tbW0ICwtrtz0sLAxms/m8zykrKzvv+LKysi6rk/qGy+nHn/rDH/6AyMjIc76pEnXE5fTi1q1b8f777+PgwYPdUCH1FZfTiwUFBdi0aRNuv/12rF27Fnl5efjNb34Dp9OJJUuWdEfZ1EtdTj/OnTsXdrsd48ePhyiKaG1txf3338/Ty6nbXSjDOBwONDY2wsfHR6LKLo4z3UQkGy+++CI++ugjfPnll/D29pa6HOpDamtrMW/ePLz77rvQ6XRSl0N9nMvlgsFgwDvvvIPhw4djzpw5ePLJJ7FixQqpS6M+KCsrC3/605/w5ptvYv/+/fjiiy+wZs0aPPvss1KXRtRjcKa7h9PpdFAqlSgvL2+3vby8HOHh4ed9Tnh4eIfGE12qy+nHs1555RW8+OKL+OGHHzBkyJCuLJP6gI72Yn5+PoqKijBz5kzPNpfLBQDw8vKCxWJBYmJi1xZNvdLlfF+MiIiASqWCUqn0bOvfvz/KysrQ0tICtVrdpTVT73U5/fjUU09h3rx5uOeeewAAgwcPRn19PRYsWIAnn3wSCgXn8Kh7XCjDBAQEyHqWG+BMd4+nVqsxfPhwbNy40bPN5XJh48aNSE1NPe9zUlNT240HgA0bNlxwPNGlupx+BICXX34Zzz77LNavX48RI0Z0R6nUy3W0F00mE44cOYKDBw96vm644QbPCqkxMTHdWT71IpfzfXHcuHHIy8vz/OEHAHJychAREcHATVfkcvqxoaHhnGB99g9Coih2XbFEP9GjM4zUK7nRlfvoo49EjUYjrlq1SszOzhYXLFggBgUFiWVlZaIoiuK8efPExYsXe8Zv27ZN9PLyEl955RXx+PHj4pIlS0SVSiUeOXJEqrdAvUhH+/HFF18U1Wq1+Nlnn4mlpaWer9raWqneAvUSHe3Fn+Lq5dRZOtqLxcXFolarFR944AHRYrGI3377rWgwGMTnnntOqrdAvUhH+3HJkiWiVqsVP/zwQ7GgoED8/vvvxcTERHH27NlSvQXqJWpra8UDBw6IBw4cEAGIr776qnjgwAHxxIkToiiK4uLFi8V58+Z5xhcUFIi+vr7i73//e/H48ePiG2+8ISqVSnH9+vVSvYVLxtDdS7z++utiv379RLVaLY4aNUrcuXOnZ9+kSZPE+fPntxv/ySefiCkpKaJarRYHDhworlmzppsrpt6sI/0YGxsrAjjna8mSJd1fOPU6Hf3e+L8YuqkzdbQXt2/fLo4ePVrUaDRiQkKC+Pzzz4utra3dXDX1Vh3pR6fTKS5dulRMTEwUvb29xZiYGPE3v/mNWFVV1f2FU6+SmZl53t8Bz/bf/PnzxUmTJp3znGHDholqtVpMSEgQV65c2e11Xw5BFHleCBEREREREVFX4DXdRERERERERF2EoZuIiIiIiIioizB0ExEREREREXURhm4iIiIiIiKiLsLQTURERERERNRFGLqJiIiIiIiIughDNxEREREREVEXYegmIiIiIiIi6iIM3URERERERERdhKGbiIiIiIiIqIswdBMRERERERF1EYZuIiIiIiIioi7C0E1ERERERETURRi6iYiIiIiIiLoIQzcRERERERFRF2HoJiIiIiIiIuoiDN1EREREREREXYShm4iIZEMQBCxdulTqMkgid9xxB+Li4tptY08QEVFPx9BNRERdatWqVRAE4YJfO3fulLrELnH69GksXboUBw8evKTxx44dw//7f/8PCQkJ8PX1hU6nw8SJE/HNN9906LhVVVXw8vLCJ598csExd9xxR7t/Ay8vL8TExODWW29FdnZ2h45HvdObb76JVatWSV0GEVGv4CV1AURE1Dc888wziI+PP2d7UlKSBNV0vdOnT2PZsmWIi4vDsGHDLjr+xIkTqK2txfz58xEZGYmGhgZ8/vnnuOGGG/D2229jwYIFl3Tc7777DoIgYOrUqT87TqPR4L333gMAtLa2Ij8/HytWrMD69euRnZ2NyMjISzpeV2tsbISXF39d6W5vvvkmdDod7rjjDqlLISLq8fhTjIiIusX06dMxYsQIqcuQrRkzZmDGjBnttj3wwAMYPnw4Xn311UsO3WvXrsW4ceMQFBT0s+O8vLzwy1/+st22MWPG4Prrr8eaNWtw7733dqj+ruLt7S11CURERFeEp5cTEZGsnTp1CnfddRfCwsKg0WgwcOBA/P3vf283JisrC4Ig4JNPPsGyZcsQFRUFrVaLW265BTU1NWhubsZDDz0Eg8EAf39/3HnnnWhubj7nWP/6178wfPhw+Pj4ICQkBLfeeitKSkrajUlLS8OgQYOQnZ2N9PR0+Pr6IioqCi+//HK7ekaOHAkAuPPOOz2ncXf0dF2lUomYmBhUV1df0niXy4X169fjuuuu69BxzgoPDweAc2aWq6ur8dBDDyEmJgYajQZJSUl46aWX4HK5PGOKioogCAJeeeUVvPPOO0hMTIRGo8HIkSOxZ8+ec4711VdfYdCgQfD29sagQYPw5Zdfnremn17TvXTpUgiCgLy8PNxxxx0ICgpCYGAg7rzzTjQ0NLR7bmNjI377299Cp9NBq9XihhtuwKlTpy7pOvHO6KnW1lY8++yzns8iLi4OTzzxxDnj4uLicP311yMrKwsjRoyAj48PBg8ejKysLADAF198gcGDB8Pb2xvDhw/HgQMHzqnXbDbjlltuQUhICLy9vTFixAh8/fXX7cacvdRj27ZtWLRoEfR6Pfz8/PCLX/wCNputXT3Hjh3D5s2bPb2blpb2s58XERFdGGe6iYioW9TU1MBut7fbJggCQkNDL/ic8vJyjBkzBoIg4IEHHoBer8e6detw9913w+Fw4KGHHmo3/oUXXoCPjw8WL16MvLw8vP7661CpVFAoFKiqqsLSpUuxc+dOrFq1CvHx8Xj66ac9z33++efx1FNPYfbs2bjnnntgs9nw+uuvY+LEiThw4EC7meOqqipce+21uOmmmzB79mx89tln+MMf/oDBgwdj+vTp6N+/P5555hk8/fTTWLBgASZMmAAAGDt27EU/p/r6ejQ2NqKmpgZff/011q1bhzlz5lzCJwzs2bMHNpvtnBnzCzn779HW1oaCggL84Q9/QGhoKK6//nrPmIaGBkyaNAmnTp3Cfffdh379+mH79u14/PHHUVpaiuXLl7d7zdWrV6O2thb33XcfBEHAyy+/jJtuugkFBQVQqVQAgO+//x4333wzBgwYgBdeeAEVFRW48847ER0dfUl1A8Ds2bMRHx+PF154Afv378d7770Hg8GAl156yTPmjjvuwCeffIJ58+ZhzJgx2Lx5c4f/IHElPXXPPffggw8+wC233IJHHnkEu3btwgsvvIDjx4+f80eGvLw8zJ07F/fddx9++ctf4pVXXsHMmTOxYsUKPPHEE/jNb37jqWf27NmwWCxQKNxzJ8eOHcO4ceMQFRWFxYsXw8/PD5988glmzZqFzz//HL/4xS/aHevBBx9EcHAwlixZgqKiIixfvhwPPPAAPv74YwDA8uXL8eCDD8Lf3x9PPvkkACAsLKxDnxsREf0PkYiIqAutXLlSBHDeL41G024sAHHJkiWex3fffbcYEREh2u32duNuvfVWMTAwUGxoaBBFURQzMzNFAOKgQYPElpYWz7jbbrtNFARBnD59ervnp6amirGxsZ7HRUVFolKpFJ9//vl2444cOSJ6eXm12z5p0iQRgPiPf/zDs625uVkMDw8Xb775Zs+2PXv2iADElStXXtoHdcZ9993n+XwUCoV4yy23iJWVlZf03Keeeqrd+7qQ+fPnn/ffIyoqSty3b1+7sc8++6zo5+cn5uTktNu+ePFiUalUisXFxaIoimJhYaEIQAwNDW1X73/+8x8RgPjNN994tg0bNkyMiIgQq6urPdu+//57EcA59f+0J5YsWSICEO+66652437xi1+IoaGhnsf79u0TAYgPPfRQu3F33HHHOa95PlfaUwcPHhQBiPfcc0+7cY8++qgIQNy0aZNnW2xsrAhA3L59u2fbd999JwIQfXx8xBMnTni2v/322yIAMTMz07PtmmuuEQcPHiw2NTV5trlcLnHs2LFicnKyZ9vZ/xcnT54sulwuz/aHH35YVCqV7f49Bg4cKE6aNOlnPyMiIro0PL2ciIi6xRtvvIENGza0+1q3bt0Fx4uiiM8//xwzZ86EKIqw2+2er2nTpqGmpgb79+9v95xf/epXntlUABg9ejREUcRdd93Vbtzo0aNRUlKC1tZWAO7Td10uF2bPnt3uOOHh4UhOTkZmZma75/v7+7e7HlqtVmPUqFEoKCi47M/nrIceeggbNmzABx98gOnTp6OtrQ0tLS2X9Ny1a9de8kyut7e359/hu+++w9tvvw1/f3/MmDEDOTk5nnGffvopJkyYgODg4HafzeTJk9HW1oYtW7a0e905c+YgODjY8/jsLP/Zz6a0tBQHDx7E/PnzERgY6Bk3ZcoUDBgw4JJqB4D777+/3eMJEyagoqICDocDALB+/XoA8MwQn/Xggw9e8jGAy++ptWvXAgAWLVrUbtwjjzwCAFizZk277QMGDEBqamq71wOAjIwM9OvX75ztZz/PyspKbNq0CbNnz0Ztba3n36eiogLTpk1Dbm4uTp061e5YCxYsgCAInscTJkxAW1sbTpw4cakfCxERdQBPLyciom4xatSoDi2kZrPZUF1djXfeeQfvvPPOecdYrdZ2j/83nADwhLqYmJhztrtcLtTU1CA0NBS5ubkQRRHJycnnPc7/hi4AiI6ObhdaACA4OBiHDx+++Bu7CJPJBJPJBMAd+KZOnYqZM2di165d5xzzf5WVlWH//v145plnLuk4SqUSkydPbrdtxowZSE5OxuOPP47PP/8cAJCbm4vDhw9Dr9ef93Uu9m9wNoBXVVUBgCfYne+zNhqN5/wh5UJ+7jgBAQE4ceIEFArFOSvmd3S1/MvtqbPH/+nxwsPDERQUdE7A7chxgP9+nnl5eRBFEU899RSeeuqp874Hq9WKqKioCx7rp/9GRETUuRi6iYhIls4u0vXLX/4S8+fPP++YIUOGtHusVCrPO+5C20VR9BxLEASsW7fuvGP9/f079Hqd6ZZbbsF9992HnJwcGI3GC45bt24dvL29kZ6eftnHio6OhtFobDd77XK5MGXKFDz22GPnfU5KSkq7x9312Uh9nEs9/s/9oaQzjnP2/5NHH30U06ZNO+/Ynwb/7uxfIiJi6CYiIpnS6/XQarVoa2s7Z0a2syUmJkIURcTHx58TIi/XpYati2lsbATgXoju56xZswbp6enw8fG5ouO1trairq7O8zgxMRF1dXWd9m8QGxsLwD2D/lMWi