bar_analysis.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "bar_analysis.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/adsk2050/btp-iitg/blob/master/bar_analysis.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8rUqUQErcrWi",
        "colab_type": "code",
        "outputId": "980ee5c2-7b44-45cd-80fa-27854a23b895",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 122
        }
      },
      "source": [
        "from google.colab import drive\n",
        "drive.mount('/content/drive')"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Go to this URL in a browser: https://accounts.google.com/o/oauth2/auth?client_id=947318989803-6bn6qk8qdgf4n4g3pfee6491hc0brc4i.apps.googleusercontent.com&redirect_uri=urn%3Aietf%3Awg%3Aoauth%3A2.0%3Aoob&scope=email%20https%3A%2F%2Fwww.googleapis.com%2Fauth%2Fdocs.test%20https%3A%2F%2Fwww.googleapis.com%2Fauth%2Fdrive%20https%3A%2F%2Fwww.googleapis.com%2Fauth%2Fdrive.photos.readonly%20https%3A%2F%2Fwww.googleapis.com%2Fauth%2Fpeopleapi.readonly&response_type=code\n",
            "\n",
            "Enter your authorization code:\n",
            "··········\n",
            "Mounted at /content/drive\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "iXBkVMj3ryu4",
        "colab_type": "code",
        "outputId": "c73085ff-a195-498f-f8f8-dab444874958",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 102
        }
      },
      "source": [
        "import numpy as np\n",
        "\n",
        "\n",
        "class Node:\n",
        "    x=0\n",
        "    def __init__(self, x):\n",
        "        self.x=x\n",
        "\n",
        "    def set_value(self, value):\n",
        "        self.value=value\n",
        "\n",
        "class Element:\n",
        "    #linear element\n",
        "    def __init__(self, a, b):\n",
        "        self.a=a\n",
        "        self.b=b\n",
        "    def __str__(self):\n",
        "        return \"First node  at: \"+str(self.a.x)+\", Second node at: \"+str(self.b.x)\n",
        "\n",
        "class Force:\n",
        "    #in newtons\n",
        "    def __init__(self, m, d):\n",
        "        self.magnitude=m\n",
        "        self.direction=d\n",
        "\n",
        "class Bar:\n",
        "    length=1\n",
        "    elements=2\n",
        "    nodes=[]\n",
        "    element_list=[]\n",
        "    def __init__(self, l, e):\n",
        "        self.length=l\n",
        "        self.elements=e\n",
        "        self.create_nodes()\n",
        "        self.create_elements()\n",
        "\n",
        "    def create_nodes(self):\n",
        "        al=np.linspace(0, self.length-1, int(self.elements+1))\n",
        "        for i in al:\n",
        "            new_node=Node(i)\n",
        "            self.nodes.append(new_node)\n",
        "\n",
        "    def create_elements(self):\n",
        "        for i in range(0, self.elements):\n",
        "            new_element = Element(self.nodes[i], self.nodes[i+1])\n",
        "            self.element_list.append(new_element)\n",
        "\n",
        "b=Bar(10, 5)\n",
        "# for e in b.element_list:\n",
        "#     print(e)\n",
        "# # print(b.element_list)\n",
        "# # print(b.nodes)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "First node  at: 0.0, Second node at: 1.8\n",
            "First node  at: 1.8, Second node at: 3.6\n",
            "First node  at: 3.6, Second node at: 5.4\n",
            "First node  at: 5.4, Second node at: 7.2\n",
            "First node  at: 7.2, Second node at: 9.0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HS3UVe42xYba",
        "colab_type": "code",
        "outputId": "6dc47b15-8525-467b-87dc-d88f8e075985",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "import numpy as np\n",
        "lm=10\n",
        "l=10\n",
        "al=np.linspace(0, l-1, int(lm))\n",
        "print(al)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[0. 1. 2. 3. 4. 5. 6. 7. 8. 9.]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4Nrcr7_jng57",
        "colab_type": "text"
      },
      "source": [
        "**From Dorival Neto**\n",
        "FEM - A 1D Finite Element Method Code to be used as basis for DGFEM creation\n",
        "Copyright (C) 2016 Dorival Piedade Neto & Sergio Persival Baroncini Proença\n",
        "\n",
        "This program is free software: you can redistribute it and/or modify\n",
        "it under the terms of the GNU General Public License as published by\n",
        "the Free Software Foundation, either version 3 of the License, or\n",
        "(at your option) any later version.\n",
        "\n",
        "This program is distributed in the hope that it will be useful,\n",
        "but WITHOUT ANY WARRANTY; without even the implied warranty of\n",
        "MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the\n",
        "GNU General Public License for more details.\n",
        "\n",
        "You should have received a copy of the GNU General Public License\n",
        "along with this program.  If not, see <http://www.gnu.org/licenses/>.\n",
        "\n",
        "Adjusted to work with python 3\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SrKnb-R2mZDk",
        "colab_type": "code",
        "outputId": "1b732f08-aa73-4975-e5bb-ee273033881d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 572
        }
      },
      "source": [
        "import numpy as np\n",
        "# from numpy import zeros, array, dot, linspace\n",
        "from numpy.linalg import solve\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "class Node(object):\n",
        "\n",
        "    def __init__(self, index, coord):\n",
        "        self._index = index\n",
        "        self._coord = coord\n",
        "        self._disp = 0.0\n",
        "\n",
        "    def __repr__(self):\n",
        "        return 'Node # %d at x = %.5f'%(self._index, self._coord)\n",
        "\n",
        "    def __str__(self):\n",
        "        return 'Node # %d at x = %.5f'%(self._index, self._coord)\n",
        "\n",
        "    @property\n",
        "    def index(self):\n",
        "        return self._index\n",
        "\n",
        "    @property\n",
        "    def coord(self):\n",
        "        return self._coord\n",
        "\n",
        "    @coord.setter\n",
        "    def coord(self, value):\n",
        "        self._coord = value\n",
        "\n",
        "    @property\n",
        "    def displacement(self):\n",
        "        return self._disp\n",
        "\n",
        "    @displacement.setter\n",
        "    def displacement(self, value):\n",
        "        self._disp = value\n",
        "\n",
        "class Imposed_displacement(object):\n",
        "\n",
        "    def __init__(self, node_number, value):\n",
        "        self._node_number = node_number\n",
        "        self._value = value\n",
        "\n",
        "    @property\n",
        "    def node_number(self):\n",
        "        return self._node_number\n",
        "\n",
        "    @node_number.setter\n",
        "    def node_number(self, number):\n",
        "        self._node_number = number\n",
        "\n",
        "    @property\n",
        "    def value(self):\n",
        "        return self._value\n",
        "\n",
        "    @value.setter\n",
        "    def value(self, val):\n",
        "        self._value = val\n",
        "\n",
        "class Force(object):\n",
        "\n",
        "    def __init__(self, node_number, value):\n",
        "        self._node_number = node_number\n",
        "        self._value = value\n",
        "\n",
        "    @property\n",
        "    def node_number(self):\n",
        "        return self._node_number\n",
        "\n",
        "    @node_number.setter\n",
        "    def node_number(self, number):\n",
        "        self._node_number = number\n",
        "\n",
        "    @property\n",
        "    def value(self):\n",
        "        return self._value\n",
        "\n",
        "    @value.setter\n",
        "    def value(self, val):\n",
        "        self._value = val\n",
        "\n",
        "class Pressure(object):\n",
        "\n",
        "    def __init__(self, element_number, values):\n",
        "        self._element_number = element_number\n",
        "        self._values = values\n",
        "\n",
        "    @property\n",
        "    def element_number(self):\n",
        "        return self._element_number\n",
        "\n",
        "    @element_number.setter\n",
        "    def element_number(self, number):\n",
        "        self._element_number = number\n",
        "\n",
        "    @property\n",
        "    def values(self):\n",
        "        return self._values\n",
        "\n",
        "    @values.setter\n",
        "    def values(self, val):\n",
        "        self._values = val\n",
        "\n",
        "\n",
        "class Element(object):\n",
        "\n",
        "    def __init__(self, index, nodes, ES):\n",
        "        self._index = index\n",
        "        self._nodes = nodes\n",
        "        self._ES = ES\n",
        "\n",
        "    def __str__(self):\n",
        "        return 'Element # %d from node # %d to node # %d, ES = %.3f'%(self._index, self._nodes[0].index, self._nodes[1].index, self._ES)\n",
        "\n",
        "    def __repr__(self):\n",
        "        return 'Element # %d from node # %d to node # %d, ES = %.3f'%(self._index, self._nodes[0].index, self._nodes[1].index, self._ES)\n",
        "\n",
        "    @property\n",
        "    def index(self):\n",
        "        return self._index\n",
        "\n",
        "    @property\n",
        "    def nodes(self):\n",
        "        return self._nodes\n",
        "\n",
        "    @nodes.setter\n",
        "    def nodes(self, nds):\n",
        "        self._nodes = nds\n",
        "\n",
        "    @property\n",
        "    def ES(self):\n",
        "        return self._ES\n",
        "\n",
        "    @ES.setter\n",
        "    def ES(self, value):\n",
        "        self._ES = value\n",
        "\n",
        "    def lenght(self):\n",
        "        n0, n1 = self._nodes\n",
        "        x0 = n0.coord\n",
        "        x1 = n1.coord\n",
        "        return x1 - x0\n",
        "\n",
        "    def stiffness_matrix(self):\n",
        "        ES = self.ES\n",
        "        L = self.lenght()\n",
        "        kl = ES / L * np.array([[1.0,-1.0],[-1.0,1.0]])\n",
        "        return kl\n",
        "\n",
        "    def force_vector(self, values):\n",
        "        pi, pj = values\n",
        "        L = self.lenght()\n",
        "        f = np.array([(2.0*pi+pj)*L/6.0, (pi+2.0*pj)*L/6.0])\n",
        "        return  f\n",
        "\n",
        "    def indexes(self):\n",
        "        ni, nj = self._nodes\n",
        "        nni = ni.index\n",
        "        nnj = nj.index\n",
        "        return (nni, nnj)\n",
        "\n",
        "    def normal_force(self):\n",
        "        ni, nj = self._nodes\n",
        "        xi = ni.coord; xj = nj.coord\n",
        "        di = ni.displacement; dj = nj.displacement\n",
        "        ES = self._ES\n",
        "        N = ES * (dj - di) / (xj -xi)\n",
        "        return N\n",
        "\n",
        "class Structure(object):\n",
        "\n",
        "    def __init__(self):\n",
        "        self._nodes = {}\n",
        "        self._elements = {}\n",
        "        self._forces = []\n",
        "        self._imposed_displacements = []\n",
        "        self._pressures = []\n",
        "\n",
        "    def insert_node(self, index, coord):\n",
        "        self._nodes[index] = Node(index,coord)\n",
        "\n",
        "    def insert_element(self, index, nodes, ES):\n",
        "        nni, nnj = nodes  # Indexes\n",
        "        ni = self._nodes[nni]\n",
        "        nj = self._nodes[nnj]\n",
        "        self._elements[index] = Element(index, [ni, nj], ES)\n",
        "\n",
        "    def apply_pressure(self, element_number, values):\n",
        "        self._pressures.append(Pressure(element_number, values))\n",
        "\n",
        "    def apply_force(self, node_number, value):\n",
        "        self._forces.append(Force(node_number,value))\n",
        "\n",
        "    def apply_imposed_displacement(self, node_number, value):\n",
        "        self._imposed_displacements.append(Imposed_displacement(node_number, value))\n",
        "\n",
        "    def solve_system_of_equation(self):\n",
        "        ndof = len(self._nodes)\n",
        "        kg = np.zeros((ndof,ndof))\n",
        "        fg = np.zeros(ndof)\n",
        "\n",
        "        # local matrices\n",
        "        for element in self._elements.values(): # self._elements is a dictonary\n",
        "            ni, nj = element.indexes()\n",
        "            row = np.array((ni,ni,nj,nj))\n",
        "            col = np.array((ni,nj,ni,nj))\n",
        "            lrow = np.array((0,0,1,1))\n",
        "            lcol = np.array((0,1,0,1))\n",
        "            kl = element.stiffness_matrix()\n",
        "            kg[row, col] += kl[lrow,lcol]\n",
        "\n",
        "        # local vector - pressures\n",
        "        for pressure in self._pressures:\n",
        "            element_number = pressure.element_number\n",
        "            values = pressure.values\n",
        "            element = self._elements[element_number]\n",
        "            indexes = element.indexes()\n",
        "            fl = element.force_vector(values)\n",
        "            indexes = np.array(indexes)\n",
        "            fg[indexes] += fl[:]\n",
        "\n",
        "        # local vector - forces\n",
        "        for force in self._forces:\n",
        "            node_number = force.node_number\n",
        "            value = force.value\n",
        "            fg[node_number] += value\n",
        "\n",
        "        # displacement boundary condition\n",
        "        self.impose_displacement_boundary_conditions(kg,fg)\n",
        "       \n",
        "        # solving the system of equation\n",
        "        sol = solve(kg,fg)\n",
        "        self.update_degrees_of_freedom(sol)\n",
        "\n",
        "\n",
        "    def impose_displacement_boundary_conditions(self,kg,fg):\n",
        "        for imp_disp in self._imposed_displacements:\n",
        "            nn = imp_disp.node_number\n",
        "            value = imp_disp.value\n",
        "            fg -= kg[nn,:] * value\n",
        "            kg[nn,:] = 0.0\n",
        "            kg[:,nn] = 0.0\n",
        "            kg[nn,nn] = 1.0\n",
        "            fg[nn] = value\n",
        "            print (kg, fg)\n",
        "\n",
        "    def update_degrees_of_freedom(self, sol):   \n",
        "        for node in self._nodes.values():\n",
        "            index = node.index\n",
        "            node.displacement = sol[index]\n",
        "\n",
        "    def print_results(self):\n",
        "        print ('Displacement at nodes')\n",
        "        print (' Node #     displacement')\n",
        "        for ni in sorted(self._nodes.keys()):\n",
        "            node = self._nodes[ni]\n",
        "            disp = node.displacement\n",
        "            print ('     %d        %.6f'%(ni,disp))\n",
        "        print ('\\n')\n",
        "        print ('Normal force at elements')\n",
        "        print (' Element #   Normal node i    Normal node j')\n",
        "        for ei in sorted(self._elements.keys()):\n",
        "            element = self._elements[ei]\n",
        "            Ni = element.normal_force()\n",
        "            Nj = Ni\n",
        "            print ('    %d          %.5f          %.5f'%(ei,Ni,Nj))\n",
        "\n",
        "    def plot_results(self, exact_disp = None, exact_N = None):\n",
        "        xs = []\n",
        "        ys = []\n",
        "        disps = []\n",
        "        Ns = []\n",
        "        for ind in sorted(self._elements.keys()):\n",
        "            element = self._elements[ind]\n",
        "            ni, nj = element.nodes\n",
        "            xi = ni.coord; di = ni.displacement\n",
        "            xj = nj.coord; dj = nj.displacement\n",
        "            N = element.normal_force()\n",
        "            xs += [xi, xj]\n",
        "            ys += [0.0, 0.0]\n",
        "            disps += [di, dj]\n",
        "            Ns += [N, N]\n",
        "        xmin = min(xs)\n",
        "        xmax = max(xs)\n",
        "        dx = xmax - xmin\n",
        "        if exact_disp and exact_N:\n",
        "            x = np.linspace(xmin,xmax,1000)\n",
        "            ed = exact_disp(x)\n",
        "            eN = exact_N(x)\n",
        "\n",
        "        fig = plt.figure(1)\n",
        "        # Displacement subplot\n",
        "        ax1 = fig.add_subplot(121)\n",
        "        ax1.plot(xs,disps,'bx-',lw=2)\n",
        "        leg1 = ['Displacement (FEM)']\n",
        "        if exact_disp and exact_N:\n",
        "            ax1.plot(x,ed,'g-',lw=2)\n",
        "            leg1 += ['Exact displacement']\n",
        "            ymin=min(ys+disps+ed.tolist())\n",
        "            ymax=max(ys+disps+ed.tolist())\n",
        "            dy = ymax - ymin\n",
        "        else:\n",
        "            ymin=min(ys+disps)\n",
        "            ymax=max(ys+disps)\n",
        "            dy = ymax - ymin\n",
        "\n",
        "        ax1.plot(xs,ys,'ko-',lw=3)\n",