6VTjnH2OC6XC4WFhe1m1fPy8jrtGJdy/NzcXPTv39+zvby8HNXV1Z7P4UolJCQAcJ+N0Zn/n3RW/xIREW8ZRkREMqVUKnHzzTfj888/x9GjR8/Z/7+3OLpSN910E5RKJZYtW3bObJ8oiqioqOjwa/r5+QHAJd/u66enaQOA0+nEP/7xD/j4+Pzs9c5OpxMbNmy47FuFnZWTkwOLxYKhQ4d6ts2ePRs7duzAd999d8746upqzzXMlyoiIgLDhg3DBx980O4PCRs2bEB2dvblF/8TZ2d933zzzXbbX3/99U47xs85u4L8T1d3f/XVVwHgiv+tzjIYDEhLS8Pbb7+N0tLSc/Zf7v8nfn5+l9y7RET08zjTTURE3WLdunUwm83nbB87dqxntu6nXnzxRWRmZmL06NG49957MWDAAFRWVmL//v344YcfUFlZ2Sm1JSYm4rnnnsPjjz+OoqIizJo1C1qtFoWFhfjyyy+xYMECPProox1+zaCgIKxYsQJarRZ+fn4YPXr0OdcYn3XffffB4XBg4sSJiIqKQllZGf7973/DbDbjL3/5yzmnuP+vrVu3wuFwdCjItba24l//+hcA9ynKRUVFWLFiBVwuF5YsWeIZ9/vf/x5ff/01rr/+etxxxx0YPnw46uvrceTIEXz22WcoKiqCTqe75OMC7tteXXfddRg/fjzuuusuVFZW4vXXX8fAgQPbzbJfieHDh+Pmm2/G8uXLUVFR4bll2NlF4rp6Jnfo0KGYP38+3nnnHVRXV2PSpEnYvXs3PvjgA8yaNeuKLgP4qTfeeAPjx4/H4MGDce+99yIhIQHl5eXYsWMHTp48iUOHDnX4NYcPH4633noLzz33HJKSkmAwGJCRkdFpNRMR9SUM3URE1C3+9/7F/2vlypUXDN1hYWHYvXs3nnnmGXzxxRd48803ERoaioEDB7a7H3NnWLx4MVJSUvDaa69h2bJlANyLWE2dOhU33HBDh19PpVLhgw8+wOOPP477778fra2tWLly5QVD95w5c/D+++/jrbfeQkVFBbRaLYYPH46XXnrposdfu3YtBgwY0KFTlpubmzFv3jzP44CAAIwcORL//Oc/cc0113i2+/r6YvPmzfjTn/6ETz/9FP/4xz8QEBCAlJQULFu2rN0K5Jfq2muvxaeffoo//vGPePzxx5GYmIiVK1fiP//5D7Kysjr8ehfyj3/8A+Hh4fjwww/x5ZdfYvLkyfj4449hNBrh7e3dace5kPfeew8JCQlYtWoVvvzyS4SHh+Pxxx9v90eNzjBgwADs3bsXy5Ytw6pVq1BRUQGDwYCrrrrqgv/fXczTTz+NEydO4OWXX0ZtbS0mTZrE0E1EdJkEkatmEBER9WgDBgzA9ddfj5dfflnqUmTv4MGDuOqqq/Cvf/0Lt99+u9TlEBFRH8CZbiIioh6spaUFc+bMwezZs6UuRXYaGxvPWVhu+fLlUCgUmDhxokRVERFRX8OZbiIiIuqVli1bhn379iE9PR1eXl5Yt24d1q1bhwULFuDtt9+WujwiIuojGLqJiIioV9qwYQOWLVuG7Oxs1NXVoV+/fpg3bx6efPJJeHnxZD8iIuoeDN1EREREREREXYT36SYiIiIiIiLqIjy3qhO4XC6cPn0aWq22y+/7SURERERERNITRRG1tbWIjIyEQnHh+WyG7k5w+vRpxMTESF0GERERERERdbOSkhJER0dfcD9DdyfQarUA3B92QECAxNWcy+l04vvvv8fUqVOhUqmkLof6OPYjyQV7keSCvUhywn4kuegJvehwOBATE+PJgxfC0N0Jzp5SHhAQINvQ7evri4CAANk2LPUd7EeSC/YiyQV7keSE/Uhy0ZN68WKXGHMhNSIiIiIiIqIuwtBNRERERERE1EUYuomIiIiIiIi6CEM3ERERERERURdh6CYiIiIiIiLqIgzdRERERERERF2EoZuIiIiIiIioizB09wHHS2uR7wBa21xSl0JERERERNSneEldAHW9lduL8OUxL3xQkIWJKQakG/WYlKJHqL9G6tKIiIiIiIh6NYbuPsDfWwVfpYiaxlZ8c+g0vjl0GoIADI0OQrrRgAyTAQMjA6BQCFKXSkRERERE1KswdPcBT19nwlUoQOSgVPyYX4lMsw3ZpQ4cLKnGwZJqvPZDDnT+GqQZ9cgwGTA+WYcAb5XUZRMREREREfV4DN19hFIAhscGY0ySAb+fZkJZTROyLFZkWqzYmmuHva4Zn+07ic/2nYSXQsDw2GBkmAxINxmQbPCHIHAWnIiIiIiIqKMYuvuo8EBv3DqqH24d1Q8trS7sKapEptkdwvNt9dhVWIldhZV4YZ0ZUUE+nlnw1MRQ+KrZNkRERERERJeC6Ymg9lJgXJIO45J0+OP1A1Bc0YDMM7PgO/IrcKq6Ef/eVYx/7yqG2kuBMQmhyDDqkW4yIDbUT+ryiYiIiIiIZIuhm87RL9QX88fGYf7YODS2tGFHgR2bzFZkmm04Vd2ILTk2bMmxYek32UjQ+SHdZEC60YCR8cHQeCmlLp+IiIiIiEg2GLrpZ/molcgwhSHDFAZRFJFnrXPPgptt2FNUiQJ7PQq2FuL9rYXwVSsxLkmHDJMBaUY9IgJ9pC6fiIiIiIhIUgzddMkEQUBymBbJYVosmJgIR5MT23LtZ05Ft8FW24wN2eXYkF0OADCFaz2LsV0VEwQvpULid0BERERERNS9GLrpsgV4qzB9cASmD46AyyUiu9ThWYztQEk1zGW1MJfV4s2sfAR4e2FiinsxtkkpeoT6a6Qun4iIiIiIqMsxdFOnUCgEDIoKxKCoQDx4TTIq61uwJceGTIsVm3NsqG5w4tvDpfj2cCkEARgSHYQMowHpJj0GRQZCoeAtyYiIiIiIqPdh6KYuEeKnxqyrojDrqii0uUQcLKnCJrMVWRYbjp124FBJNQ6VVOO1H3Kg89cgzahHutGA8ck6BPqopC6fiIiIiIioUzB0U5dTKgQMjw3B8NgQ/H6aCeWOJmSdWYxta54d9rpmfLbvJD7bd/LM2GD3teBGA1LC/CEInAUnIiIiIqKeiaGbul1YgDfmjOyHOSP7oaXVhb1Flci0WLHJbEW+rR67Cyuxu7ASL64zIyrIxzMLPjYpFL5qtiwREREREfUcTDAkKbWXAmOTdBibpMOT1w1AcUUDsnKsyDRbsT2/AqeqG/HvXcX4965iqL0UGJMQivQzITxO5yd1+URERERERD+LoZtkpV+oL36VGodfpcahsaUNOwsqPLPgJ6sasSXHhi05Niz7JhsJOj+knVmMbVR8CDReSqnLJyIiIiIiaoehm2TLR61E+pn7fC+7QUSetQ5ZFveK6LsLK1Fgr0eBvRB/31YIX7US45J0SDcakGbUIzLIR+ryiYiIiIiIGLqpZxAEAclhWiSHaXHvxATUNjmxLc+OTLM7hFtrm7EhuxwbsssBAKZwrTuwGw24ul8QvJQKid8BERERERH1Rb06dL/wwgv44osvYDab4ePjg7Fjx+Kll16C0Wj0jElLS8PmzZvbPe++++7DihUrurtc6gCttwrXDorAtYMiIIoijp12INNsRVaODQeKq2Auq4W5rBZvZeUjwNsLE1Pc14FPMuqh89dIXT4REREREfURvTp0b968GQsXLsTIkSPR2tqKJ554AlOnTkV2djb8/P67CNe9996LZ555xvPY19dXinLpMgmCgEFRgRgUFYgHr0lGVX0LtuTakGm2YnOODVUNTnx7uBTfHi6FIABDooM8i7ENjgqEQsFbkhERERERUdfo1aF7/fr17R6vWrUKBoMB+/btw8SJEz3bfX19ER4efsmv29zcjObmZs9jh8MBAHA6nXA6nVdYdec7W5Mca+sK/moBMwYaMGOgAW0uEYdP1iArx47NuTYcO12LQyXVOFRSjeU/5CLUT42JKTqkJeswPikUAT4qqcvv9fpaP5J8sRdJLtiLJCfsR5KLntCLl1qbIIqi2MW1yEZeXh6Sk5Nx5MgRDBo0CID79PJjx45BFEWEh4dj5syZeOqpp352tnvp0qVYtmzZOdtXr17NWXKZq2kBjlcLyK4SYK4R0Nz231luBUTEa4EBwS4MCBYR4QMInAQnIiIiIqLzaGhowNy5c1FTU4OAgIALjuszodvlcuGGG25AdXU1tm7d6tn+zjvvIDY2FpGRkTh8+DD+8Ic/YNSoUfjiiy8u+Frnm+mOiYmB3W7/2Q9bKk6nExs2bMCUKVOgUnEm96yWVhf2F1cjK8eGrBw78m317fZHBHpj0plZ8NTEEPiqe/WJId2G/UhywV4kuWAvkpywH0kuekIvOhwO6HS6i4buPpMiFi5ciKNHj7YL3ACwYMECz38PHjwYERERuOaaa5Cfn4/ExMTzvpZGo4FGc+5iXCqVSrYNAci/vu6mUgETjGGYYAzDUwBKKhuQabEiy2LDtjw7Smua8NGek/hoz0molQqMTghButGADJMBcTq/i74+/Tz2I8kFe5Hkgr1IcsJ+JLmQcy9eal19InQ/8MAD+Pbbb7FlyxZER0f/7NjRo0cDcJ+KfqHQTb1TTIgvfpUah1+lxqHJ2YYdBRXIMluxyWJFSWUjfsy148dcO575NhvxOj+kGfXIMBkwKj4EGi+l1OUTEREREZEM9erQLYoiHnzwQXz55ZfIyspCfHz8RZ9z8OBBAEBEREQXV0dy5q1SIt3ovs/3UlFEvq0eWRYrNpmt2FNUiUJ7PQrt9Vi5rQi+aiXGJuqQbnKviB4Z5CN1+UREREREJBO9OnQvXLgQq1evxn/+8x9otVqUlZUBAAIDA+Hj44P8/HysXr0aM2bMQGhoKA4fPoyHH34YEydOxJAhQySunuRCEAQkGfyRZPDHPRMSUNvkxLa8CmSarci0WGGtbcYPx8vxw/FyAIApXIs0owHpRj2GxwbDS6mQ+B0QEREREZFUenXofuuttwC4Vyj/XytXrsQdd9wBtVqNH374AcuXL0d9fT1iYmJw8803449//KME1VJPofVW4dpB4bh2UDhEUUR2qQNZFhs2ma04UFwFc1ktzGW1WLE5H1pvL0xMcc+Apxn10PmfuxYAERERERH1Xr06dF9sYfaYmBhs3ry5m6qh3kgQBAyMDMTAyEAsTE9CVX0LtuTakGm2YnOODVUNTqw5XIo1h0sBAEOjA92z4CYDhkQFQqHgPcmIiIiIiHqzXh26ibpbsJ8aNw6Lwo3DotDmEnHoZLXnNPSjpxw4dLIGh07W4K8bcxHqp8Yko3sWfGKyHoG+8lyVkYiIiIiILh9DN1EXUSoEXN0vGFf3C8YjU42wOpqQleOeBf8x146K+hZ8sf8Uvth/CkqFgOH9gpFmcq+IbgzTQhA4C05ERERE1NMxdBN1E0OAN2aPiMHsETFoaXVh34kqZFqsyDRbkWutw+6iSuwuqsTL6y2ICPRG2pl7go9NDIWfhv+rEhERERH1RPxNnkgCai8FUhNDkZoYiidm9EdJZQOyLFZkWmzYnm9HaU0TPtxdjA93F0OtVGB0QognhMfr/KQun4iIiIiILhFDN5EMxIT4Yl5qHOalxqHJ2YYdBRXIMluxyWJFSWUjfsy148dcO579Nhtxob6eAD4qPgTeKqXU5RMRERER0QUwdBPJjLdKiXSjAelGA5aKIgrs9Z7F2HYXVqKoogGrthdh1fYi+KiUGJcUinSTAWlGA6KCfKQun4iIiIiI/gdDN5GMCYKARL0/EvX+uGdCAuqaW7E1137mVHQryh3N+OG4FT8ctwIAjGFa92JsRgOujg2GSqmQ+B0QEREREfVtDN1EPYi/xgvXDgrHtYPCIYoisksdyLK4V0TfX1wFS3ktLOW1eHtzAbTeXpiYrEe6yYBJKXrotRqpyyciIiIi6nMYuol6KEEQMDAyEAMjA7EwPQnVDS3YfOaWZJtzbKhqcGLNkVKsOVIKABgSHeg+bd1kwJCoQCgUvCUZEREREVFXY+gm6iWCfNW4cVgUbhwWhTaXiEMnq5Fldq+IfuRUDQ6fdH/9dWMuQv3UmJTingWfmKxHoK9K6vKJiIiIiHolhm6iXkipEHB1v2Bc3S8Yi6YaYXU0ISvHhiyLFT/m2FFR34IvDpzCFwdOnRkbhHSTe/E2U7gWgsBZcCIiIiKizsDQTdQHGAK8MXtEDGaPiIGzzYW9RVWexdhyyuuwp6gKe4qq8PJ6CyICvZFmNCDdqMe4JB38NPw2QURERER0ufjbNFEfo1IqkJoYitTEUDw+oz9OVjUg02JDltmKbfl2lNY04cPdxfhwdzHUSgVGxYcgzahHhsmAeJ0fZ8GJiIiIiDqAoZuoj4sO9sW8MbGYNyYWTc427CyoOHNfcBuKKxuwNc+OrXl2PLfmOGJDfZFuNCDNqMeYhFB4q5RSl09EREREJGsM3UTk4a1SIs1oQJrRgKWiiAJ7PTLNVmRZbNhVWIETFQ1Ytb0Iq7YXwVulwLhEHdJM7lPRo4N9pS6fiIiIiEh2GLqJ6LwEQUCi3h+Jen/cMyEBdc2t2JZnd18LbrahzNGEjWYrNpqtAICUMP8zs+AGjIgLhkqpkPgdEBERERFJj6GbiC6Jv8YL0waGY9rAcIiiiOOltci0WJFlsWLfiSrklNchp7wOb28pgFbjhQkpujOz5noYtN5Sl09EREREJAmGbiLqMEEQMCAyAAMiA7AwPQnVDS3YkmtHltmKrBwbKutbsPZIGdYeKQMADI4KRLpRjzSTAQPC/CSunoiIiIio+zB0E9EVC/JV44ahkbhhaCTaXCIOn6x2r4huseLwyRocOeX++tumPAT7qpDoq0Db4VJk9A9HkK9a6vKJiIiIiLoMQzcRdSqlQsBV/YJxVb9gLJqSAmttEzZbbMiy2LAlx4aqBif2Niiw99MjUAhHcHW/YKSb3KehD4gI4C3JiIiIiKhXYegmoi5l0Hrj/42Iwf8bEQNnmwu78m1YuX43ilu1yLXWY++JKuw9UYU/f2dBWIDGsxjb+GQd/DX8FkVEREREPRt/oyWibqNSKjA6PgQVsS7MmDEO5XVOZJ05DX1bXgXKHc34aE8JPtpTApVSwKj4EE8IT9T7cRaciIiIiHochm4ikkx0sC9+OSYWvxwTiyZnG3YVViLTbEWmxYoTFQ3YlleBbXkVeG7NcfQL8fUsxpaaEApvlVLq8omIiIiILoqhm4hkwVulxKQUPSal6LFEHIACez2yLDZkmq3YVViB4soGfLDjBD7YcQLeKgXGJurcIdxoQEyIr9TlExERERGdF0M3EcmOIAhI1PsjUe+Pu8fHo765Fdvy7Mg8E8LLHE3YZLZik9kK4BiSDf6exdhGxoVApVRI/RaIiIiIiAAwdBNRD+Cn8cLUgeGYOjAcoijCXFaLTWYrsixW7DtRhVxrHXKtdXhnSwG0Gi+MT9aduRZcD0OAt9TlExEREVEfxtBNRD2KIAjoHxGA/hEBWJiehJoGJ7bkumfAs3JsqKxvwbqjZVh3tAwAMCgqAOlGA9JNBgyNDoJSwcXYiIiIiKj7MHQTUY8W6KvCzKGRmDk0Ei6XiMOnajyLsR0+WYOjpxw4esqB1zflIdhXhUkpeqSbDJiYrEewn1rq8omIiIiol2PoJqJeQ6EQMCwmCMNigvDwlBTYapuxOcc9C74l14aqBie+OngaXx08DYUAXNUvGOlGdwgfEBHAW5IRERERUadj6CaiXkuv1eCW4dG4ZXg0nG0u7D9RhU0WK7LMNljKa7HvRBX2najCK9/nICxAg7QU92no45N18Nfw2yMRERERXTn+VklEfYJKqcDohFCMTgjF49P741R1o/s6cIsV2/IqUO5oxsd7S/Dx3hKolAJGxoV4rgVP1PtxFpyIiIiILgtDNxH1SVFBPvjlmFj8ckwsmpxt2F1YiU1nrgU/UdGA7fkV2J5fgefXHkdMiI8ngKcmhMJbpZS6fCIiIiLqIWR5M9tnnnkGDQ0N52xvbGzEM888c8mv88ILL2DkyJHQarUwGAyYNWsWLBZLuzFNTU1YuHAhQkND4e/vj5tvvhnl5eVX/B6IqOfwVikxMUWPpTcMxObfpyPz0TQ8ff0ATEjWQa1UoKSyEf/YcQJ3rtyDocu+x50rd+OfO4pQUnnu9ykiIiIiov8ly9C9bNky1NXVnbO9oaEBy5Ytu+TX2bx5MxYuXIidO3diw4YNcDqdmDp1Kurr6z1jHn74YXzzzTf49NNPsXnzZpw+fRo33XRTp7wPIuqZ4nV+uGt8PP5592gceHoK3v3VCNw2qh8iAr3R3OpCpsWGp/5zDBNezsTkVzfj+TXZ2J5vR0urS+rSiYiIiEhmZHl6uSiK571+8tChQwgJCbnk11m/fn27x6tWrYLBYMC+ffswceJE1NTU4P3338fq1auRkZEBAFi5ciX69++PnTt3YsyYMed93ebmZjQ3N3seOxwOAIDT6YTT6bzk+rrL2ZrkWBv1PT2tH9UKIC05BGnJIRCvNyKnvA5ZOXZk5dhwoKQGedY65Fnr8O6PhfDTKDEuMRRpKXpMStHBoNVIXT79jJ7Wi9R7sRdJTtiPJBc9oRcvtTZBFEWxi2u5ZMHBwRAEATU1NQgIaH/7nra2NtTV1eH+++/HG2+8cVmvn5eXh+TkZBw5cgSDBg3Cpk2bcM0116CqqgpBQUGecbGxsXjooYfw8MMPn/d1li5det4Z99WrV8PX1/eyaiOinqehFbBUCzhWLeB4lYC61vZ/LIz2EzEgSMSAYBdi/QEF12IjIiIi6jUaGhowd+5cT369EFmF7g8++ACiKOKuu+7C8uXLERgY6NmnVqsRFxeH1NTUy3ptl8uFG264AdXV1di6dSsAd0i+8847281aA8CoUaOQnp6Ol1566byvdb6Z7piYGNjt9p/9sKXidDqxYcMGTJkyBSqVSupyqI/rrf3ocok4etqBrBwbNufYcfiUo93+IB8VJiS7Z8EnJIci2FctUaV0Vm/tRep52IskJ+xHkoue0IsOhwM6ne6ioVtWp5fPnz8fABAfH4+xY8d26oe7cOFCHD161BO4r4RGo4FGc+5poyqVSrYNAci/PupbemM/Do/XYXi8Do9MA2y1zdicY0OmxYotOTZUNzrxzeEyfHO4DAoBGBYThAyTAWlGAwZGBvCWZBLqjb1IPRN7keSE/UhyIedevNS6ZBW6z5o0aRJcLhdycnJgtVrhcrVfnGjixIkder0HHngA3377LbZs2YLo6GjP9vDwcLS0tKC6urrd6eXl5eUIDw+/ovdARH2bXqvBLcOjccvwaLS2ubC/uBqbztwX3FxWi/3F1dhfXI1Xvs+BQatBmlGPDJMB45J00HrL8wcLEREREXWcLEP3zp07MXfuXJw4cQI/PftdEAS0tbVd0uuIoogHH3wQX375JbKyshAfH99u//Dhw6FSqbBx40bcfPPNAACLxYLi4uLLPo2diOinvJQKjIoPwaj4ECyebsLp6kZkWqzINNuwLc8Oa20zPtl7Ep/sPQkvhYCRcSHIMBmQbtIjUe/PWXAiIiKiHkyWofv+++/HiBEjsGbNGkRERFz2L5wLFy7E6tWr8Z///AdarRZlZWUAgMDAQPj4+CAwMBB33303Fi1ahJCQEAQEBODBBx9EamrqBVcuJyK6UpFBPrh9dCxuHx2LJmcbdhdWItNiRZbFhkJ7PXYUVGBHQQWeX3sc0cE+SDcakGEyYExCKHzUSqnLJyIiIqIOkGXozs3NxWeffYakpKQrep233noLAJCWltZu+8qVK3HHHXcAAF577TUoFArcfPPNaG5uxrRp0/Dmm29e0XGJiC6Vt0qJiSl6TEzRY8lMoNBej0yzFZkWK3YVVOJkVSP+ufME/rnzBDReCqQmhrpnwY0GxITwbglEREREcifL0D169Gjk5eVdcei+lIXZvb298cYbb1z2bciIiDpTvM4P8ePjcdf4eNQ3t2J7fsWZU9GtKK1pQpbFhiyLDcAxJOr9PLPgI+JCoPZSSF0+EREREf2ELEP3gw8+iEceeQRlZWUYPHjwOavCDRkyRKLKiIi6j5/GC1MGhGHKgDCIoghLeS0yze4V0fedqEK+rR75tkK8t7UQfmolxifrPCuihwV4S10+EREREUGmofvsomZ33XWXZ5sgCBBFsUMLqRER9RaCIMAUHgBTeAB+nZaImkYnfsy1YZPZfUsye10LvjtWju+OlQMABkQEeBZjGxYTDKWCi7ERERERSUGWobuwsFDqEoiIZC3QR4Xrh0Ti+iGRcLlEHDlV4z4N3WLD4ZPVyC51ILvUgf/LzEOQrwoTk923JJuYokeIn1rq8omIiIj6DFmG7tjYWKlLICLqMRQKAUNjgjA0JggPTU6Bva4Zmy3u09C35NhQ3eDE14dO4+tDpyEIwLCYIGQYDUg3GTAgIgAKzoITERERdRlZhm4A+Oc//4kVK1agsLAQO3bsQGxsLJYvX474+HjceOONUpdHRCRbOn8Nbh4ejZuHR6O1zYX9xdWexdjMZbU4UFyNA8XV+MuGHOi1GqQb9Ug3GjAuWYcAb9XFD0BEREREl0yWofutt97C008/jYceegjPP/+85xruoKAgLF++nKGbiOgSeSkVGBUfglHxIfjDtSacrm5E1plZ8G15dthqm/HJ3pP4ZO9JeCkEjIwLQbrJHcKTDP4QBM6CExEREV0JWYbu119/He+