        "        ax1.set_xlim((xmin-0.1*dx,xmax+0.1*dx))\n",
        "        ax1.set_ylim((ymin-0.1*dy,ymax+0.4*dy))\n",
        "        ax1.set_xlabel('x')\n",
        "        ax1.set_ylabel('Disp.')\n",
        "        ax1.legend(leg1)\n",
        "\n",
        "        # Displacement subplot\n",
        "        ax2 = fig.add_subplot(122)\n",
        "        ax2.plot(xs,Ns,'bx-',lw=2)\n",
        "        leg2 = ['Normal force (FEM)']\n",
        "        if exact_disp and exact_N:\n",
        "            ax2.plot(x,eN,'g-',lw=2)\n",
        "            leg2 += ['Exact Normal Force']\n",
        "            ymin=min(ys+Ns+eN.tolist())\n",
        "            ymax=max(ys+Ns+eN.tolist())\n",
        "            dy = ymax - ymin\n",
        "        else:\n",
        "            ymin=min(ys+Ns)\n",
        "            ymax=max(ys+Ns)\n",
        "            dy = ymax - ymin\n",
        "\n",
        "        ax2.plot(xs,ys,'ko-',lw=3)\n",
        "        ax2.set_xlim((xmin-0.1*dx,xmax+0.1*dx))\n",
        "        ax2.set_ylim((ymin-0.1*dy,ymax+0.4*dy))\n",
        "        ax2.set_xlabel('x')\n",
        "        ax2.set_ylabel('Normal Force')\n",
        "        ax2.legend(leg2)\n",
        "\n",
        "        plt.show()\n",
        "\n",
        "e = Structure()\n",
        "\n",
        "e.insert_node(0,0.0)\n",
        "e.insert_node(1,1.0)\n",
        "e.insert_node(2,2.0)\n",
        "e.insert_node(3,3.0)\n",
        "\n",
        "\n",
        "e.insert_element(0,(0,1),100.0)\n",
        "e.insert_element(1,(1,2),100.0)\n",
        "e.insert_element(2,(2,3),100.0)\n",
        "\n",
        "e.apply_imposed_displacement(0,0.0)\n",
        "e.apply_force(3,1.0)\n",
        "\n",
        "# e.apply_pressure(0,(0.5,0.5))\n",
        "# e.apply_pressure(1,(0.5,0.5))\n",
        "\n",
        "e.solve_system_of_equation()\n",
        "e.print_results()\n",
        "\n",
        "def exact_u(x):\n",
        "    return -0.5*x**2/(2.0*100.0) + 0.5 * x * 2.0 / 100.0\n",
        "\n",
        "def exact_N(x):\n",
        "    return -0.5 * x  + 0.5 * 2.0\n",
        "\n",
        "e.plot_results(exact_u,exact_N)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[   1.    0.    0.    0.]\n",
            " [   0.  200. -100.    0.]\n",
            " [   0. -100.  200. -100.]\n",
            " [   0.    0. -100.  100.]] [0. 0. 0. 1.]\n",
            "Displacement at nodes\n",
            " Node #     displacement\n",
            "     0        0.000000\n",
            "     1        0.010000\n",
            "     2        0.020000\n",
            "     3        0.030000\n",
            "\n",
            "\n",
            "Normal force at elements\n",
            " Element #   Normal node i    Normal node j\n",
            "    0          1.00000          1.00000\n",
            "    1          1.00000          1.00000\n",
            "    2          1.00000          1.00000\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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thWtoDYbKLE0WyutoLYVraQ2GygxNFsrraC2Fa2kNhsoMTRbKq2gthXtoDYZy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\nNKaMAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tKouoTZqn6-d",
        "colab_type": "code",
        "outputId": "3b96abc6-e8eb-4dfd-ecde-3e3fab993ab9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 375
        }
      },
      "source": [
        "import numpy as np\n",
        "from numpy.linalg import solve\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "class Node(object):\n",
        "\n",
        "    def __init__(self, index, coord):\n",
        "        self._index = index\n",
        "        self._coord = coord\n",
        "        self._disp = 0.0\n",
        "\n",
        "    def __repr__(self):\n",
        "        return 'Node # %d at x = %.5f'%(self._index, self._coord)\n",
        "\n",
        "    def __str__(self):\n",
        "        return 'Node # %d at x = %.5f'%(self._index, self._coord)\n",
        "\n",
        "    @property\n",
        "    def index(self):\n",
        "        return self._index\n",
        "\n",
        "    @property\n",
        "    def coord(self):\n",
        "        return self._coord\n",
        "\n",
        "    @coord.setter\n",
        "    def coord(self, value):\n",
        "        self._coord = value\n",
        "\n",
        "    @property\n",
        "    def displacement(self):\n",
        "        return self._disp\n",
        "\n",
        "    @displacement.setter\n",
        "    def displacement(self, value):\n",
        "        self._disp = value\n",
        "\n",
        "class Force(object):\n",
        "\n",
        "    def __init__(self, node_number, value):\n",
        "        self._node_number = node_number\n",
        "        self._value = value\n",
        "\n",
        "    @property\n",
        "    def node_number(self):\n",
        "        return self._node_number\n",
        "\n",
        "    @node_number.setter\n",
        "    def node_number(self, number):\n",
        "        self._node_number = number\n",
        "\n",
        "    @property\n",
        "    def value(self):\n",
        "        return self._value\n",
        "\n",
        "    @value.setter\n",
        "    def value(self, val):\n",
        "        self._value = val\n",
        "\n",
        "class Element(object):\n",
        "\n",
        "    def __init__(self, index, nodes, ES):\n",
        "        self._index = index\n",
        "        self._nodes = nodes\n",
        "        self._ES = ES\n",
        "\n",
        "    def __str__(self):\n",
        "        return 'Element # %d from node # %d to node # %d, ES = %.3f'%(self._index, self._nodes[0].index, self._nodes[1].index, self._ES)\n",
        "\n",
        "    def __repr__(self):\n",
        "        return 'Element # %d from node # %d to node # %d, ES = %.3f'%(self._index, self._nodes[0].index, self._nodes[1].index, self._ES)\n",
        "\n",
        "    @property\n",
        "    def index(self):\n",
        "        return self._index\n",
        "\n",
        "    @property\n",
        "    def nodes(self):\n",
        "        return self._nodes\n",
        "\n",
        "    @nodes.setter\n",
        "    def nodes(self, nds):\n",
        "        self._nodes = nds\n",
        "\n",
        "    @property\n",
        "    def ES(self):\n",
        "        return self._ES\n",
        "\n",
        "    @ES.setter\n",
        "    def ES(self, value):\n",
        "        self._ES = value\n",
        "\n",
        "    def lenght(self):\n",
        "        n0, n1 = self._nodes\n",
        "        x0 = n0.coord\n",
        "        x1 = n1.coord\n",
        "        return x1 - x0\n",
        "\n",
        "    def stiffness_matrix(self):\n",
        "        ES = self.ES\n",
        "        L = self.lenght()\n",
        "        kl = ES / L * np.array([[1.0,-1.0],[-1.0,1.0]])\n",
        "        return kl\n",
        "\n",
        "    def force_vector(self, values):\n",
        "        pi, pj = values\n",
        "        L = self.lenght()\n",
        "        f = np.array([(2.0*pi+pj)*L/6.0, (pi+2.0*pj)*L/6.0])\n",
        "        return  f\n",
        "\n",
        "    def indexes(self):\n",
        "        ni, nj = self._nodes\n",
        "        nni = ni.index\n",
        "        nnj = nj.index\n",
        "        return (nni, nnj)\n",
        "\n",
        "    def normal_force(self):\n",
        "        ni, nj = self._nodes\n",
        "        xi = ni.coord; xj = nj.coord\n",
        "        di = ni.displacement; dj = nj.displacement\n",
        "        ES = self._ES\n",
        "        N = ES * (dj - di) / (xj -xi)\n",
        "        return N\n",
        "\n",
        "class Structure(object):\n",
        "\n",
        "    def __init__(self, l, e):\n",
        "        self.no_elements=e\n",
        "        self.length=l\n",
        "        self._nodes = {}\n",
        "        self._elements = {}\n",
        "        self._forces = []\n",
        "        self._imposed_displacements = []\n",
        "        self.create_nodes()\n",
        "        self.create_elements()        \n",
        "\n",
        "    def create_nodes(self):\n",
        "        al=np.linspace(0, self.length-1, int(self.no_elements+1))\n",
        "        for i in range(0, len(al)):\n",
        "            new_node=Node(i, al[i])\n",
        "            self._nodes[i]=new_node\n",
        "\n",
        "    def create_elements(self):\n",
        "        for i in range(0, int(self.no_elements)):\n",
        "            new_element = Element((self.nodes[i], self.nodes[i+1]), 0)\n",
        "            self._elements[i] = new_element\n",
        "\n",
        "    def insert_node(self, index, coord):\n",
        "        self._nodes[index] = Node(index,coord)\n",
        "\n",
        "    def insert_element(self, index, nodes, ES):\n",
        "        nni, nnj = nodes  # Indexes\n",
        "        ni = self._nodes[nni]\n",
        "        nj = self._nodes[nnj]\n",
        "        self._elements[index] = Element(index, [ni, nj], ES)\n",
        "\n",
        "    def apply_force(self, node_number, value):\n",
        "        self._forces.append(Force(node_number,value))\n",
        "\n",
        "    def apply_imposed_displacement(self, node_number, value):\n",
        "        self._imposed_displacements.append(Imposed_displacement(node_number, value))\n",
        "\n",
        "    def solve_system_of_equation(self):\n",
        "        ndof = len(self._nodes)\n",
        "        kg = np.zeros((ndof,ndof))\n",
        "        fg = np.zeros(ndof)\n",
        "\n",
        "        # local matrices\n",
        "        for element in self._elements.values(): # self._elements is a dictonary\n",
        "            ni, nj = element.indexes()\n",
        "            row = np.array((ni,ni,nj,nj))\n",
        "            col = np.array((ni,nj,ni,nj))\n",
        "            lrow = np.array((0,0,1,1))\n",
        "            lcol = np.array((0,1,0,1))\n",
        "            kl = element.stiffness_matrix()\n",
        "            kg[row, col] += kl[lrow,lcol]\n",
        "\n",
        "        # local vector - forces\n",
        "        for force in self._forces:\n",
        "            node_number = force.node_number\n",
        "            value = force.value\n",
        "            fg[node_number] += value\n",
        "\n",
        "        # displacement boundary condition\n",
        "        self.impose_displacement_boundary_conditions(kg,fg)\n",
        "       \n",
        "        # solving the system of equation\n",
        "        sol = solve(kg,fg)\n",
        "        self.update_degrees_of_freedom(sol)\n",
        "\n",
        "    def impose_displacement_boundary_conditions(self,kg,fg):\n",
        "        for imp_disp in self._imposed_displacements:\n",
        "            nn = imp_disp.node_number\n",
        "            value = imp_disp.value\n",
        "            fg -= kg[nn,:] * value\n",
        "            kg[nn,:] = 0.0\n",
        "            kg[:,nn] = 0.0\n",
        "            kg[nn,nn] = 1.0\n",
        "            fg[nn] = value\n",
        "            print(kg, fg)\n",
        "\n",
        "    def update_degrees_of_freedom(self, sol):   \n",
        "        for node in self._nodes.values():\n",
        "            index = node.index\n",
        "            node.displacement = sol[index]\n",
        "\n",
        "    def print_results(self):\n",
        "        print('Displacement at nodes')\n",
        "        print(' Node #     displacement')\n",
        "        for ni in sorted(self._nodes.keys()):\n",
        "            node = self._nodes[ni]\n",
        "            disp = node.displacement\n",
        "            print('     %d        %.6f'%(ni,disp))\n",
        "        print('\\n')\n",
        "        print('Normal force at elements')\n",
        "        print(' Element #   Normal node i    Normal node j')\n",
        "        for ei in sorted(self._elements.keys()):\n",
        "            element = self._elements[ei]\n",
        "            Ni = element.normal_force()\n",
        "            Nj = Ni\n",
        "            print('    %d          %.5f          %.5f'%(ei,Ni,Nj))\n",
        "\n",
        "    def plot_results(self, exact_disp = None, exact_N = None):\n",
        "        xs = []\n",
        "        ys = []\n",
        "        disps = []\n",
        "        Ns = []\n",
        "        for ind in sorted(self._elements.keys()):\n",
        "            element = self._elements[ind]\n",
        "            ni, nj = element.nodes\n",
        "            xi = ni.coord; di = ni.displacement\n",
        "            xj = nj.coord; dj = nj.displacement\n",
        "            N = element.normal_force()\n",
        "            xs += [xi, xj]\n",
        "            ys += [0.0, 0.0]\n",
        "            disps += [di, dj]\n",
        "            Ns += [N, N]\n",
        "        xmin = min(xs)\n",
        "        xmax = max(xs)\n",
        "        dx = xmax - xmin\n",
        "        if exact_disp and exact_N:\n",
        "            x = np.linspace(xmin,xmax,1000)\n",
        "            ed = exact_disp(x)\n",
        "            eN = exact_N(x)\n",
        "\n",
        "        fig = plt.figure(1)\n",
        "        # Displacement subplot\n",
        "        ax1 = fig.add_subplot(121)\n",
        "        ax1.plot(xs,disps,'bx-',lw=2)\n",
        "        leg1 = ['Displacement (FEM)']\n",
        "        if exact_disp and exact_N:\n",
        "            ax1.plot(x,ed,'g-',lw=2)\n",
        "            leg1 += ['Exact displacement']\n",
        "            ymin=min(ys+disps+ed.tolist())\n",
        "            ymax=max(ys+disps+ed.tolist())\n",
        "            dy = ymax - ymin\n",
        "        else:\n",
        "            ymin=min(ys+disps)\n",
        "            ymax=max(ys+disps)\n",
        "            dy = ymax - ymin\n",
        "\n",
        "        ax1.plot(xs,ys,'ko-',lw=3)\n",
        "        ax1.set_xlim((xmin-0.1*dx,xmax+0.1*dx))\n",
        "        ax1.set_ylim((ymin-0.1*dy,ymax+0.4*dy))\n",
        "        ax1.set_xlabel('x')\n",
        "        ax1.set_ylabel('Disp.')\n",
        "        ax1.legend(leg1)\n",
        "\n",
        "        # Displacement subplot\n",
        "        ax2 = fig.add_subplot(122)\n",
        "        ax2.plot(xs,Ns,'bx-',lw=2)\n",
        "        leg2 = ['Normal force (FEM)']\n",
        "        if exact_disp and exact_N:\n",
        "            ax2.plot(x,eN,'g-',lw=2)\n",
        "            leg2 += ['Exact Normal Force']\n",
        "            ymin=min(ys+Ns+eN.tolist())\n",
        "            ymax=max(ys+Ns+eN.tolist())\n",
        "            dy = ymax - ymin\n",
        "        else:\n",
        "            ymin=min(ys+Ns)\n",
        "            ymax=max(ys+Ns)\n",
        "            dy = ymax - ymin\n",
        "\n",
        "        ax2.plot(xs,ys,'ko-',lw=3)\n",
        "        ax2.set_xlim((xmin-0.1*dx,xmax+0.1*dx))\n",
        "        ax2.set_ylim((ymin-0.1*dy,ymax+0.4*dy))\n",
        "        ax2.set_xlabel('x')\n",
        "        ax2.set_ylabel('Normal Force')\n",
        "        ax2.legend(leg2)\n",
        "\n",
        "        plt.show()\n",
        "\n",
        "\n",
        "\n",
        "e = Structure(100, 10)\n",
        "\n",
        "# e.insert_node(0,0.0)\n",
        "# e.insert_node(1,1.0)\n",
        "# e.insert_node(2,2.0)\n",
        "\n",
        "# e.insert_element(0,(0,1),100.0)\n",
        "# e.insert_element(1,(1,2),100.0)\n",
        "\n",
        "e.apply_imposed_displacement(0,0.0)\n",
        "e.apply_force(2,1.0)\n",
        "\n",
        "e.solve_system_of_equation()\n",
        "e.print_results()\n",
        "\n",
        "def exact_u(x):\n",
        "    return -0.5*x**2/(2.0*100.0) + 0.5 * x * 2.0 / 100.0\n",
        "\n",
        "def exact_N(x):\n",
        "    return -0.5 * x  + 0.5 * 2.0\n",
        "\n",
        "e.plot_results(exact_u,exact_N)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "error",
          "ename": "AttributeError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-2-b3a81e3c18b3>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m    293\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    294\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 295\u001b[0;31m \u001b[0me\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mStructure\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m100\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m10\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    296\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    297\u001b[0m \u001b[0;31m# e.insert_node(0,0.0)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m<ipython-input-2-b3a81e3c18b3>\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, l, e)\u001b[0m\n\u001b[1;32m    133\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_imposed_displacements\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    134\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcreate_nodes\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 135\u001b[0;31m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcreate_elements\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    136\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    137\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mcreate_nodes\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m<ipython-input-2-b3a81e3c18b3>\u001b[0m in \u001b[0;36mcreate_elements\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    143\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mcreate_elements\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    144\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mno_elements\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 145\u001b[0;31m             \u001b[0mnew_element\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mElement\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnodes\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnodes\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    146\u001b[0m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_elements\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnew_element\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    147\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mAttributeError\u001b[0m: 'Structure' object has no attribute 'nodes'"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "S01fIpPtEGkn",