++y5mzZqFF1980bN9xIgRePTRRyWsjIioZ4sM8sHc0f0wd3Q/NLe2YXdhJTaZrciy2FBor8eOggrsKKjAn9aaER3sg3SjezG21AQdfNRKqcsnIiIi6nFkGboLCwtx1VVXnbNdo9Ggvr5egoqIiHofjZcSE5L1mJCsx5KZQKG9HlkWKzaZrdhVUImTVY34584T+OfOE9B4KZCaGOoO4UYD+oX6Sl0+ERERUY8gy9AdHx+PgwcPnrOg2vr169G/f3+JqiIi6t3idX6I18XjznHxaGhpxfa8Cs+14KdrmpBlsSHLYsMSHEOi3u/MLLgBI+NCoPZSSF0+ERERkSzJMnQvWrQICxcuRFNTE0RRxO7du/Hhhx/ihRdewHvvvSd1eUREvZ6v2guTB4Rh8oAwiKKInPI6TwDfe6IK+bZ65NsK8d7WQviplRifrEO60YA0owHhgd5Sl09EREQkG7IM3ffccw98fHzwxz/+EQ0NDZg7dy4iIyPx17/+FbfeeqvU5RER9SmCIMAYroUxXIv7JyWiptGJbXl2z7Xg9rpmfHesHN8dKwcADIgI8CzGdlW/YCh5SzIiIiLqw2QZugHg9ttvx+23346GhgbU1dXBYDBIXRIREQEI9FFhxuAIzBgcAZdLxNHTNZ4V0Q+WVCO71IHsUgfeyMxHkK8KE5P1SDfpMSnFgBA/tdTlExEREXUr2Ybus3x9feHrywV7iIjkSKEQMCQ6CEOig/Dba5JRUdeMLbk2ZJpt2JxjQ3WDE18fOo2vD52GIADDYoI8i7ENjAyAgrPgRERE1MvJMnRXVFTg6aefRmZmJqxWK1wuV7v9lZWVElVGREQ/J9Rfg19cFY1fXBWN1jYXDpZUe05Dzy514EBxNQ4UV+PVDTnQazVIS9Ej3WTA+GQdArxVUpdPRERE1OlkGbrnzZuHvLw83H333QgLC4MgcCaEiKin8VIqMCIuBCPiQvDYtSaU1TQhy2JFpsWKrbl22Gqb8em+k/h030l4KQSMiAtGutGADJMBSQZ/fu8nIiKiXkGWofvHH3/E1q1bMXToUKlLISKiThIe6I1bR/XDraP6obm1DXuLqpBptmKTxYoCWz12FlRiZ0ElXlhnRlSQj2cxtrGJOviolVKXT0RERHRZZBm6TSYTGhsbpS6DiIi6iMZLiXFJOoxL0uGP1w/AiYp6ZFls2GS2YkdBBU5VN+JfO4vxr53FUHspkJoQinSjHhmmMPQL5TofRERE1HPIMnS/+eabWLx4MZ5++mkMGjQIKlX76/wCAgIkqoyIiLpCbKgf5o/1w/yxcWhsacOOAjsyze4Qfqq6EZtz3AuzLf0mGwl6P89p6CPjQqD2UkhdPhEREdEFyTJ0BwUFweFwICMjo912URQhCALa2tokqoyIiLqaj1qJDFMYMkxheEYUkWetwyaz+1rwvUVVKLDVo8BWiPe3FsJP7Z4xTze5V0QPD/SWunwiIiKidmQZum+//XaoVCqsXr2aC6kREfVhgiAgOUyL5DAt7puUCEeTE9ty7e4V0XNssNU24/vscnyfXQ4A6B8RgHSje0X0q2KC4KXkLDgRERFJS5ah++jRozhw4ACMRqPUpRARkYwEeKswfXAEpg+OgMslIrvU4VmM7WBJNY6XOnC81IE3s/IR6KPCxBQ90o16TErRI9RfI3X5RERE1AfJMnSPGDECJSUlDN1ERHRBCoWAQVGBGBQViAevSUZlfQu25LivA9+cY0NNoxPfHDqNbw6dhiAAQ6ODPNeCD4zk2iBERETUPWQZuh988EH87ne/w+9//3sMHjz4nIXUhgwZIlFlREQkVyF+asy6KgqzropCa5sLh05Wu68FN9uQXerAwZJqHCypxms/5EDnr8HE5FAE1AuY0OREyE9+zhARERF1FlmG7jlz5gAA7rrrLs82QRC4kBoREV0SL6UCw2NDMDw2BL+fZkJZTRM251ixyWzF1lw77HXN+OLAaQBK/OuFLAyPDUa6yT0Lnmzw51oiRERE1GlkGboLCwulLoGIiHqR8EBvzBnZD3NG9kNLqwt7iyrxQ3YZ1hwoQnkjsKuwErsKK/HiOjOignyQZtQjw2RAamIofNWy/FFJREREPYQsf5OIjY2VugQiIuql1F4KjE3SYWRsIIaK+Rg0Jg1b86uwyWzFzoIKnKpuxL93FePfu4qh9lJgTEIo0s+E8NhQP6nLJyIioh5GlqEbAPLz87F8+XIcP34cADBgwAD87ne/Q2JiosSVERFRb9IvxBfzwwIxf2wcGlvasKPAjkyze0G2U9WN2JJjw5YcG5Z9k40EnR/SzizGNjI+GBovpdTlExERkczJMnR/9913uOGGGzBs2DCMGzcOALBt2zYMHDgQ33zzDaZMmSJxhURE1Bv5qJXIMIUhwxSGZ0QR+bY6z2Jse4oqUWCvR4G9EH/fVghftRLjknTIMBmQZtQjItBH6vKJiIhIhmQZuhcvXoyHH34YL7744jnb//CHPzB0ExFRlxMEAUkGLZIMWiyYmIjaJie25tqRabEi02KDrbYZG7LLsSG7HABgCtd6FmO7KiYIXkqFxO+AiIiI5ECWofv48eP45JNPztl+1113Yfny5d1fEBER9XlabxWmD47A9MERcLlEZJc6kGm2ItNixYGSapjLamEuq8VbWfkI8PbCxBT3deCTUvQI9ddIXT4RERFJRJahW6/X4+DBg0hOTm63/eDBgzAYDBJVRURE5KZQCBgUFYhBUYF48JpkVNa3YEuODZkWKzbn2FDd4MS3h0vx7eFSCAIwJDoIGUYD0k16DIoMhELBW5IRERH1FbIM3ffeey8WLFiAgoICjB07FoD7mu6XXnoJixYtkrg6IiKi9kL81Jh1VRRmXRWFNpeIgyVVyDS7Q/ix0w4cKqnGoZJqvPZDDnT+GqQZ9Ug3GjA+WYdAH5XU5RMREVEXkmXofuqpp6DVavGXv/wFjz/+OAAgMjISS5cuxW9/+9sOvdaWLVvw5z//Gfv27UNpaSm+/PJLzJo1y7P/jjvuwAcffNDuOdOmTcP69euv+H0QEVHfo1QIGB4bguGxIXh0mhHljiZkWazYZLZiW14F7HXN+GzfSXy27+SZscHIMBmQbjQgJcwfgsBZcCIiot5ElqFbEAQ8/PDDePjhh1FbWwsA0Gq1l/Va9fX1GDp0KO666y7cdNNN5x1z7bXXYuXKlZ7HGg2vvSMios4RFuCNOSP7Yc7IfmhpdWFvUaVnMbY8ax12F1Zid2ElXlxnRlSQj2cWfGxSKHzVsvwxTURERB0g+5/mlxu2z5o+fTqmT5/+s2M0Gg3Cw8Ov6DhEREQXo/ZSYGySDmOTdHjyOqCkssEdwM1WbM+vwKnqRvx7VzH+vasYai8FxiSEIv1MCI/T+UldPhEREV0GWYbuiooKPP3008jMzITVaoXL5Wq3v7KyslOPl5WVBYPBgODgYGRkZOC5555DaGjoBcc3NzejubnZ89jhcAAAnE4nnE5np9bWGc7WJMfaqO9hP5JcyKEXw7Uq3DYiCreNiEKTsw07CyuxOceOLIsNJ6ubsCXHhi05Niz7Jhvxob6YlKLDpBQ9RsYFQ+PFW5L1FnLoRaKz2I8kFz2hFy+1NkEURbGLa+mwGTNmIC8vD3fffTfCwsLOub5t/vz5l/W6giCcc033Rx99BF9fX8THxyM/Px9PPPEE/P39sWPHDiiVyvO+ztKlS7Fs2bJztq9evRq+vr6XVRsREdFZogiUNwLZ1QKyqwTk1wpwif/9WahWiDAGihgQLKJ/kIhgXhVFRETU7RoaGjB37lzU1NQgICDgguNkGbq1Wi22bt2KoUOHdurrni90/1RBQQESExPxww8/4JprrjnvmPPNdMfExMBut//shy0Vp9OJDRs2YMqUKVCpuEouSYv9SHLRk3qxtqkV2/MrkJVjx5ZcO6y1ze32m8L8MSlFj0kpOlwVEwgvJWfBe5Ke1IvU+7EfSS56Qi86HA7odLqLhm5Znl5uMpnQ2NgoybETEhKg0+mQl5d3wdCt0WjOu9iaSqWSbUMA8q+P+hb2I8lFT+jFEJUK1w+LxvXDoiGKIo6ddiDrzGJsB4qrYC6vg7m8Dm//WIgAby9MTHFfBz7JqIfOn9PgPUVP6EXqO9iPJBdy7sVLrUuWofvNN9/E4sWL8fTTT2PQoEHnvJmunE0+efIkKioqEBER0WXHICIiulyCIGBQVCAGRQXigYxkVNW3YEuuDZlmKzbn2FDV4MS3h0vx7eFSCAIwJDrIsxjb4KhAKBS8JRkREVF3kmXoDgoKgsPhQEZGRrvtoihCEAS0tbVd8mvV1dUhLy/P87iwsBAHDx5ESEgIQkJCsGzZMtx8880IDw9Hfn4+HnvsMSQlJWHatGmd9n6IiIi6SrCfGjcOi8KNw6LQ5hJxsKT6zCy4FUdPOXCopBqHSqqx/Idc6PzVmJRiQLpJjwnJegT6yHPmgIiIqDeRZei+/fbboVKpsHr16vMupNYRe/fuRXp6uufxokWLALgXY3vrrbdw+PBhfPDBB6iurkZkZCSmTp2KZ599lvfqJiKiHkepEDA8NhjDY4PxyFQjyh1N2GyxIdNixY+5dtjrWvD5/pP4fP9Jz9h0ozuEG8O0V/TzloiIiM5PlqH76NGjOHDgAIxG4xW/VlpaGn5urbjvvvvuio9BREQkR2EB3pg9MgazR8agpdWFvUWVyMqxYZPZijxrHXYXVmJ3YSVeWm9GZKA30kwGpBsNGJsYCj+NLH9FICIi6nFk+RN1xIgRKCkp6ZTQTURERIDaS4GxSTqMTdLhiRn9UVLZ4FmMbVueHadrmrB6VzFW7yqGWqnA6ISQM7PgBsTr/KQun4iIqMeSZeh+8MEH8bvf/Q6///3vMXjw4HMWUhsyZIhElREREfUOMSG+mJcah3mpcWhytmFHQQWyzFZsslhRUtmIH3Pt+DHXjme+zUa8zg9pZxZjG50QAo2XUuryiYiIegxZhu45c+YAAO666y7PNkEQLmshNSIiIvp53iqle1bbaMBSUUS+rR5ZFis2ma3YU1SJQns9Cu31WLmtCL5qJcYm6pBucofwyCAfqcsnIiKSNVmG7sLCQqlLICIi6pMEQUCSwR9JBn/cMyEBtU1ObMurQKbZvSK6tbYZPxwvxw/HywEApnAt0owGpBv1GB4bDC+lQuJ3QEREJC+yDN2xsbFSl0BEREQAtN4qXDsoHNcOCocoijh22oHNZxZjO1BcBXNZLcxltVixOR9aby9MTHHPgKcZ9dD5804gREREsgzdREREJD+CIGBQVCAGRQViYXoSqupbsCXXhkyzFZtzbKhqcGLN4VKsOVwKABgaHYg0owEZJgMGRwVCoeAtyYiIqO9h6CYiIqLLEuynxo3DonDjsCi0uUQcOlntOQ396CkHDp2swaGTNfjrxlyE+qkx6cxibBOT9Qj0VV38AERERL0AQzcRERFdMaVCwNX9gnF1v2A8MtUIq6MJWTnuWfAfc+2oqG/BF/tP4Yv9p6BUCBjeLxhpJj0yTAYYw7QQBM6CExFR78TQTURERJ3OEOCN2SNiMHtEDFpaXdh3ogqZZ1ZEz7PWYXdRJXYXVeLl9RZEBHp7TkMfmxgKPw1/PSEiot6DP9WIiIioS6m9FEhNDEVqYiiemNEfJZUNnlnw7fl2lNY04cPdxfhwdzHUSgVGJ4R4Qni8zk/q8omIiK6ILEN3cHDweU8zEwQB3t7eSEpKwh133IE777xTguqIiIjoSsSE+GLemFjMGxOLJmcbdha4b0m2yWJFSWUjfsy148dcO579Nhtxob6eAD4qPgTeKqXU5RMREXWILEP3008/jeeffx7Tp0/HqFGjAAC7d+/G+vXrsXDhQhQWFuLXv/41Wltbce+990pcLREREV0ub5USaUYD0owGLBVFFNjrPYux7S6sRFFFA1ZtL8Kq7UXwUSkxLinUfV9wkwFRQT5Sl09ERHRRsgzdW7duxXPPPYf777+/3fa3334b33//PT7//HMMGTIEf/vb3xi6iYiIeglBEJCo90ei3h/3TEhAXXMrtuXZPSG83NGMH45b8cNxKwDAGKZFusmAdKMeV8cGQ6VUSPwOiIiIziXL0P3dd9/hpZdeOmf7Nddcg0ceeQQAMGPGDCxevLi7SyMiIqJu4q/xwrSB4Zg2MByiKOJ4aS0yLVZkmq3YX1wFS3ktLOW1WLE5H1pvL0xM1iPdZMCkFD30Wo3U5RMREQGQaegOCQnBN998g4cffrjd9m+++QYhISEAgPr6emi1WinKIyIiom4mCAIGRAZgQGQAFqYnobqhBVty3bPgm3NsqKxvwZojpVhzpBQAMCQ6EOlnTkMfEhUIhYK3JCMiImnIMnQ/9dRT+PWvf43MzEzPNd179uzB2rVrsWLFCgDAhg0bMGnSJCnLJCIiIokE+apxw9BI3DA0Em0uEYdPVp85Dd2GI6dqcPik++uvG3MR6qfGJKMe6UYDJibrEeirkrp8IiLqQ2QZuu+9914MGDAA//d//4cvvvgCAGA0GrF582aMHTsWADynmRMREVHfplQIuKpfMK7qF4xFU42w1jZhs8WGTIsVP+bYUVHfgi/2n8IX+09BqRBwdb+gM9eCG2AK1573jilERESdRZahGwDGjRuHcePGSV0GERER9TAGrTf+34gY/L8RMXC2ubC3qApZFvdibDnlddhTVIU9RVV4eb0FEYHe7tXQjXqMS9LBTyPbX42IiKiHku1PFpfLhby8PFitVrhcrnb7Jk6cKFFVRERE1JOolAqkJoYiNTEUj8/oj5NVDci02JBltmJbvh2lNU34cHcxPtxdDLVSgVHxIZ4V0eN1fpwFJyKiKybL0L1z507MnTsXJ06cgCiK7fYJgoC2tjaJKiMiIqKeLDrYF/PGxGLemFg0Oduws6ACWRYbNpmtKK5swNY8O7bm2fHst0BsqK9nMbbR8SHwVimlLp+IiHogWYbu+++/HyNGjMCaNWsQERHBvzITERFRp/NWKZFmNCDNaMCSmQNQaK/HJrMVWRYbdhVW4ERFA1ZtL8Kq7UXwUSkxNjHUPQtuMiAqyEfq8omIqIeQZejOzc3FZ599hqSkJKlLISIioj5AEAQk6P2RoPfHPRMSUNfcim15dve14GYbyhxN2Gi2YqPZCgBICfP3zIIPjw2GSqmQ+B0QEZFcyTJ0jx49Gnl5eQzdREREJAl/jRemDQzHtIHhEEURx0trkWmxIstixb4TVcgpr0NOeR3e3lIArbcXJibrkWbUY5JRD4PWW+ryiYhIRmQZuh988EE88sgjKCsrw+DBg6FStb+f5pAhQySqjIiIiPoaQRAwIDIAAyIDsDA9CdUNLdiSa0eW2YqsHBsq61uw5kgp1hwpBQAMjgr0LMY2JDoISgUvkyMi6stkGbpvvvlmAMBdd93l2SYIAkRR5EJqREREJKkgXzVuGBqJG4ZGos0l4vDJaveK6BYrDp+swZFT7q+/bcxFiJ8aaSl6pJkMmJisQ5CvWuryiYiom8kydBcWFkpdAhEREdFFKRUCruoXjKv6BWPRlBRYa5uw2WJDpsWKH3PsqKxvwRcHTuGLA6egEIDhscFn7gtuQP8ILReLJSLqA2QZumNjY6UugYiIiKjDDFpv/L8RMfh/I2LgbHNh34kqZFqsyDRbkVNehz1FVdhTVIU/f2dBeIA30k16TEgMRRNP4iMi6rVkE7q//vprTJ8+HSqVCl9//fXPjr3hhhu6qSoiIiKiy6NSKjAmIRRjEkLx+PT+OFnVgKwzp6Fvy6tAmaMJH+4uwYe7S6AUlPhPxV5kmMKQbjIgQefHWXAiol5CNqF71qxZKCsrg8FgwKxZsy44jtd0ExERUU8UHeyLX46JxS/HxKLJ2YZdhZXINFuxyVyO4spGbM+vxPb8Sjy35jhiQ32RbjQgzajHmIRQeKuUUpdPRESXSTah2+Vynfe/iYiIiHobb5USk1L0mJSixxPXJuODL9ZBjBiILbkV2FVYgRMVDVi1vQirthfBW6XAuEQd0s6siB4d7Ct1+URE1AGyCd1EREREfZEgCDD4ADPGxmLBpCTUN7diW579zH3BbSitacJGsxUbzVYAQEqY/5lZcANGxAVDpVRI/A6IiOjnyCZ0/+1vf7vksb/97W+7sBIiIiIi6fhpvDB1YDimDgyHKIowl9W6A7jZhn3FVcgpr0NOeR3e3lIArcYLE1J0SDtzKrpB6y11+URE9BOyCd2vvfZau8c2mw0NDQ0ICgoCAFRXV8PX1xcGg4Ghm4iIiPoEQRDQPyIA/SMC8Ju0JNQ0OLEl131Lss0WGyrqW7D2SBnWHikDAAyOCkS60X1f8KHRQVAquBgbEZHUZHM+UmFhoefr+eefx7Bhw3D8+HFUVlaisrISx48fx9VXX41nn322Q6+7ZcsWzJw5E5GRkRAEAV999VW7/aIo4umnn0ZERAR8fHwwefJk5ObmduI7IyIiIuocgb4qzBwaiVdnD8OeJyfjq4Xj8LtrkjEkOhAAcORUDf62KQ83vbkdI5//AQ9/fBD/OXgK1Q0tEldORNR3yWam+3899dRT+Oyzz2A0Gj3bjEYjXnvtNdxyyy24/fbbL/m16uvrMXToUNx111246aabztn/8ssv429/+xs++OADxMfH46mnnsK0adOQnZ0Nb2+eokVERETypFAIGBYThGExQXh4Sgpstc3YnOOeBd+SY0NlfQu+PHAKXx44BYUAXN0vGOkmA9KNBvSP0PKWZERE3USWobu0tBStra3nbG9ra0N5eXmHXmv69OmYPn36efeJoojly5fjj3/8I2688UYAwD/+8Q+EhYXhq6++wq233nre5zU3N6O5udnz2OFwAACcTiecTmeH6usOZ2uSY23U97AfSS7YiyQXndWLQd4K3DgkDDcOCYOzzYX9xdXYkmtHlsWOHGsd9p6owt4TVfjzdxaEaTWYlKLDpBQdxiaGwl8jy18JSQL83khy0RN68VJrE0RRFLu4lg6bOXMmTp06hffeew9XX301AGDfvn1YsGABoqKi8PXXX1/W6wqCgC+//NJzH/CCggIkJibiwIEDGDZsmGfcpEmTMGzYMPz1r3897+ssXboUy5YtO2f76tWr4evL23gQERGRvFQ2A8erBWRXCcipEdDi+u8st1IQkRggYkCQiAHBIgzeACfBiYgurqGhAXPnzkVNTQ0CAgIuOE6Wf9b8+9//jvnz52PEiBFQqVQAgNbWVkybNg3vvfdepx2nrMy96EhYWFi77WFhYZ595/P4449j0aJFnscOhwMxMTGYOnXqz37YUnE6ndiwYQOmTJni+TyJpMJ+JLlgL5JcdHcvNjvbsPtEFbIsdmzOseNEZQNyagTk1ABfnQBign2QlqJDmlGPUXHB8FYpu7wmkg9+byS56Am9ePaM54uRZejW6/VYu3YtcnJyYDabAQAmkwkpKSkSV+am0Wig0WjO2a5SqWTbEID866O+hf1IcsFeJLnorl5UqVTI6B+BjP4RAIBCez0yzVZkWqzYVVCJkqpG/HNXCf65qwTeKgXGJurcK6IbDYgJ4Rl9fQW/N5JcyLkXL7UuWYbus1JSUro0aIeHhwMAysvLERER4dleXl7e7nRzIiIiot4qXueH+PHxuGt8POqbW7E9vwKbzFZkWaworWnCJrMVm8xWAMeQbPBHusl9T/CRcSFQKWVzIxwiItmSZehua2vDqlWrsHHjRlitVrhcrnb7N23a1CnHiY+PR3h4ODZu3OgJ2Q6HA7t27cKvf/3rTjkGERERUU/hp/HClAFhmDIgDKIowlxWiyyLDZlmK/YVVyHXWodcax3e2VIArcYL45N1SDe6Q7ghgHd9ISI6H1mG7t/97ndYtWoVrrvuOgwaNOiKbmlRV1eHvLw8z+PCwkIcPHgQISEh6NevHx566CE899xzSE5O9twyLDIy0rPYGhEREVFfJAgC+kcEoH9EAH6dloiaBid+zLNhk9mKzRYbKupbsO5oGdYdda+DMygqAOlGA9JNBgyNDoJSwdXYiIgAmYbujz76CJ988glmzJhxxa+1d+9epKenex6fXQBt/vz5WLVqFR577DHU19djwYIFqK6uxvjx47F+/Xreo5uIiIjofwT6qnD9kEhcPyQSLpeII6dqPKehHzpZg6OnHDh6yoHXN+Uh2FeFSSl6pJsMmJisR7CfWuryiYgkI8vQrVarkZSU1CmvlZaWhp+7K5ogCHjmmWfwzDPPdMrxiIiIiHo7hULA0JggDI0JwsNTUmCrbcbmHBsyLVZsybGhqsGJrw6exlcHT0MhAFf1C0a60R3CB0QEXNFZjEREPY0sQ/cjjzyCv/71r/i///s/flMmIiIikjm9VoNbhkfjluHRaG1zYX9xNTaZrcg0W2Epr8W+E1XYd6IKr3yfg7AADdJS3Kehj0/WwV8jy19HiYg6jSy/y23duhWZmZlYt24dBg4ceM5S7F988YVElRERERHRz/FSKjAqPgSj4kOweLoJp6sbkWmxItNsw7Y8O8odzfh4bwk+3lsClVLAyLgQz7XgiXo/TrgQUa8jy9AdFBSEX/ziF1KXQURERERXKDLIB7ePjsXto2PR5GzD7sJKZFqsyLLYUGivx/b8CmzPr8Dza48jJsTHE8BTE0LhrVJKXT4R0RWTZeheuXKl1CUQERERUSfzVikxMUWPiSl6LJkJFNrrkWm2ItNixa6CSpRUNuIfO07gHztOQOOlwNjEUGSYDEgzGhAT4it1+UREl0WWoRsAWltbkZWVhfz8fMydOxdarRanT59GQEAA/P39pS6PiIiIiK5QvM4P8ePjcdf4eNQ3t2J7fsWZU9GtKK1pQqbFhkyLDcAxJBn8zwRwPUbEhkDtpZC6fCKiSyLL0H3ixAlce+21KC4uRnNzM6ZMmQKtVouXXnoJzc3NWLFihdQlEhEREVEn8tN4YcqAMEwZEAZRFGEpr0Wm2YZMsxX7iquQZ61DnrUO72wpgL/GCxOSdUg3ukO4IYC3eiUi+ZJl6P7d736HESNG4NChQwgNDfVs/8UvfoF7771XwsqIiIiIqKsJggBTeABM4QH4dVoiahqc+DHPhkyzDZtzrLDXtWDd0TKsO1oGABgYGeC5FnxYTBCUCi7GRkTyIcvQ/eOPP2L79u1Qq9XttsfFxeHUqVMSVUVEREREUgj0VeH6IZG4fkgkXC4RR07VuE9Dt9hw+GQ1jp124NhpB/4vMw9BvipMStEjw2TAxGQ9gv3UFz8AEVEXkmXodrlcaGtrO2f7yZMnodVqJaiIiIiIiORAoRAwNCYIQ2OC8NDkFNjrmrHZYkOmxYotOTZUNzjxn4On8Z+Dp6EQgGExQZ7F2AZGBvCWZETU7WQZuqdOnYrly5fjnXfeAeA+xaiurg5LlizBjBkzJK6OiIiIiORC56/BzcOjcfPwaLS2ubC/uNqzGJu5rBb7i6uxv7gar3yfA4NWgzSjexZ8XJIOWm+V1OUTUR8gy9D9l7/8BdOmTcOAAQPQ1NSEuXPnIjc3FzqdDh9++KHU5RERERGRDHkpFRgVH4JR8SH4w7UmlNY0uhdjs1ixLc8Oa20zPtl7Ep/sPQkvhYCRcSHIMBmQbtIjUe/PWXAi6hKyDN3R0dE4dOgQPv74Yxw6dAh1dXW4++67cfvtt8PHx0fq8oiIiIioB4gI9MHc0f0wd3Q/NLe2YU9hFTaZrciyWFFgr8eOggrsKKjA82uPIzrYxx3AjQaMSQiFj1opdflE1EvIMnQDgJeXF26//XbcfvvtUpdCRERERD2cxkuJ8ck6jE/W4emZA1Bkr0emxYpNZit2FVbiZFUj/rHjBP6x4wQ0XgqMTQxF+pkQHhPiK3X5RNSDyTJ0V1RUeG4VVlJSgnfffReNjY2YOXMmJk6cKHF1RERERNTTxen8cKcuHneOi0dDSyu251V4rgU/XdOETIsNmRYbgGNI1Pt5ZsFHxIVA7aWQunwi6kFkFbqPHDmCmTNnoqSkBMnJyfjoo49w7bXXor6+HgqFAq+99ho+++wzzJo1S+pSiYiIiKiX8FV7YfKAMEweEAZRFJFrrcMmszuA7z1RhXxbPfJthXj3x0L4a7wwPkmHdJMeaUYDwgK8pS6fiGROVqH7sccew+DBg/Hvf/8b//znP3H99dfjuuuuw7vvvgsAePDBB/Hiiy8ydBMRERFRlxAEASlhWqSEaXH/pETUNDqxNdeOTIsVWRYb7HXNWH+sDOuPlQEABkYGIN3oXoxtWEwwlAouxkZE7ckqdO/ZswebNm3CkCFDMHToULzzzjv4zW9+A4XCfQrPgw8+iDFjxkhcJRERERH1FYE+Klw3JALXDYmAyyXi6Okaz4roh05W49hpB46dduD/MvMQ5KvCpBQ90o0GTEzRI8RPLXX5RCQDsgrdlZWVCA8PBwD4+/vDz88PwcHBnv3BwcGora2VqjwiIiIi6sMUCgFDooMwJDoIv5ucDHtdM7bk2LDJbMWWHBuqG5z4z8HT+M/B0xAE4KqYoDOz4AYMiAiAgrPgRH2SrEI3gHPuj8j7JRIRERGRHOn8Nbjp6mjcdHU0WttcOFBSjUyzFZkWG46XOrC/uBr7i6vxlw050Gs1SDe6Z8HHJesQ4K2Sunwi6iayC9133HEHNBoNAKCpqQn3338//Pz8AADNzc1SlkZEREREdF5eSgVGxoVgZFwIHrvWhNKaRmRZbMg0W7E1zw5bbTM+2XsSn+w9CS+FgJFxIUg3uUN4ksGfE01EvZisQvf8+fPbPf7lL395zphf/epX3VUOEREREdFliQj0wW2j+uG2Uf3Q3NqGPYVV7luSWawosNVjR0EFdhRU4E9rzYgO9vEsxpaaoIOPWil1+UTUiWQVuleuXCl1CUREREREnUrjpcT4ZB3GJ+vw1PUDUGSvR5bFfRr6joIKnKxqxD93nsA/d56AxkuB1MRQdwg3GtAv1Ffq8onoCskqdBMRERER9XZxOj/coYvHHePi0dDSiu15FcjKsSLTbMOpavdp6VkWG5bgGBL1fp7F2EbGhUDtpZC6fCLqIIZuIiIiIiKJ+Kq9MHlAGCYPCIMoisi11iHTbMUmsxV7T1Qh31aPfFsh3ttaCD+1e8Y83WhAmtGA8EBvqcsnokvA0E1EREREJAOCICAlTIuUMC3um5QIR5MTW3PtnhXR7XXN+O5YOb47Vg4AGBAR4FmM7ap+wVDylmREssTQTUREREQkQwHeKswYHIEZgyPgcok4dtqBTIt7FvzQyWpklzqQXerAG5n5CPJVYWKyHukmPSalGBDip5a6fCI6g6GbiIiIiEjmFAoBg6MDMTg6EL+9JhkVdc3YkmvDJrMNW3JsqG5w4utDp/H1odMQBGBYTJBnMbaBkQFQcBacSDIM3UREREREPUyovwa/uCoav7gqGq1tLhwoqUaWxYpNZhuOlzpwoLgaB4qr8eqGHOi1GqSl6JFuMmB8sg4B3iqpyyfqUxi6iYiIiIh6MC+lAiPjQjAyLgS/n2ZCWU3TmQBuxdY8O2y1zfh030l8uu8kvBQCRsQFI91oQIbJgCSDPwSBs+BEXYmhm4iIiIioFwkP9Mato/rh1lH90Nzahr1FVdhktiLTYkWBrR47Cyqxs6ASL6wzIyrIx7MY29hEHbyYv4k6HUM3EREREVEvpfFSYlySDuOSdHjq+gE4UVGPLIsNm8xW7CiowKnqRvxrZzH+tbMYai8FxsQHQ+8UMKiyAYlhgVKXT9QrMHQTEREREfURsaF+mD/WD/PHxqGxpQ07CuzINLtD+KnqRmzJrQCgxOevbUWC3s9zGvrIuBCovRRSl0/UI/X50L106VIsW7as3Taj0Qiz2SxRRUREREREXc9HrUSGKQwZpjA8I4rIs9bhh+wyfL7DjKI6JQps9SiwFeL9rYXwU7tnzNNN7hXRwwO9pS6fqMfo86EbAAYOHIgffvjB89jLix8LEREREfUdgiAgOUyLuBBvRDqyMSHjGuwqqsEmsxVZOTbYapvxfXY5vs8uBwD0jwhAulGPDJMBw2KC4KXkLDjRhTBdwh2yw8PDpS6DiIiIiEgWtN4qTB8cgemDI+ByicgudXgWYztYUo3jpQ4cL3Xgzax8BPqoMDFFjwyTHhOT9Qj110hdPpGsMHQDyM3NRWRkJLy9vZGamooXXngB/fr1u+D45uZmNDc3ex47HA4AgNPphNPp7PJ6O+psTXKsjfoe9iPJBXuR5IK9SHJyoX40GnxhNMTh1xPjUFnfgh/zKpBlseHHPDtqGp345tBpfHPoNAQBGBIViLQUHdJS9BgQoYVCwSXRqeN6wvfGS61NEEVR7OJaZG3dunWoq6uD0WhEaWkpli1bhlOnTuHo0aPQarXnfc75rgMHgNWrV8PX17erSyYiIiIikoU2ESiuA45VKZBdJeBUQ/uArVWJ6B8kYmCwCGOgCB9O+VEv0tDQgLlz56KmpgYBAQEXHNfnQ/dPVVdXIzY2Fq+++iruvvvu844530x3TEwM7Hb7z37YUnE6ndiwYQOmTJkClUoldTnUx7EfSS7YiyQX7EWSkyvtxzJHE37MtSPTYsf2/ArUt7R59nkpBFzdLwhpRh3SkvVIMvhBEDgLTufXE743OhwO6HS6i4Zu/q3pJ4KCgpCSkoK8vLwLjtFoNNBozr1WRaVSybYhAPnXR30L+5Hkgr1IcsFeJDm53H6MCVVhbqgWc8fEo6XVhb1FlZ5rwfNt9dhdVIXdRVV4+btcRAX5IN2kR7rRgNTEUPiqGU3oXHL+3nipdbGzf6Kurg75+fmYN2+e1KUQEREREfVYai8FxibpMDZJhz9ePwDFFQ3ItLgD+I78CpyqbsS/dhbjXzuLofZSYExCqGdF9NhQP6nLJ+o0fT50P/roo5g5cyZiY2Nx+vRpLFmyBEqlErfddpvUpRERERER9Rr9Qn0xf2wc5o+NQ2NLG3YU2JFptmGT2YpT1Y3YkmPDlhwbln2TjQSdH9KMBmSYDBgZHwyNl1Lq8okuW58P3SdPnsRtt92GiooK6PV6jB8/Hjt37oRer5e6NCIiIiKiXslHrUSGKQwZpjA8I4rIt9W5T0M327CnqBIF9noU2Avx922F8FUrMS5JhwyTAWlGPSICfaQun6hD+nzo/uijj6QugYiIiIiozxIEAUkGLZIMWiyYmIjaJie25trPnIpug622GRuyy7EhuxwAYArXIsNkQLrJgKtiguClVEj8Doh+Xp8P3UREREREJB9abxWmD47A9MERcLlEZJc6kHlmMbYDJdUwl9XCXFaLN7PyEeDthYkp7uvAJ6XoEep/7mLHRFJj6CYiIiIiIllSKAQMigrEoKhAPHhNMirrW7Alx4ZMixWbc2yobnDi28Ol+PZwKQQBGBIdhAyjAekmPQZFBkKh4C3JSHoM3URERERE1COE+Kkx66oozLoqCm0uEQdLqpBpdofwY6cdOFRSjUMl1Xjthxzo/DVIM7pvSTY+WYdAH3nedop6P4ZuIiIiIiLqcZQKAcNjQzA8NgSPTjOi3NGETLMVWRYbtubZYa9rxmf7TuKzfSfPjA12XwtuNCAlzB+CwFlw6h4M3URERERE1OOFBXjj1lH9cOuofmhpdWFvUaVnMbY8ax12F1Zid2ElXlxnRlSQj2cWfGxSKHzVjEXUddhdRERERETUq6i9FBibpMPYJB2evA4ormhAVo4Vm8xW7MivwKnqRvx7VzH+vasYai8FxiSEIv1MCI/T+UldPvUyDN1ERERERNSr9Qv1xa9S4/Cr1Dg0trRhZ0EFMi3uEH6yqhFbcmzYkmPDsm+ykaDzQ9qZxdhGxYdA46WUunzq4Ri6iYiIiIioz/BRK5F+5j7fy24QkW+r8yzGtruwEgX2ehTYC/H3bYXwVSsxLkmHdKMBaUY9IoN8pC6feiCGbiIiIiIi6pMEQUCSQYskgxb3TkxAbZMT2/LsnhBurW3GhuxybMguBwCYwrXuwG404Op+QfBSKiR+B9QTMHQTEREREREB0HqrcO2gCFw7KAKiKOLYaQeyzizGdqC4CuayWpjLavFWVj4CvL0wMcV9Hfgkox46f43U5ZNMMXQTERERERH9hCAIGBQViEFRgXggIxlV9S3YkmvDJrMVW3JsqGpw4tvDpfj2cCkEARgSHeRZjG1wVCAUCt6SjNwYuomIiIiIiC4i2E+NG4dF4cZhUWhziThYUn1mFtyKo6ccOFRSjUMl1Vj+Qy50/mpMSnEvxjYhWY9AH5XU5ZOEGLqJiIiIiIg6QKkQMDw2GMNjg/HIVCPKHU3YbHFfB/5jrh32uhZ8vv8kPt9/0jM23WhAhsmAlDB/CAJnwfsShm4iIiIiIqIrEBbgjdkjYzB7ZAxaWl3Ye6ISWRb3qeh51jrsLqzE7sJKvLTejMhAb6SdWYxtXFIofNWMZL0d/4WJiIiIiIg6idpLgbGJOoxN1OGJGf1RUtngWYxtW54dp2uasHpXMVbvKoZaqcDohBDPLHiczk/q8qkLMHQTERERERF1kZgQX8xLjcO81Dg0OduwI78CWRYrNlmsKKlsxI+5dvyYa8cz32YjXueHtDOLsY1OCIHGSyl1+dQJGLqJiIiIiIi6gbdK6b7Pt8mApaKIfFu9O4CbrdhTVIlCez0K7fVYua0IvmolxibqkG5yh/DIIB+py6fLxNBNRERERETUzQRBQJLBH0kGf9wzIQG1TU5sy6tAptmKrBwryh3N+OF4OX44Xg4AMIVrkWY0IN2ox/DYYHgpFRK/A7pUDN1EREREREQS03qrcO2gcFw7KByiKCK71OFZjO1AcRXMZbUwl9VixeZ8BHh7YUKKewY8zaiHzl8jdfn0Mxi6iYiIiIiIZEQQBAyMDMTAyEAsTE9CVX0LtuTakGm2YnOODVUNTqw5XIo1h0sBAEOjA5F2ZjG2wVGBUCh4SzI5YegmIiIiIiKSsWA/NW4cFoUbh0WhzSXiYEk1Np9ZjO3oKQcOnazBoZM1+OvGXIT6qTHpzGJsE5P1CPRVSV1+n8fQTURERERE1EMoFQKGxwZjeGwwFk01wupoQlaOexb8x1w7Kupb8MX+U/hi/yn32H7BSDPpkWEywBimhSBwFry7MXQTERERERH1UIYAb8weEYPZI2LQ0urCvhNVyLRYkWm2Itdah91FldhdVImX11sQEejtWYxtXJIOfhrGwe7AT5mIiIiIiKgXUHspkJoYitTEUDwxoz9KKhuQZbEi02LD9nw7Smua8OHuYny4uxhqpQKjE0I814LH6/ykLr/XYugmIiIiIiLqhWJCfDEvNQ7zUuPQ5GzDzgL3Lck2WawoqWzEj7l2/Jhrx7PfZiMu1NcTwEfFh8BbpZS6/F6DoZuIiIiIiKiX81YpkWY0IM1owFJRRIG9HplmKzItVuwurERRRQNWbS/Cqu1F8FEpMS4p1H0qusmAqCAfqcvv0Ri6iYiIiIiI+hBBEJCo90ei3h/3TEhAXXMrtubaz5yKbkW5oxk/HLfih+NWAIAxTIt0k/ta8Ktjg6FSKiR+Bz0LQzcREREREVEf5q/xwrWDwnHtoHCIoojsUgeyLO4V0fcXV8FSXgtLeS1WbM6H1tsLE5P1SDcZMClFD71WI3X5ssfQTURERERERADcs+ADIwMxMDIQC9OTUN3Qgs05NmRZbMiyWFHV4MSaI6VYc6QUADAkOhDpZ05DHxIVCIWCtyT7KYZuIiIiIiIiOq8gXzVuHBaFG4dFoc0l4tDJamSdWYzt6CkHDp+sweGTNfjrxlyE+qkxyahHutGAicl6BPqqpC5fFhi6iYiIiIiI6KKUCgFX9wvG1f2CsWiqEVZHE7Jy3DPgP+bYUVHfgi/2n8IX+0+dGRt05lpwA0zhWghC35wFZ+gmIiIiIiKiDjMEeGP2iBjMHhEDZ5sLe4uqPIux5ZTXYU9RFfYUVeHl9RZEBHq7V0M36jEuSQc/Td+Jon3nnV7EG2+8gT//+c8oKyvD0KFD8frrr2PUqFFSl0VERERERCR7KqUCqYmhSE0MxeMz+uNkVQMyLTZkma3Ylm9HaU0TPtxdjA93F0OtVGB0QognhCfo/aUuv0sxdAP4+OOPsWjRIqxYsQKjR4/G8uXLMW3aNFgsFhgMBqnLIyIiIiIi6lGig30xb0ws5o2JRZOzDTsLKpBlsWGT2Yriygb8mGvHj7l2PPstEBfq67kn+Oj4EHirlFKX36kYugG8+uqruPfee3HnnXcCAFasWIE1a9bg73//OxYvXixxdURERERERD2Xt0qJNKMBaUYDlswcgEJ7PTaZrciy2LCrsAJFFQ1Ytb0Iq7YXwUelxNjEUExMDoWrWerKO0efD90tLS3Yt28fHn/8cc82hUKByZMnY8eOHed9TnNzM5qb/9sBDocDAOB0OuF0Oru24MtwtiY51kZ9D/uR5IK9SHLBXiQ5YT9Sd4gJ0mD+mBjMHxODuuZW7MivxOZcG7Jy7Ch3NGOj2YqNZisAL+iTSzFtUITUJZ/Xpf5/0udDt91uR1tbG8LCwtptDwsLg9lsPu9zXnjhBSxbtuyc7d9//z18fX27pM7OsGHDBqlLIPJgP5JcsBdJLtiLJCfsR+puY1VA6gDgdAOQXS0gu0qBE3WAI/8A1hYfkLq882poaLikcX0+dF+Oxx9/HIsWLfI8djgciImJwdSpUxEQECBhZefndDqxYcMGTJkyBSoV75VH0mI/klywF0ku2IskJ+xHkgun04lv1m/AzGvl24tnz3i+mD4funU6HZRKJcrLy9ttLy8vR3h4+Hmfo9FooNFoztmuUqlk2xCA/OujvoX9SHLBXiS5YC+SnLAfSQ68lfLuxUutS9HFdcieWq3G8OHDsXHjRs82l8uFjRs3IjU1VcLKiIiIiIiIqKfr8zPdALBo0SLMnz8fI0aMwKhRo7B8+XLU19d7VjMnIiIiIiIiuhwM3QDmzJkDm82Gp59+GmVlZRg2bBjWr19/zuJqRERERERERB3B0H3GAw88gAceeEDqMoiIiIiIiKgX6fPXdBMRERERERF1FYZuIiIiIiIioi7C0E1ERERERETURRi6iYiIiIiIiLoIF1LrBKIoAgAcDofElZyf0+lEQ0MDHA6HbG8sT30H+5Hkgr1IcsFeJDlhP5Jc9IRePJv/zubBC2Ho7gS1tbUAgJiYGIkrISIiIiIiou5UW1uLwMDAC+4XxIvFcrool8uF06dPQ6vVQhAEqcs5h8PhQExMDEpKShAQECB1OdTHsR9JLtiLJBfsRZIT9iPJRU/oRVEUUVtbi8jISCgUF75ymzPdnUChUCA6OlrqMi4qICBAtg1LfQ/7keSCvUhywV4kOWE/klzIvRd/bob7LC6kRkRERERERNRFGLqJiIiIiIiIughDdx+g0WiwZMkSaDQaqUshYj+SbLAXSS7YiyQn7EeSi97Ui1xIjYiIiIiIiKiLcKabiIiIiIiIqIswdBMRERERERF1EYZuIiIiIiIioi7C0E1ERERERETURRi6e4k33ngDcXFx8Pb2xujRo7F79+6fHf/pp5/CZDLB29sbgwcPxtq1a7upUuoLOtKP7777LiZMmIDg4GAEBwdj8uTJF+1fokvV0e+NZ3300UcQBAGzZs3q2gKpz+hoL1ZXV2PhwoWIiIiARqNBSkoKf1ZTp+loPy5fvhxGoxE+Pj6IiYnBww8/jKampm6qlnqrLVu2YObMmYiMjIQgCPjqq68u+pysrCxcffXV0Gg0SEpKwqpVq7q8zs7A0N0LfPzxx1i0aBGWLFmC/fv3Y+jQoZg2bRqsVut5x2/fvh233XYb7r77bhw4cACzZs3CrFmzcPTo0W6unHqjjvZjVlYWbrvtNmRmZmLHjh2IiYnB1KlTcerUqW6unHqbjvbiWUVFRXj00UcxYcKEbqqUeruO9mJLSwumTJmCoqIifPbZZ7BYLHj33XcRFRXVzZVTb9TRfly9ejUWL16MJUuW4Pjx43j//ffx8ccf44knnujmyqm3qa+vx9ChQ/HGG29c0vjCwkJcd911SE9Px8GDB/HQQw/hnnvuwXfffdfFlXYCkXq8UaNGiQsXLvQ8bmtrEyMjI8UXXnjhvONnz54tXnfdde22jR49Wrzvvvu6tE7qGzrajz/V2toqarVa8YMPPuiqEqmPuJxebG1tFceOHSu+99574vz588Ubb7yxGyql3q6jvfjWW2+JCQkJYktLS3eVSH1IR/tx4cKFYkZGRrttixYtEseNG9eldVLfAkD88ssvf3bMY489Jg4cOLDdtjlz5ojTpk3rwso6B2e6e7iWlhbs27cPkydP9mxTKBSYPHkyduzYcd7n7Nixo914AJg2bdoFxxNdqsvpx59qaGiA0+lESEhIV5VJfcDl9uIzzzwDg8GAu+++uzvKpD7gcnrx66+/RmpqKhYuXIiwsDAMGjQIf/rTn9DW1tZdZVMvdTn9OHbsWOzbt89zCnpBQQHWrl2LGTNmdEvNRGf15AzjJXUBdGXsdjva2toQFhbWbntYWBjMZvN5n1NWVnbe8WVlZV1WJ/UNl9OPP/WHP/wBkZGR53xTJeqIy+nFrVu34v3338fBgwe7oULqKy6nFwsKCrBp0ybcfvvtWLt2LfLy8vCb3/wGTqcTS5Ys6Y6yqZe6nH6cO3cu7HY7xo8fD1EU0draivvvv5+nl1O3u1CGcTgcaGxshI+Pj0SVXRxnuolINl588UV89NFH+PLLL+Ht7S11OdSH1NbWYt68eXj33Xeh0+mkLof6OJfLBYPBgHfeeQfDhw/HnDlz8OSTT2LFihVSl0Z9UFZWFv70pz/hzTffxP79+/HFF19gzZo1ePbZZ6UujajH4Ex3D6fT6aBUKlFeXt5ue3l5OcLDw8/7nPDw8A6NJ7pUl9OPZ73yyit48cUX8cMPP2DIkCFdWSb1AR3txfz8fBQVFWHmzJmebS6XCwDg5eUFi8WCxMTEri2aeqXL+b4YEREBlUoFpVLp2da/f3+UlZWhpaUFarW6S2um3uty+vGpp57CvHnzcM899wAABg8ejPr6eixYsABPPvkkFArO4VH3uFCGCQgIkPUsN8CZ7h5PrVZj+PDh2Lhxo2eby+XCxo0bkZqaet7npKamthsPABs2bLjgeKJLdTn9CAAvv/wynn32Waxfvx4jRozojlKpl+toL5pMJhw5cgQHDx70fN1www2eFVJjYmK6s3zqRS7n++K4ceOQl5fn+cMPAOTk5CAiIoKBm67I5fRjQ0PDOcH67B+ERFHsumKJfqJHZxipV3KjK/fRRx+JGo1GXLVqlZidnS0uWLBADAoKEsvKykRRFMV58+aJixcv9ozftm2b6OXlJb7yyivi8ePHxSVLlogqlUo8cuSIVG+BepGO9uOLL74oqtVq8