        "colab_type": "code",
        "outputId": "757afb0f-48ff-4a15-fe77-b70efebb729e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 980
        }
      },
      "source": [
        "import numpy as np\n",
        "# from numpy import zeros, array, dot, linspace\n",
        "from numpy.linalg import solve\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "class Node(object):\n",
        "\n",
        "    def __init__(self, index, coord):\n",
        "        self._index = index\n",
        "        self._coord = coord\n",
        "        self._disp = 0.0\n",
        "\n",
        "    def __repr__(self):\n",
        "        return 'Node # %d at x = %.5f'%(self._index, self._coord)\n",
        "\n",
        "    def __str__(self):\n",
        "        return 'Node # %d at x = %.5f'%(self._index, self._coord)\n",
        "\n",
        "    @property\n",
        "    def index(self):\n",
        "        return self._index\n",
        "\n",
        "    @property\n",
        "    def coord(self):\n",
        "        return self._coord\n",
        "\n",
        "    @coord.setter\n",
        "    def coord(self, value):\n",
        "        self._coord = value\n",
        "\n",
        "    @property\n",
        "    def displacement(self):\n",
        "        return self._disp\n",
        "\n",
        "    @displacement.setter\n",
        "    def displacement(self, value):\n",
        "        self._disp = value\n",
        "\n",
        "class Imposed_displacement(object):\n",
        "\n",
        "    def __init__(self, node_number, value):\n",
        "        self._node_number = node_number\n",
        "        self._value = value\n",
        "\n",
        "    @property\n",
        "    def node_number(self):\n",
        "        return self._node_number\n",
        "\n",
        "    @node_number.setter\n",
        "    def node_number(self, number):\n",
        "        self._node_number = number\n",
        "\n",
        "    @property\n",
        "    def value(self):\n",
        "        return self._value\n",
        "\n",
        "    @value.setter\n",
        "    def value(self, val):\n",
        "        self._value = val\n",
        "\n",
        "class Force(object):\n",
        "\n",
        "    def __init__(self, node_number, value):\n",
        "        self._node_number = node_number\n",
        "        self._value = value\n",
        "\n",
        "    @property\n",
        "    def node_number(self):\n",
        "        return self._node_number\n",
        "\n",
        "    @node_number.setter\n",
        "    def node_number(self, number):\n",
        "        self._node_number = number\n",
        "\n",
        "    @property\n",
        "    def value(self):\n",
        "        return self._value\n",
        "\n",
        "    @value.setter\n",
        "    def value(self, val):\n",
        "        self._value = val\n",
        "\n",
        "class Element(object):\n",
        "\n",
        "    def __init__(self, index, nodes, ES):\n",
        "        self._index = index\n",
        "        self._nodes = nodes\n",
        "        self._ES = ES\n",
        "\n",
        "    def __str__(self):\n",
        "        return 'Element # %d from node # %d to node # %d, ES = %.3f'%(self._index, self._nodes[0].index, self._nodes[1].index, self._ES)\n",
        "\n",
        "    def __repr__(self):\n",
        "        return 'Element # %d from node # %d to node # %d, ES = %.3f'%(self._index, self._nodes[0].index, self._nodes[1].index, self._ES)\n",
        "\n",
        "    @property\n",
        "    def index(self):\n",
        "        return self._index\n",
        "\n",
        "    @property\n",
        "    def nodes(self):\n",
        "        return self._nodes\n",
        "\n",
        "    @nodes.setter\n",
        "    def nodes(self, nds):\n",
        "        self._nodes = nds\n",
        "\n",
        "    @property\n",
        "    def ES(self):\n",
        "        return self._ES\n",
        "\n",
        "    @ES.setter\n",
        "    def ES(self, value):\n",
        "        self._ES = value\n",
        "\n",
        "    def lenght(self):\n",
        "        n0, n1 = self._nodes\n",
        "        x0 = n0.coord\n",
        "        x1 = n1.coord\n",
        "        return x1 - x0\n",
        "\n",
        "    def stiffness_matrix(self):\n",
        "        ES = self.ES\n",
        "        L = self.lenght()\n",
        "        kl = ES / L * np.array([[1.0,-1.0],[-1.0,1.0]])\n",
        "        return kl\n",
        "\n",
        "    def force_vector(self, values):\n",
        "        pi, pj = values\n",
        "        L = self.lenght()\n",
        "        f = np.array([(2.0*pi+pj)*L/6.0, (pi+2.0*pj)*L/6.0])\n",
        "        return  f\n",
        "\n",
        "    def indexes(self):\n",
        "        ni, nj = self._nodes\n",
        "        nni = ni.index\n",
        "        nnj = nj.index\n",
        "        return (nni, nnj)\n",
        "\n",
        "    def normal_force(self):\n",
        "        ni, nj = self._nodes\n",
        "        xi = ni.coord; xj = nj.coord\n",
        "        di = ni.displacement; dj = nj.displacement\n",
        "        ES = self._ES\n",
        "        N = ES * (dj - di) / (xj -xi)\n",
        "        return N\n",
        "\n",
        "class Structure(object):\n",
        "\n",
        "    def __init__(self):\n",
        "        self._nodes = {}\n",
        "        self._elements = {}\n",
        "        self._forces = []\n",
        "        self._imposed_displacements = []\n",
        "        self._pressures = []\n",
        "\n",
        "    def insert_node(self, index, coord):\n",
        "        self._nodes[index] = Node(index,coord)\n",
        "\n",
        "    def insert_element(self, index, nodes, ES):\n",
        "        nni, nnj = nodes  # Indexes\n",
        "        ni = self._nodes[nni]\n",
        "        nj = self._nodes[nnj]\n",
        "        self._elements[index] = Element(index, [ni, nj], ES)\n",
        "\n",
        "    def apply_force(self, node_number, value):\n",
        "        self._forces.append(Force(node_number,value))\n",
        "\n",
        "    def apply_imposed_displacement(self, node_number, value):\n",
        "        self._imposed_displacements.append(Imposed_displacement(node_number, value))\n",
        "\n",
        "    def solve_system_of_equation(self):\n",
        "        ndof = len(self._nodes)\n",
        "        kg = np.zeros((ndof,ndof))\n",
        "        fg = np.zeros(ndof)\n",
        "\n",
        "        # local matrices\n",
        "        for element in self._elements.values(): # self._elements is a dictonary\n",
        "            ni, nj = element.indexes()\n",
        "            row = np.array((ni,ni,nj,nj))\n",
        "            col = np.array((ni,nj,ni,nj))\n",
        "            lrow = np.array((0,0,1,1))\n",
        "            lcol = np.array((0,1,0,1))\n",
        "            kl = element.stiffness_matrix()\n",
        "            kg[row, col] += kl[lrow,lcol]\n",
        "\n",
        "        # local vector - forces\n",
        "        for force in self._forces:\n",
        "            node_number = force.node_number\n",
        "            value = force.value\n",
        "            fg[node_number] += value\n",
        "\n",
        "        # displacement boundary condition\n",
        "        self.impose_displacement_boundary_conditions(kg,fg)\n",
        "       \n",
        "        # solving the system of equation\n",
        "        sol = solve(kg,fg)\n",
        "        self.update_degrees_of_freedom(sol)\n",
        "\n",
        "\n",
        "    def impose_displacement_boundary_conditions(self,kg,fg):\n",
        "        for imp_disp in self._imposed_displacements:\n",
        "            nn = imp_disp.node_number\n",
        "            value = imp_disp.value\n",
        "            fg -= kg[nn,:] * value\n",
        "            kg[nn,:] = 0.0\n",
        "            kg[:,nn] = 0.0\n",
        "            kg[nn,nn] = 1.0\n",
        "            fg[nn] = value\n",
        "            print (kg, fg)\n",
        "\n",
        "    def update_degrees_of_freedom(self, sol):   \n",
        "        for node in self._nodes.values():\n",
        "            index = node.index\n",
        "            node.displacement = sol[index]\n",
        "\n",
        "    def print_results(self):\n",
        "        print ('Displacement at nodes')\n",
        "        print (' Node #     displacement')\n",
        "        for ni in sorted(self._nodes.keys()):\n",
        "            node = self._nodes[ni]\n",
        "            disp = node.displacement\n",
        "            print ('     %d        %.6f'%(ni,disp))\n",
        "        print ('\\n')\n",
        "        print ('Normal force at elements')\n",
        "        print (' Element #   Normal node i    Normal node j')\n",
        "        for ei in sorted(self._elements.keys()):\n",
        "            element = self._elements[ei]\n",
        "            Ni = element.normal_force()\n",
        "            Nj = Ni\n",
        "            print ('    %d          %.5f          %.5f'%(ei,Ni,Nj))\n",
        "\n",
        "    def plot_results(self, exact_disp = None, exact_N = None):\n",
        "        xs = []\n",
        "        ys = []\n",
        "        disps = []\n",
        "        Ns = []\n",
        "        for ind in sorted(self._elements.keys()):\n",
        "            element = self._elements[ind]\n",
        "            ni, nj = element.nodes\n",
        "            xi = ni.coord; di = ni.displacement\n",
        "            xj = nj.coord; dj = nj.displacement\n",
        "            N = element.normal_force()\n",
        "            xs += [xi, xj]\n",
        "            ys += [0.0, 0.0]\n",
        "            disps += [di, dj]\n",
        "            Ns += [N, N]\n",
        "        xmin = min(xs)\n",
        "        xmax = max(xs)\n",
        "        dx = xmax - xmin\n",
        "        if exact_disp and exact_N:\n",
        "            x = np.linspace(xmin,xmax,1000)\n",
        "            ed = exact_disp(x)\n",
        "            eN = exact_N(x)\n",
        "\n",
        "        fig = plt.figure(1)\n",
        "        # Displacement subplot\n",
        "        ax1 = fig.add_subplot(121)\n",
        "        ax1.plot(xs,disps,'bx-',lw=2)\n",
        "        leg1 = ['Displacement (FEM)']\n",
        "        if exact_disp and exact_N:\n",
        "            ax1.plot(x,ed,'g-',lw=2)\n",
        "            leg1 += ['Exact displacement']\n",
        "            ymin=min(ys+disps+ed.tolist())\n",
        "            ymax=max(ys+disps+ed.tolist())\n",
        "            dy = ymax - ymin\n",
        "        else:\n",
        "            ymin=min(ys+disps)\n",
        "            ymax=max(ys+disps)\n",
        "            dy = ymax - ymin\n",
        "\n",
        "        ax1.plot(xs,ys,'ko-',lw=3)\n",
        "        ax1.set_xlim((xmin-0.1*dx,xmax+0.1*dx))\n",
        "        ax1.set_ylim((ymin-0.1*dy,ymax+0.4*dy))\n",
        "        ax1.set_xlabel('x')\n",
        "        ax1.set_ylabel('Disp.')\n",
        "        ax1.legend(leg1)\n",
        "\n",
        "        # Displacement subplot\n",
        "        ax2 = fig.add_subplot(122)\n",
        "        ax2.plot(xs,Ns,'bx-',lw=2)\n",
        "        leg2 = ['Normal force (FEM)']\n",
        "        if exact_disp and exact_N:\n",
        "            ax2.plot(x,eN,'g-',lw=2)\n",
        "            leg2 += ['Exact Normal Force']\n",
        "            ymin=min(ys+Ns+eN.tolist())\n",
        "            ymax=max(ys+Ns+eN.tolist())\n",
        "            dy = ymax - ymin\n",
        "        else:\n",
        "            ymin=min(ys+Ns)\n",
        "            ymax=max(ys+Ns)\n",
        "            dy = ymax - ymin\n",
        "\n",
        "        ax2.plot(xs,ys,'ko-',lw=3)\n",
        "        ax2.set_xlim((xmin-0.1*dx,xmax+0.1*dx))\n",
        "        ax2.set_ylim((ymin-0.1*dy,ymax+0.4*dy))\n",
        "        ax2.set_xlabel('x')\n",
        "        ax2.set_ylabel('Normal Force')\n",
        "        ax2.legend(leg2)\n",
        "        plt.show()\n",
        "\n",
        "def E(x):\n",
        "    return 100.0\n",
        "\n",
        "e = Structure()\n",
        "no_elements = 10\n",
        "for i in range(0, no_elements+2):\n",
        "    e.insert_node(i,0.0+i)\n",
        "\n",
        "for i in range(0, no_elements+1):\n",
        "    e.insert_element(i,(i,i+1),E(i))\n",
        "\n",
        "e.apply_imposed_displacement(0,0.0)\n",
        "e.apply_force(no_elements+1,1.0)\n",
        "\n",
        "e.solve_system_of_equation()\n",
        "e.print_results()\n",
        "\n",
        "def exact_u(x):\n",
        "    return -0.5*x**2/(2.0*100.0) + 0.5 * x * 2.0 / 100.0\n",
        "\n",
        "def exact_N(x):\n",
        "    return -0.5 * x  + 0.5 * 2.0\n",
        "\n",
        "e.plot_results(exact_u,exact_N)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[   1.    0.    0.    0.    0.    0.    0.    0.    0.    0.    0.    0.]\n",
            " [   0.  200. -100.    0.    0.    0.    0.    0.    0.    0.    0.    0.]\n",
            " [   0. -100.  200. -100.    0.    0.    0.    0.    0.    0.    0.    0.]\n",
            " [   0.    0. -100.  200. -100.    0.    0.    0.    0.    0.    0.    0.]\n",
            " [   0.    0.    0. -100.  200. -100.    0.    0.    0.    0.    0.    0.]\n",
            " [   0.    0.    0.    0. -100.  200. -100.    0.    0.    0.    0.    0.]\n",
            " [   0.    0.    0.    0.    0. -100.  200. -100.    0.    0.    0.    0.]\n",
            " [   0.    0.    0.    0.    0.    0. -100.  200. -100.    0.    0.    0.]\n",
            " [   0.    0.    0.    0.    0.    0.    0. -100.  200. -100.    0.    0.]\n",
            " [   0.    0.    0.    0.    0.    0.    0.    0. -100.  200. -100.    0.]\n",
            " [   0.    0.    0.    0.    0.    0.    0.    0.    0. -100.  200. -100.]\n",
            " [   0.    0.    0.    0.    0.    0.    0.    0.    0.    0. -100.  100.]] [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]\n",
            "Displacement at nodes\n",
            " Node #     displacement\n",
            "     0        0.000000\n",
            "     1        0.010000\n",
            "     2        0.020000\n",
            "     3        0.030000\n",
            "     4        0.040000\n",
            "     5        0.050000\n",
            "     6        0.060000\n",
            "     7        0.070000\n",
            "     8        0.080000\n",
            "     9        0.090000\n",
            "     10        0.100000\n",
            "     11        0.110000\n",
            "\n",
            "\n",
            "Normal force at elements\n",
            " Element #   Normal node i    Normal node j\n",
            "    0          1.00000          1.00000\n",
            "    1          1.00000          1.00000\n",
            "    2          1.00000          1.00000\n",
            "    3          1.00000          1.00000\n",
            "    4          1.00000          1.00000\n",
            "    5          1.00000          1.00000\n",
            "    6          1.00000          1.00000\n",
            "    7          1.00000          1.00000\n",
            "    8          1.00000          1.00000\n",
            "    9          1.00000          1.00000\n",