bPPPhNLS0s9X7W1tVK9BeolOtqLP8XVy6mzdLQXi4uLRa1WKz7wwAOixWIRv/32W9FgMIjPPfecVG+BepGO9uOSJUtErVYrfvjhh2JBQYH4/fffi4mJieLs2bOlegvUS9TW1ooHDhwQDxw4IAIQX331VfHAgQPiiRMnRFEUxcWLF4vz5s3zjC8oKBB9fX3F3//+9+Lx48fFN954Q1QqleL69euleguXjKG7l3j99dfFfv36iWq1Whw1apS4c+dOz75JkyaJ8+fPbzf+k08+EVNSUkS1Wi0OHDhQXLNmTTdXTL1ZR/oxNjZWBHDO15IlS7q/cOp1Ovq98X8xdFNn6mgvbt++XRw9erSo0WjEhIQE8fnnnxdbW1u7uWrqrTrSj06nU1y6dKmYmJgoent7izExMeJvfvMbsaqqqvsLp14lMzPzvL8Dnu2/+fPni5MmTTrnOcOGDRPVarWYkJAgrly5stvrvhyCKPK8ECIiIiIiIqKuwGu6iYiIiIiIiLoIQzcRERERERFRF2HoJiIiIiIiIuoiDN1EREREREREXYShm4iIiIiIiKiLMHQTERERERERdRGGbvr/7duxCrFhGMfh+zOwiE3OwEIZZHUInIfZKRhlcwBWo0yUUhYZZFZKWRyAMvBt3049ve9X1zU+03/9db8vAAAAiYhuAAAASER0AwAAQCKiGwAAABIR3QAAAJCI6AYAvvJ4PKJer8d4PP73tt/vo1gsxmazyXAZAOTPn8/n88l6BADwf1mtVjEYDGK/30ej0Yh2ux39fj8mk0nW0wAgV0Q3APCT4XAY6/U6Op1OnM/nOBwOUSqVsp4FALkiugGAnzyfz2g2m3G73eJ4PEar1cp6EgDkjn+6AYCfXC6XuN/v8X6/43q9Zj0HAHLJpRsA+Nrr9YputxvtdjsajUZMp9M4n89Rq9WyngYAuSK6AYCvjUajWCwWcTqdolwuR6/Xi2q1GsvlMutpAJArPi8HAL6y3W5jOp3GfD6PSqUShUIh5vN57Ha7mM1mWc8DgFxx6QYAAIBEXLoBAAAgEdENAAAAiYhuAAAASER0AwAAQCKiGwAAABIR3QAAAJCI6AYAAIBERDcAAAAkIroBAAAgEdENAAAAiYhuAAAASOQvfGSSoavti38AAAAASUVORK5CYII=\n"
},
"metadata": {}
}
],
"source": [
"for e, f in forces_vis.items():\n",
" x = np.linspace(0, 1, 100) # x-coordinates along the beam\n",
"\n",
" # Assuming linear variation of the forces\n",
" F_axial = np.linspace(f[0], f[3], 100)\n",
" F_shear = np.linspace(f[1], f[4], 100)\n",
" M_bending = np.linspace(f[2], f[5], 100)\n",
"\n",
" plt.figure(figsize=(10, 10))\n",
"\n",
" plt.subplot(311)\n",
" plt.plot(x, F_axial)\n",
" plt.ylabel('Axial force')\n",
" plt.title(f'Element {e} / Axial force')\n",
" plt.grid(True)\n",
"\n",
" plt.subplot(312)\n",
" plt.plot(x, F_shear)\n",
" plt.ylabel('Shear force')\n",
" plt.title(f'Element {e} / Shear force')\n",
" plt.grid(True)\n",
"\n",
" plt.subplot(313)\n",
" plt.plot(x, M_bending)\n",
" plt.ylabel('Bending moment')\n",
" plt.title(f'Element {e} / Bending moment')\n",
" plt.grid(True)\n",
"\n",
" plt.xlabel('x')\n",
" plt.tight_layout()\n",
" plt.show()\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "6f5ebd80-9eed-4c61-a612-d8f31f853442",
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"source": [
"**Ermittlung der Lagerreaktionen**\n",
"In diesem Code wird die Funktion calculate_reaction_forces definiert, die die Reaktionskräfte in einem Strukturmodell berechnet. Diese Funktion nimmt die globale Steifigkeitsmatrix K und den Verschiebungsvektor d als Eingabe und berechnet die resultierenden Kräfte F durch Multiplikation von K und d.\n",
"\n",
"Anschließend wird die globale Steifigkeitsmatrix K erstellt, indem die Funktion assemble_global_stiffness aufgerufen wird, die die Steifigkeitsmatrizen aller Elemente in der Struktur zusammenfügt.\n",
"\n",
"Die Reaktionskräfte F werden dann durch Aufruf der Funktion calculate_reaction_forces mit K und d als Argumenten berechnet.\n",
"\n",
"Schließlich wird für jeden Knoten in der Struktur, der eine Unterstützung hat (d.h., an dem Randbedingungen angewendet werden), die resultierende Reaktionskraft in x-, y- und z-Richtung ausgegeben. Diese Kräfte sind im globalen Koordinatensystem."
]
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"output_type": "stream",
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"text": [
"Global stiffness matrix for element 1:\n"
]
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"Matrix([\n",
"[ 1.64e+4, 0, -2.59e+4, -1.64e+4, 0, -2.59e+4],\n",
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"Global stiffness matrix after adding element 1:\n"
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"text": [
"Global stiffness matrix for element 2:\n"
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"Global stiffness matrix after adding element 2:\n"
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"Global stiffness matrix for element 3:\n"
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"output_type": "stream",
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"text": [
"Reaction forces at Node 1:\n",
"Fx = -0.000\n",
"Fy = -44.325\n",
"Mz = -12.826\n",
"Reaction forces at Node 4:\n",
"Fx = 0.000\n",
"Fy = -20.362\n",
"Mz = 0.000\n"
]
}
],
"source": [
"def calculate_reaction_forces(K, d, loads):\n",
" \"\"\"Calculate the reaction forces.\"\"\"\n",
" dof = len(nodes) * 3 # Degrees of freedom (3 per node for 2D beam)\n",
" F_external = np.zeros(dof)\n",
" for node, load in loads.items():\n",
" F_external[node*3-3:node*3] = load # Apply loads\n",
" F_internal = K @ d\n",
" F_reaction = F_external - F_internal\n",
" return F_reaction\n",
"\n",
"# Assemble the global stiffness matrix without applying boundary conditions\n",
"K = assemble_global_stiffness(nodes, elements)\n",
"\n",
"# Calculate the reaction forces\n",
"F = calculate_reaction_forces(K, d, loads)\n",
"\n",
"# Now, F contains the reaction forces at the degrees of freedom where boundary conditions are applied.\n",
"# You can print these forces as follows:\n",
"\n",
"for node, support in supports.items():\n",
" if -1 in support: # If the node is supported\n",
" print(f\"Reaction forces at Node {node}:\")\n",
" print(f\"Fx = {F[node*3-3]:.3f}\")\n",
" print(f\"Fy = {F[node*3-2]:.3f}\")\n",
" print(f\"Mz = {F[node*3-1]:.3f}\")\n"
]
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