            "    10          1.00000          1.00000\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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du1O1alU6derE1atX7esSfxVdvnyZ+++/n/DwcEJCQuzHCA4OtndJHRkZmWbL1k8++YQ6\ndeoQHh5O586d7b/qT506RadOnQgPDyc8PNz+y2r27NlERkZSo0YNnnzySeLi4gAoWLAgAwcOtLeY\n//XXX2natCkVK1Zk2bJlgO1DPXDgQOrUqUNYWBgff/wxYPuV2bRpU7p06cJdd93Fww8/jIgwceJE\njh8/TrNmzezdYauclxPlHCA8PJzChQuzcuXKVOt++OEHatasSWhoKI899pi9g83g4GBeeeUVatWq\nxYIFC2jatCkvvvgiERERVK1alc2bN/PAAw9QqVIlhg0bZj9eesMQZIaIMHDgQEJCQggNDbW/p7Vr\n19KoUSPat29PtWrVAPj8888JCwsjPDycnj17ArbuiDp37kydOnWoU6cOGzZsyFIctwzQm6Ysd40+\nHJdMGfHz87N3fRweHi7z5s0TEZHvv/9e6tWrJ3PnzpWWLVvat0/sgjk2NlaaNGkiO3bskGvXrkmF\nChXk119/FRGRCxcuyI0bN2T69OnSv3//NM87duxY6dOnj4iI7NixQ/z9/WXz5s0icrNb9YULF8rj\njz9u3+f8+fP29YndN8+cOdPeKj1p18xnzpyx7zd06FCZOHGiiIh069bN3o16bGysnD9/Xvbs2SNt\n27aV69evi4hIv379ZObMmbb/F0jW/fW9995r7xo7PDxcREQ+/vhjGTFihIiIxMTESO3ateXQoUP2\nLqf/+ecfiYuLk3r16slPP/2U7D1mxFUtwrF1obMGW6/Ou4HnM9rHKV2j+1g5T+w14ccff5TGjRuL\niMj9998va9askatXr0rZsmVl//79IiLSs2dPe9kMCgqSkSNH2o/TpEkTGTRokIiIjB8/XsqUKSPH\njx+XmJgYueOOO+zlPa1hCBKPl1Z5CwoKkpCQEAkPD5fIyEgREVm4cKG0aNFCYmNj5eTJk1KuXDk5\nfvy4rFmzRgICAuzdse/atUsqVaqUagiEHj162Mv533//LXfddVeq83pki3Blk95l+7333suCBQvo\n379/sk7/vvzyS6ZOnUpsbCwnTpxgz549GGMoU6aMvZ+dQoUKZXjedevW2YeSDQsLIywsLNU2oaGh\nvPTSS7zyyiu0bds2WcdtPXr0sP998cUXU+27a9cuhg0bxvnz57l06RItW7YEYPXq1Xz++eeA7T53\n4cKFmTVrFlu3brXHf/XqVXsvv3ny5EnW/XXevHntXWMn9sPz/fff8/vvv9s7p7tw4QJ//PEHefLk\nITIy0t6NfGLfPSk7dbRILPCSiGwzxgQCW40xK0VkT0Y7eiKrynmixo0bA7auzxPt37+fChUqULly\nZQB69erF5MmTeeGFFwDs/Uklat/e1hlFaGgo1atXp0yZMgBUrFiRf/75h+LFi6c5DEHx4sVvGVvK\n21Pr16+nR48e+Pv7c9ttt9GkSRM2b95MoUKFiIyMtHfHvnr1arp27WrfN7F79lWrVrFnz81idPHi\nRS5dukTBggUd/ve6FU0aCeQN92oZHx8fz969ewkICODcuXOULVuWv/76izFjxrB582aKFi1K7969\nndbtc1oqV67Mtm3bWLFiBcOGDaN58+a8/vrrQPIu2FP2yAu2UdeWLl1KeHg4M2bMuGXFo4jQq1cv\n3nvvvVTrUnZ/nbI79sT9J02aZE9MidauXZusO3Z/f3+XDhuaGSJyAjiR8DraGLMX29AALk0avlzO\nhw4dyttvv+1wXcCtumVPOUxAbGxssmEIAgICaNq0qdM/n450zx4fH8+mTZvIly+fU8+dSOs03NS4\nceOoWrUqc+bMoU+fPty4cYOLFy9SoEABChcuzKlTp/jmG9vwIlWqVOHEiRNsTuiKNDo6mtjY2Ft2\nO964cWP72Ny7du3i999/T7XN8ePHCQgI4JFHHmHgwIFs27bNvi7xPuv8+fO5++67U+0bHR1NmTJl\nuHHjBl988YV9efPmzZkyZQpgq4u4cOECzZs3Z+HChZw+fRqwdTP9999/O/xv1bJlS6ZMmWIf7vPA\ngQMZjtdwq3+bnGaMCcbWOecv1kaS81xdzpO67777OHfunL2sV6lShcOHD9vr5GbNmkWTJk2y/F7S\nG4Ygsxo1asT8+fOJi4sjKiqKdevWERkZmWq7e+65hwULFtj7sErsnv2+++5j0qRJ9u2c/QCCXmlY\nLLFr9EStWrWiT58+fPrpp/z6668EBgbSuHFj3n77bd58801q1qzJXXfdRbly5WjQoAFgu4Uzf/58\nnn32Wa5evUr+/PlZtWoVzZo14/3336dGjRoMGTIk2eV2v3796NOnD1WrVqVq1arUrl07VWw7d+5k\n4MCB9gFvEr/sAc6dO0dYWBh58+Zl7ty5qfYdMWIEdevWpWTJktStW9f+oZ4wYQJ9+/Zl2rRp+Pv7\nM2XKFO6++27efvtt7rvvPuLj48mdOzeTJ08mKMixIeEff/xxDh8+TK1atRARSpYsydKlS2+5T9++\nfWnVqhW33347a5w5KEomGWMKAouAF0TkYhrr+wJ9AcqXL5/D0TmPVeU8paFDh9KhQwcA8uXLx/Tp\n0+natSuxsbHUqVOHp556KsvvsVWrVnz00UdUrVqVKlWq2IchyKxOnTqxceNGwsPDMcYwatQoSpcu\nbR9DJ1H16tUZOnQoTZo0wd/fn5o1azJjxgwmTpxI//79CQsLIzY2lsaNG/PRRx9l+X2lpB0Wakdu\nmRYcHMyWLVsy/ZigJ3Jlh4XGmNzAcuA7Efkgo+21w0LlLNphoVIextgqaqYBex1JGEq5C709pTLN\nWUNV+rgGQE9gpzEm8abzqyLi/S0rlUfz+aQhImk+/aOUK2/dish6IMcKnpZzlSi75dqnb0/ly5eP\ns2fPuvTLQXkmEeHs2bMue2wxJ2k5V4mcUa59+kqjbNmyHD16lKioKKtDUW4oX7589oaBnkzLuUoq\nu+Xap5NG7ty57a0rlfJWWs6VM/n07SmllFKZo0lDKaWUwzRpKKWUcpgmDaWUUg7TpKGUUsphmjSU\nUko5TJOGUkoph2nSUEop5TBNGkoppRymSUMppZTDNGkopZRymCYNpZRSDtOkoZRSymGaNJRSSjlM\nk4ZSSimHadJQPmfUKFizJvmyNWtsy3OSMeYzY8xpY8wuZx43M++vTRv44IPkyz74wLY8LZnZXo+d\n87HkSNkWEa+aateuLUrdyurVIiVK2P6mNZ8RYIs4oawCjYFawC5Htne0bCe+n1U/xGX4/saOFTHG\n9jet+exsr8fO+ViyU7YdLdeWf8k7e9KkoRwxc6ZI/vwi4eGZSxgizksatkMR7OykISKy7PtzQq9m\nQshcAdHJRydX/BjS21PKZ8TGwldfwX33Qa9ecPUq7NgBPXtCs2ZWR5c2Y0xfY8wWY8yWzIzxHVVi\nMVRYAx17QdA6F0ao3Fm/fs4v25YmDWNMK2PMfmPMn8aYwWmsb2yM2WaMiTXGdLEiRuX5Tp2Cd9+F\nihWhY0dYuRJy54Z8+eDxx2HWrNT3gd2FiEwVkQgRiShZsqTD+wWf60O+Hc9CruuYHh2Yvnxvur9H\nx44FY6BRI9vfsWNv/fs1M9vrsXM+ltWroUQJeO01mDLFBWXbWZfZWbgs9wcOAhWBPMAOoFqKbYKB\nMOBzoIsjx9XbU76ndevU93jHjBGpV0/koYdEcue++ZH6z39E+vUTKV7c+joNuVnGXVKnsfKHWOkw\nt4MwHPEbECwLvz2Ralt3uh/vC8d2dSxeXacB3A18l2R+CDAknW1naNJQ6Un6QYqOFunSRZL99vLz\nE2nfXuS770Ti4kRGjkz9IVq92rbcEe6eNJK+v8vXL0vkJ5HCcOSON2vLpWuXkm2bVsIdO9a2PC2Z\n2V6PnfOxZKdse0LS6AJ8mmS+J/BhOttq0lC39MorNxNEYrIoWVJkyBCRw4edey5nJQ1gLnACuAEc\nBf57q+2zWrZPXTolFSdUFIYjbee0lRtxN7L4zpU3c7Rce0VFeFYrC5Vni42FxYuheXMYOdK2LD4e\nAgNh9mz45x9bXUZQkLVxpkdEeohIGRHJLSJlRWSaK85TqkApvnn4G4rlL8byA8t57pvnEpOWUplm\nZdI4BpRLMl82YVmmSRYrC5VnOnECRoyA4GDo3NlW8Zc7t21dzZpw6ZKt8jtvXkvDdCuVi1dmWfdl\n5PXPy5QtUxj982irQ1IeysqksRmoZIypYIzJA3QHllkYj3IjKVvCikD//lCmDJQvD6+/DseOQeXK\n0KGD7apj7FjYtg3GjIGXX07dktbXNSjfgNkPzMZgeGXVK8zbNc/qkJQHsixpiEgs8AzwHbAX+FJE\ndhtj3jLGtAcwxtQxxhwFugIfG2N2WxWvylktWti++N97z/bYYJky8L//wcmTtltQnTrBqlWwbx9c\nv25LFAMG2PYdMMA2v2qVte/BHXWp1oUx940BoNfSXqz7W9twqMwx3nZvMyIiQrZs2WJ1GCqbdu+G\nvn3h559vLitYEF54wba8XLn093U1Y8xWEYnI6fM6q2yLCM9/+zyTfp1EkXxF+Pmxn6lasqoTIlSe\nzNFy7RUV4co73LgBCxZA06YQEpI8Ydx1F5w9a6vLsDJheANjDONajqNDlQ6cjzlPmzltOHnppNVh\nKQ+hSUNZ7tgxGD7c9pRTt27w449QoADcfffNlrD798OHH1odqffw9/NnTuc5RN4RyeHzh2k7py2X\nr1+2OizlATRpqByRVsX200/b6iqCguDNN21PRVWtaksOr74KmzbZ6ibWrdPKbVcIyB3A1z2+pmLR\nimw9sZXui7oTGx9rdVjKzeWyOgDlGxIrtmNioFAh222m06dt6/z9oUsX29NRTZrYri7atElduQ22\nyu3E1yr7Ettw3D3tbnsbjsltJmOMsTo05aa0IlzliJ07bRXYmzbdXBYYCC+9BE88Abffbl1smeXp\nFeFp2XBkA80/b861uGuMbDGSQQ0GueQ8yn1pRbiy3PXrMG+erU4iLCx5wkis2H7jDc9KGN5K23Ao\nR2nSUE73zz+2bpnLl4cePWD9ettVRf36ySu2J02yOlKVlLbhUI7QpKGyLGnltoitviE01JYs3n7b\n1pVHSIitcd6QIbBxo1Zsu7sX673Is5HPcj3uOh3mdWBv1F6rQ1JuRivCVZYlVm6vWwd798KBA7bl\nxtgene3fHxo21IptT5LYhuPIhSN8tf8r2sxpw8b/bqR0wdJWh6bchF5pqCzZvt3WhUeuXLYhVBMT\nRsuWcPz4zbqMxIdwVqxInRwGDLAtd3d///03qxL6JLl69Sp4+edG23CoW/Hqwq+c69o1+OILW91E\nzZrwySe2VtyFC9vWN2wI334Lpb3oR+knn3xCly5dePLJJwE4evQowH8sDSoHaBsOlR5NGsouZQM8\nsM03a2ZrbFeuHDzyiK1uonBheP55eOUVuHjRdlWxYYP31VFMnjyZDRs2UKhQIQAqVaoEPnJbV8fh\nUGnRpKHsEusoPvjA1pPsk0/a2lGsXWvrbTYqCsLDYepUW9cf5cvDqFHeXbmdN29e8uTJY5+PjfWt\nX9s6DodKSZOGshswAN56y5YoChSwJQeAPHng4YdtVxK//WZrjFeggK0S29u7JG/SpAnvvvsuV69e\nZeXKlXTt2hXggjOObYxpZYzZb4z50xgz2BnHdAVtw6GScWRMWE+adIzwrNmyReSxx0Ty5bs5xnae\nPCLvvity6pTV0VknLi5Opk6dKl26dJHOnTvL1KlTnTJGOOAPHAQqAnmAHUC1W+2TmbI9e/ZsCQoK\nEmOMBAUFyezZs9Pdtl+/fuLv7y+A+Pv7S79+/dLcbsyGMcJwxEQa8fP3y3D7zBw7K9t76rFdHUtm\n/u+TcrRcW/4l7+xJk4bjrl4VmTlTJDLyZqJInKpVEzFGZOxYq6O01qVLlyQ2NtY+HxsbK8A2yX7S\nuBv4Lsn8EGDIrfZxtGzPnj1bAgICBLBPAQEBaX559OvXL9l2iVNaX0zx8fES0ibE4e0zc+zMbu+p\nx3Z1LJn5v09Jk4YSEZHWrVN/8b/6qkiFCiLFi99MEkWKiDRunDxRjB2riaNu3boSHR1tn4+Ojhbg\nkmQ/aXQBPk0y3xP48Fb7OFq2g4KC0vyi0cl3p6CgoAzLDQ4mDZ94CsSXJVZux8dDtWq2+op9+26u\nr1XL1give3dbT7PaAC+5mJgYChYsaJ9PeJ1jdYHGmL5AX4Dy5cs7tM+RI0dcGZLyQM4sE5o0vNyj\nj8KaNTBw4M1l/v62iu2nn4Z9a960AAAgAElEQVTIyOQN8FIaMMB3EwZAgQIF2LZtG7Vq1QJg69at\nAPFOOPQxIOkYhGUTliUjIlOBqWDr5daRA5cvX56///7bCSEqb+HoDw5H6NNTXkgEfv0VevWCsmVh\n+fKb64KD4eRJmDkT6ta9mTBU2iZMmEDXrl1p1KgRDRs25MEHHwRwxs+2zUAlY0wFY0weoDuwzAnH\n5Z133iEgICDZsoCAAGbPnp3qVkO/fv3SPEa/fv3SvDWR3vbV2lQjPj7eJcdOa3tPPbarY5k9e3aa\n//fvvPNOmsfJEkfuYXnS5Mt1Gpcvi0ybJlK7togtddjqJO66y/a3YUOto8iMuLg42bBhg1y/fl12\n7twpO3fulOvXrzt87zejCWgDHMD2FNXQjLa3+umptLb38/cTE2mE4cio9aOcemx9eiprx9anpzRp\nJJNWxfaQISLBwSJFi95MFsWKiQwcaFunldtZV6NGjVTLnJU0Mju5a9n+cteXwnCE4ci8nfOsDkdl\nkaPlWm9PeZjEiu0xY2DZMqhSxdZa+/BhOHfOVkcxYwYcPWprrb19u/c3wHOl5s2bs2jRosQrA5WG\nrtW7MuZe2zgcjy59lJ/+/sniiJQr6XCvHub0aejdG7755uYyf39bhffTT0NEjg9C6t0CAwO5fPky\n/v7+5M+fHxHh0qVL8SLin9OxuHPZFhGe++Y5Ptz8IUXzFeXn//7MXSXusjoslQmODveqT095ABFb\nJ4H/+x8sWGAbRjVRhQqweTMUL25dfN4sOjo61TJjzG8WhOLWjDGMbzWeIxePsGz/Mlp/0ZpN/93E\nbQVvszo05WR6e8qNXb5s6368Vi1o0MDWLfmNG7b2FsbYuiI/fNj2JJRynWXLlvHyyy/z8ssvszzp\no2gqGX8/f+Z2nntzHI65Og6HN9Kk4QZSdkl+4AA0bgxFikDfvrZ6iRIlYPBgWxfle/fa6iV++sk7\ne5Z1J4MHD2bChAlUq1aNatWqMWHCBIA7rI7LXSWOw1GhSAW2HN+i43B4I0dqyz1pctcnTG4l8Ymm\n3r1FWrS4+QQUiNx9t8isWbZ+okTSfnpq7FjbcuV8oaGhEhcXZ59P6HvqimjZvqV9Ufuk2MhiwnCk\n3/J+Eh8fb3VIKgNoNyKe4dQpuHIFAgNtTz0lqlvXVoeR0BDZTltt57zz589TrFgxAC5ccEqv6F6v\nSokqfNX9K1p83oIpW6ZQoUgFBjYYmPGOyu1p0rCAiG1sismTYdEiWz0FQL58EBMD9erZKr6V9YYM\nGULNmjVp1qwZIsK6desATlgdlydoWL4hszrNotvCbgxaNYjyhcvzYMiDVoelsknrNFwgvWFT77sP\nPv4YatSwDY86bx7ExUHHjra6i2vXbMt/+UXrKNxFjx492LRpEw888ACdO3dmoy2bn7M6Lk+hbTi8\nkCP3sNKagFpZ3deVkzvc903Z6nrQIFv9RJ48N+sqSpUSGTpU5MiR1Ntrq23rTZo0yf56165dydah\nLcIzJT4+Xp75v2eE4UjR94vK3qi9Voek0uBouc5O0vgkq/u6cnKXD9aoUbYv/sKFJVnFdsOGInPm\niFy7dnNbrdx2PzVr1kzztYgmjayIjYuV9nPbC8OR4PHBcjL6pNUhqRQcLddZvj0lIk8440rH2xw/\nDm++CePH29LEhQvg5wdPPgk7dtgek+3RwzbudqIVK1JXZA8YkHalt8p5ts+Tyg5tw+E9HK4IN8Y8\nADTENhLUehFZ4rKoPIwI/Pij7WmnJUsgNslj6RUrwl9/QeXKEBZmXYwqc86fP8+SJUuIj4/n4sWL\nLF68OOnqIlbF5ckS23DU+7SevQ3HkgeXkMtPn8fxJA79bxlj/gf8B5ibsOhJY0wLEenvssjcTJs2\nts4Ck14RvPuurZU2wJ49tr/+/hAaCrt2wejRtpHyPvjA1gAP9NFYT9GkSROWLbMNb9G4cWO+/vrr\npKs1aWRRqQKl+Obhb6j/WX2WH1jOc988x+Q2kzE6sIvncOQeFrCPhM4NE+b9gL2O7JvTk6vu+yat\nnN65U6R+/eR1FaVLi7z+usjRo1pH4e3QOo1s++nvnyTviLzpjsOhcp6j5dqhXm6NMcuB/iLyd8J8\nEPChiLRzUS7LMlf1BHr9Ojz+OMyalWRhvvPUbn6YZp0OU/quw5y5eorzMee5cO0CF69dJF7iMcZg\nMOTxz0PRfEUpmr8oxfIXo2yhslQoUoGKRStSJrAMfkaffvYUjvYG6mzu3MttVizYvYBuC7sBMK/z\nPG3DYTFn93IbCOw1xvyaMF8H2GKMWQYgIu2zFqb7O3oUpk6Fj2ee43T+n6DZFij9G353bCe+4FG2\nAluPAkezfo6A3AGE3xZOrTK1qFWmFvXL1adK8Sp6ya68WtfqXRl9YTQDVw7k0aWPcnvg7TQKamR1\nWCoDjiaN111xcmNMK2AC4A98KiLvp1ifF/gcqA2cBR4UkcOuiCUpEVj5QywjPl/HhtMrkKA10Oc3\nMDevyuKB3OSncsmKBBcJJrhIMGUKlqFo/qIUzluYQnkL4Wf8EGz7xMTGcO7qOc7FnOPslbMcuXiE\nQ+cO8de5v4i6EsXGoxvZePRmM/DbA2/nngr30LxCc9pWbkuJgBKuftsqhxhjugLDgapApIh4z+VD\nJr1090scPn+YyZsn02FeBx2HwxM4cg8LKAD4JbyuDLQHcjuy7y2O6Y9tbOSKQB5gB1AtxTZPAx8l\nvO4OzM/ouI7e9x05UuTVV5OPpfvCgJkS+cjXUujR3sKgYvYhLBmO+L2RW6hSWjBGADHGX+CpdBvg\nZWZc3zOXz0i7h9uJ8bMdG4MQcfPc/m/6yz0z75EPf/lQTkSfcKvxiD312BmNo7xo0aJ0J+BPyV7Z\nrwpUAdYCEY7u5011GknFxsVKuznttA2HxXBm4z5gKxCArUvow8AC4AtH9r3FMe8GvksyPwQYkmKb\n74C7E17nAs6QpEI+rcnRD9arr84WCLB9SSdOuRAeuPllXXx4ZXl6ySBZeXCllC3/RPJtE6Zy5VJ/\nOfXr1y/NbdP7Iktv+wYPNJCWs1pKrrdy3UxgEam3y8qx09reWXG7+7Fnz54tAQHJ/+8DAgKSJY7e\nvXunOwFnJBtlX26Wb00aCS5duyR1ptYRhiMRUyPk0rVLVofkc5ydNLYl/H0WGJTweocj+97imF2w\n3ZJKnO+JrXI96Ta7gLJJ5g8CJW51XEc/WEFBQWl+0ejku1NQUJBTP1wOfAbWoknD7mT0SakwvoIw\nHGk3p53ExsVaHZJPcbRcO1qnYYwxdwMPA/9NWOY2j/sYY/oCfQHKly/v0D5HjhxxZUjKA6VXJv7v\n//6P3bt3ExMTk7ioTEbHMsasAkqnsWqoiHzlaExZKdue6raCt9nbcHx94GvbmONtPtQHQtyMo1/8\nL2C7fbRERHYbYyoCa7J57mNAuSTzZROWpbmNMSYXUBhbhXgyIjJVRCJEJKJkyZIOndzbP4Aq89Iq\nE0899RTz589n0qRJiAgLFiwAWx3cLYlICxEJSWNyOGEkHCfTZduTJY7Dkdc/L//b8j/GbhxrdUgq\nJUcuR1wxYaujOARU4GZFePUU2/QneUX4lxkdN1t1GgTIq6/OTnN7d79/X6VVFfF/018YjuQZkUee\nXfGsvdLcneN21zqNRKGhocn+RkdHCxAtenvKpebvmm+vx5u/a77V4fgEnFGnAYxP+Ps1sCzl5MgJ\nMjh+G+AAtrqKoQnL3gLaJ7zOh63S/U/gV6BiRsfMztNTr746W0aOTH8fd39S6MCZA/LQoofEDDfC\ncKTguwVl1PpR0vepvm4dtxXHzujpqUSRkZEiIlK3bl05duyYxMTECBAj2Sv3nbC17LkGnCLJAyG3\nmnwpaYiIjN4w2v4jaN3hdVaH4/UcTRq3bBFujKktIluNMU3SWi8iP6a7s0W8rdVsVuw8tZOhq4fy\n9QFbf0lVildhQqsJtPxPS4sj8zwjRozg2Wef5YcffqB///4YYzh58uQJEbk9p2PxtbItIjz7zbNM\n3jyZovmKsvG/G6lSoorVYXktR1uEO9SNSMIBSwKISFQ2Y3MpX/tg3cq3f37L898+z4GzBwDoXLUz\nk9tM5raCt1kcmWe6du0aMTExFClSRLsRySFx8XF0mt+Jrw98TYUiFdj4341afl3E0aSRYUW4MWa4\nMeYMsB84YIyJMsa4pIW4cq5W/2nFzn47GdViFAXzFGTR3kVU+181Zv8+G0d/LPi6uLg4li1bxsSJ\nE5k8eTLTpk0D0G+tHJI4Dked2+vw1/m/aDe3nY7DYbFbJg1jzACgAVBHRIqJSFGgLtDAGPNiTgSo\nsiePfx4GNhjIrn67uO/O+/j36r/0XNKT9vPaczz6uNXhub127doxY8YMzp49S3R0NNHR0eBGj5v7\nggJ5CvB1D9uVxubjm+mxqAdx8XFWh+WzMqrT+A24V0TOpFheEvheRGq6OL5M88VLeEeJCDO2z+DF\n717kwrULlAgowfQO02lbua3VobmtsLAwfv/992TLtJdba+w/s5/6n9Xn36v/8nTE09qGw8mcdXsq\nd8qEAfZ6jdxZDU5ZwxhDn5p92NN/D/dWvJczV87Qbm47nv/mea7FXrM6PLfUunVrvv/+e6vDUGgb\nDneRUdK4nsV1yo3dHng73z7yLaNajCKXXy4m/jqRup/W5Y+zf1gdmtupV68enTp1In/+/BQqVIjA\nwEAAt7vC9hUNyzfk806fAzBw5UC+3P2lxRH5noySRrgx5mIaUzQQmhMBKtfwM34MbDCQnx/7mTuL\n3smOUzuo80kd/u/A/1kdmlsZMGAAGzdu5MqVK1y8eDGxTuM3q+PyZd2qd2P0vaMB6LmkJz/9/ZPF\nEfmWWyYNEfEXkUJpTIEiorenvECdO+qw7cltdLqrExeuXaDd3Ha8ve5t4iXe6tDcQrly5QgJCdF7\n527mpbtfon+d/lyPu06HeR3Yf2a/1SH5DEc7LFRerFDeQizstpD317/PsNXDeG3Na2w9sZXPO35O\nYN5Aq8OzVMWKFWnatCmtW7cmb968iYv1kVuLGWOY0GoCRy4c4esDX9P6i9bahiOH6KODCrDdrnq1\n0assf2g5hfMWZum+pTSe0ZhjF1P2IelbKlSoQPPmzbl+/bo+cutmtA2HNRxuEe4pfP2xRGf44+wf\n3D/nfv749w/KFirLiodWEHqb71VhxcXF8corrzBmzJhky/WRW/dy6tIp7p52ty1xVG7HkgeX4O/n\nb3VYHsdpLcKV76lUvBIb/7uRBuUacPTiURp81oCVB1daHVaO8/f3Z8OGDVaHoTKQOA5HsfzF7ONw\neNuPYXeiSUOlqXhAcVY9uopu1bsRfT2aNnPaMGvHLKvDynE1atSgffv2zJo1i8WLF7N48WKAIlbH\npZLTNhw5RyvCVbry5crH3M5zCS4czKifR/Ho0keJvh7N03Wetjq0HBMTE0Px4sVZvXp10sWaNNxQ\nw/INmdlxJt0XdWfgyoGUL1yebtW7WR2W19GkoW7Jz/gx8t6RlAgowaBVg+i/oj8Xr11kcMPBVoeW\nI6ZPn55q2YwZMw7nfCTKEQ+GPMiRC0cYtGoQPZf0pEzBMjQKamR1WF5Fb08phwxsMJCP7v8Ig2HI\nD0N49YdXfeK+8dGjR+nUqROlSpWiVKlSdO7cGbQLHbf2cv2XeTriaW3D4SKaNJTDnox4ktkPzMbf\n+PPe+vcY8N0Ar08cffr0oX379hw/fpzjx4/Trl07gGCLw1K3YIxhQusJtKvcjnMx52j9RWtOXTpl\ndVheQ5OGypSHQh9iUbdF5PbLzfhfxjNw5UCvThxRUVH06dOHXLlykStXLnr37g16peH2cvnlYm7n\nuUTcHqFtOJxMk4bKtA53dWBht4Xk8svF2I1jvfpWVfHixZk9ezZxcXHExcUxe/ZsgNjsHNMYM9oY\ns88Y87sxZokxRivWXaBAngIs77Gc4CLBOg6HE2nSUFnSvkp75neZj7/x5/0N7/PG2jesDsklPvvs\nM7788ktKly5NmTJlWLhwIcDhbB52JRAiImHAAWBINo+n0pHYhqNovqLahsNJNGmoLHug6gPM6TwH\nP+PHiHUjeHvd21aH5HRBQUEsW7aMqKgoTp8+zdKlSyGbwwKIyPcikni1sgkom904VfruKnEXX3X/\nijz+ebQNhxPoI7cqW7pV70ZcfByPLHmE19a8RomAEjwV8ZTVYWXbW2+9davVZZx4qseA+emtNMb0\nBfoClC9f3omn9S2NghrxecfPtQ2HE+iVhsq2HqE9mHL/FACe/r+nWbhnocURZV+BAgVSTQDTpk0D\nKJ3R/saYVcaYXWlMHZJsMxRb/cgX6R1HRKaKSISIRJQsWTLb78uXPRjyIKNajAJ0HI7s0CsN5RR9\na/cl6nIUw9YM4+HFD1M0X1GaV2xudVhZ9tJLL9lfR0dHM2HCBKZPn0737t0ZNWrUzoz2F5EWt1pv\njOkNtAWai95kzzEv13+Zw+cP878t/6PDvA5s/O9GqpSoYnVYHkWvNJTTvNroVZ6LfI7rcdfpOL8j\nW49vtTqkbPn3338ZNmwYYWFhxMbGsm3bNkaOHAnZf3qqFTAIaC8iV5wRq3KMtuHIPk0aymmMMYxr\nNY6HQh/i0vVLtJnThr/O/WV1WFkycOBA6tSpQ2BgIDt37mT48OEULVrUWYf/EAgEVhpjthtjPnLW\ngVXGtA1H9uh4Gsrprsddp+2ctqw8tJJqJaux4bENFMnnWU0R/Pz8yJs3L7ly5Uo21KuIcOnSpXgR\nyfEBG7RsO9epS6eoN60eh88fpn2V9izuttinx+HQ8TSUZfL452FB1wVUL1mdPVF76LqgKzfiblgd\nVqbEx8dz9epVoqOjuXjxon1KGLnvN6vjU9mXtA3Hsv3LeP7b57UNhwM0aSiXKJyvMMsfWk6pAqVY\ndWgV/Vf01w+kcjtJ23BM3jyZDzZ+YHVIbk+ThnKZ4CLBLOu+jHy58vHJtk8Y8/OYjHdSKocltuEA\neHnlyyzYvcDiiNybJg3lUnXL1rV/IAetGsTX+7+2OCKlUkvZhmP9kfUWR+S+NGkol+tavStvN7N1\nMfLIkkd0fAPllhLH4bgWd03H4bgFTRoqR7za6FW6VOvCxWsX6Ti/IxevXbQ6JKWSSdqG49+r/2ob\njnRo0lA5whjD9A7TqV6yOvvO7KPnkp7ES7zVYSmVjLbhyJgmDZVjCuYpyNLuSymSrwjL9i9jxI8j\nrA5JqVRSjsPx0OKHdByOJDRpqBz1n2L/YW7nuRgMw38czrL9y6wOSalUtA1H+jRpqBzX6j+teOee\ndwDotbSXx3Y1orybtuFImyYNZYnBDQfTvkp7zsec58GFD3I9LlvjGinlEtqGIzVNGsoSiRXjQYWD\n2Hx8M4NWDrI6JKXS9GDIg4xsMRLQNhxgUdIwxhQzxqw0xvyR8DfN7kONMd8aY84bY5bndIzK9Yrl\nL8b8LvPJ7ZebCb9MYPHexVaHpFSaBtYfSL+IftqGA+uuNAYDP4hIJeCHhPm0jAZ65lhUKsfVLVuX\nUffaWuI+9tVjHDp3yOKIlErNGMPE1hNpW7mtz7fhsCppdABmJryeCXRMayMR+QGIzqmglDWer/s8\nHe/qyIVrF+i2oBvXYq9ZHZJSqeTyy8W8zvOoXaa2T7fhsCpp3CYiJxJenwRusygO5QaMMXzW/jOC\niwSz9cRWXlvzmtUhKZWmAnkKsPwh327D4bKkYYxZZYzZlcbUIel2CeMjZ+sBaGNMX2PMFmPMlqio\nqGzFraxRNH9RvnjgC/yMH2N+HsPqv1ZbHZJSaSpdsDQrHlrhs204XJY0RKSFiISkMX0FnDLGlAFI\n+Hs6m+eaKiIRIhJRsmRJZ4SvLFC/XH1ea/wagvDokkf59+q/VofkMsaYEcaY3xOGe/3eGHO71TEp\nx1UtWZWl3Zf6ZBsOq25PLQN6JbzuBXxlURzKzQxrPIx6ZetxLPoYTy5/0pt/wY0WkTARqQEsB163\nOiCVOY2DGjOzo61q1pfacFiVNN4H7jXG/AG0SJjHGBNhjPk0cSNjzE/AAqC5MeaoMaalJdGqHJPL\nLxezO82mYJ6CLNyzkJk7Zma8kwcSkaTd/BYgm7dolTW6h3T3uTYcliQNETkrIs1FpFLCbax/E5Zv\nEZHHk2zXSERKikh+ESkrIt9ZEa/KWXcWu5NJrScB8Ow3z3Lw34MWR+Qaxph3jDH/AA+jVxoey9fa\ncGiLcOWWeoX3omu1rly6folHlz7qkU+oZPQwiIgMFZFywBfAM+kcQx/ycHO+1oZDk4ZyS8YYPmr7\nEWUKluHnf35mwi8TrA4p0zJ4GCSpL4DO6RxDH/LwAL7UhkOThnJbxfIXY2q7qQAMXT3Uqy77jTGV\nksx2APZZFYtyDl9pw6FJQ7m1tpXb0iu8FzGxMfT5qo83fQjfT7hV9TtwH/C81QGp7EvZhuOFb1/w\nuicANWkotze+1XhuD7ydjUc3Mm7TOKvDcQoR6ZxwqypMRNqJyDGrY1LOkbQNx4ebP/SaMptIk4Zy\ne0XyFeHTdrYnsYetHsbeqL0WR6TUrSVtw/HS9y95VRsOTRrKI7Su1Jo+NfpwLe6at92mUl4qZRuO\nDUc2WByRc2jSUB7jg5YfULZQWX459ovXXfIr75S0DUf7ee05cPaA1SFlmyYN5TGK5CvC1La2p6ne\nWPuGji2u3F5abThOX85WV3uW06ShPErrSq3pEdKDKzeu0O//+nndkynK+yRtw3Ho3CHazW3HlRtX\nrA4ryzRpKI8zruU4iuYryncHv2PurrlWh6NUhpK24fj12K88tMhz23Bo0lAe57aCtzHmvjEAvPDt\nC5y9ctbiiJTKWNI2HF/t/8pj23Bo0lAeqU+NPjQNbkrUlSgGrhxodThKOcQb2nBo0lAeyRjDx20/\nJq9/XqZvn64j/SmP4eltODRpKI9VuXhlhjUeBsCTy58kJjbG4oiUckz3kO683/x9wPPacGjSUB5t\nUINBVC9ZnT///ZPRG0ZbHY5SDhvUYBBP1X7K49pwaNJQHi2Pfx4mt5kMwLvr39W2G8pjGGOY1GYS\n91e636PacGjSUB6vSXATHg59mJjYGF747gWrw1HKYbn8cjGvi2e14dCkobzC6HtHE5gnkGX7l7H8\nwHKrw1HKYQXzFGT5Q8sJKhzkEW04NGkor1AmsAxvNn0TgOe/fV4rxZVHKV2wNN88/A1F8hVx+zYc\nmjSU13gm8hlCSoVw6NwhRm0YZXU4SmVK1ZJV+ar7V27fhkOThvIauf1z2yvF31v/HofOHbI4IqUy\np3FQY2Z0mAG4bxsOTRrKqzQOanyzUvxb968UN8a8ZIwRY0wJq2NR7qFHaA+3bsOhSUN5ncRK8a8P\nfM33B7+3Opx0GWPKYRsf/IjVsSj34s5tODRpKK9TJrCMvaX4gO8GEBsfa3FE6RoHDALcs8ZTWcad\n23Bo0lBe6fm6z1OxaEV2R+1m6tapVoeTijGmA3BMRHZYHYtyT+7ahkOThvJKeXPlZfS9tm5FXl/z\nOueunsvxGIwxq4wxu9KYOgCvAq87cIy+xpgtxpgtUVFRrg9auRV3bMOhSUN5rU53daJJUBPOXj3L\niHUjcvz8ItJCREJSTsAhoAKwwxhzGCgLbDPGlE7jGFNFJEJEIkqWLJmzb0C5BXdrw6FJQ3ktYwzj\nWo7DYJj06yS3qUwUkZ0iUkpEgkUkGDgK1BKRkxaHptyUO7Xh0KShvFrNMjV5rOZjxMbH8vL3L1sd\njlJZ5i5tODRpKK/3zj3v2B/BXXlwpdXhpJJwxXHG6jiU+3OHNhyaNJTXu63gbQxtNBSAAd8PsLwi\nUanssLoNhyYN5ROer/c8wUWC2XV6F5/v+NzqcJTKMqvbcGjSUD4hX658vN3sbQBeW/OaWzzvrlRW\npWzD0X5u+xwr05o0lM/oEdqDmqVrciz6GBN/mWh1OEplS9I2HL8c+4WHFz+cI7deNWkon+Fn/Bh1\nr63L9PfWv8eZK1r3rDxb0jYcS/ct5cXvXnR5Gw5NGsqntKjYgpZ3tuTitYu8s+4dq8NRKtuStuGY\n9Oskxm8a79LzadJQPmdki5EYDJM3T9YxN5RXSNmGY+GehS47lyYN5XPCS4fTM7wnN+JvMHT1UKvD\nUcopeoT24L3m7yEIjyx+hJ//+dkl57EkaRhjihljVhpj/kj4WzSNbWoYYzYaY3YbY343xjxoRazK\nO41oNoK8/nlZuGch/1z4x+pwlHKKVxq8wpO1n+Ra3DXe/eldl5wjl0uOmrHBwA8i8r4xZnDC/Csp\ntrkCPCoifxhjbge2GmO+E5HzOR2s8j7lC5fnk3afEHF7BOUKl7M6HKWcwhjDh20+JLhIMM/Vfc4l\n57AqaXQAmia8ngmsJUXSEJEDSV4fN8acBkoCmjSUU/QM72l1CEo5XS6/XAxuONhlx7eqTuM2ETmR\n8PokcNutNjbGRAJ5gIOuDkwppVT6XHalYYxZBaQaHwBIVvMoImKMSffBYmNMGWAW0EtE4tPZpi/Q\nF6B8+fJZjlkppdStuSxpiEiL9NYZY04ZY8qIyImEpJBmxynGmELA/wFDRWTTLc41FZgKEBERoeMt\nK6WUi1h1e2oZ0CvhdS/gq5QbGGPyAEuAz0XEdQ8dK6WUcphVSeN94F5jzB9Ai4R5jDERxphPE7bp\nBjQGehtjtidMNawJVymlFFj09JSInAWap7F8C/B4wuvZwOwcDk0ppdQtaItwpZRSDtOkoVQOM8YM\nN8YcS3LbtY3VMSnlKKsa9ynl68aJyBirg1Aqs/RKQymllMM0aShljWcSOuL8LK0OOxMZY/oaY7YY\nY7ZERUXlZHxKpUmThlIuYIxZZYzZlcbUAZgC3AnUAE4AY9M7johMFZEIEYkoWbJkDkWvVPqMq4cG\nzGnGmCjg70zuVgLwhbE/feF95sR7DBIRp3yDG2OCgeUiEuLAtlq20+YL7xFc/z4dKtdeVxGelQ+z\nMWaLiES4Ih534gvv086w1mEAAAMYSURBVBPeY2IXOgmznYBdjuynZTttvvAewX3ep9clDaU8wKiE\n3g0EOAw8aW04SjlOk4ZSOUxEdCAP5bG0ItxmqtUB5BBfeJ++8B4zwxf+PXzhPYKbvE+vqwhXSinl\nOnqloZRSymE+nzSMMa2MMfuNMX8aY1w3sK6FjDGHjTE7E/o52mJ1PM6S0DDutDFmV5JlxYwxK40x\nfyT8TbfhnDfzhXINWratiM2nk4Yxxh+YDLQGqgE9jDHVrI3KZZqJSA13eGTPiWYArVIsGwz8ICKV\ngB8S5n2Kj5Vr0LKdo3w6aQCRwJ8ickhErgPzgA4Wx6QcJCLrgH9TLO4AzEx4PRPomKNBuQct1x7O\nncu2ryeNO4B/kswfTVjmbQT43hiz1RjT1+pgXOy2JA3nTgK3WRmMRXylXIOW7Ryn7TR8Q0MROWaM\nKQWsNMbsS/gl49VERIwx+nigd9OyncN8/UrjGFAuyXzZhGVeRUSOJfw9DSzBdvvCW50yxpQBW3cd\nwGmL47GCT5Rr0LJtRRC+njQ2A5WMMRWMMXmA7sAyi2NyKmNMAWNMYOJr4D4c7OvIQy0DeiW87gV8\nZWEsVvH6cg1atrGobPv07SkRiTXGPAN8B/gDn4nIbovDcrbbgCXGGLD9f88RkW+tDck5jDFzgaZA\nCWPMUeAN4H3gS2PMf7H1CNvNugit4SPlGrRsW1K2tUW4Ukoph/n67SmllFKZoElDKaWUwzRpKKWU\ncpgmDaWUUg7TpKGUUsphmjSUUko5TJOGUkoph2nS8FHGmDrGmN+NMfkSWtbuNsaEWB2XUtmlZdu1\ntHGfDzPGvA3kA/IDR0XkPYtDUsoptGy7jiYNH5bQL9FmIAaoLyJxFoeklFNo2XYdvT3l24oDBYFA\nbL/KlPIWWrZdRK80fJgxZhm2Ud0qAGVE5BmLQ1LKKbRsu45P93Lry4wxjwI3RGROwpjSPxtj7hGR\n1VbHplR2aNl2Lb3SUEop5TCt01BKKeUwTRpKKaUcpklDKaWUwzRpKKWUcpgmDaWUUg7TpKGUUsph\nmjSUUko5TJOGUkoph/0/QFnDcKjFyz0AAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}