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Truss_Element.ipynb

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+{
+  "nbformat": 4,
+  "nbformat_minor": 0,
+  "metadata": {
+    "colab": {
+      "private_outputs": true,
+      "provenance": [],
+      "authorship_tag": "ABX9TyMxahuOixvTTe6EdHJBA9EE",
+      "include_colab_link": true
+    },
+    "kernelspec": {
+      "name": "python3",
+      "display_name": "Python 3"
+    },
+    "language_info": {
+      "name": "python"
+    }
+  },
+  "cells": [
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "view-in-github",
+        "colab_type": "text"
+      },
+      "source": [
+        "<a href=\"https://colab.research.google.com/github/GEORMC/Nnumerical_Methods_Course/blob/main/Truss_Element.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "id": "7_YgV2riW2t1"
+      },
+      "outputs": [],
+      "source": [
+        "import numpy as np\n",
+        " # Input data\n",
+        "coordinates = np.array([\n",
+        " [0, 0],\n",
+        " [4, 0],\n",
+        " [8, 0],\n",
+        " [4, -6]\n",
+        "])\n",
+        "connectivity = np.array([\n",
+        " [0, 3],\n",
+        " [1, 3],\n",
+        " [2, 3]\n",
+        "])\n",
+        "E = 1 # Young's Modulus (Pa)\n",
+        "A = 1  # Cross-sectional area (m^2)\n",
+        " # Define supports (0 for not supported, 1 for supported)\n",
+        "supports = np.array([\n",
+        " [1, 1],\n",
+        " [1, 1],\n",
+        " [1, 1],\n",
+        " [0, 0]\n",
+        "])\n",
+        " # Define applied loads (0 for no load, specify direction and value)\n",
+        "applied_loads = np.array([\n",
+        " [0, 0],\n",
+        " [0, 0], # Node 1, applied horizontal load\n",
+        " [0, 0], # Node 2, applied vertical load\n",
+        " [100, -100]\n",
+        "])\n",
+        " # Create freedom matrix\n",
+        "num_nodes = len(coordinates)\n",
+        "num_dofs = 2 * num_nodes\n",
+        "num_elements=len(connectivity)\n",
+        "dofs = np.zeros((num_elements, 4), dtype=int)\n",
+        "NodeDof=np.zeros((num_nodes, 2) , dtype=int)\n",
+        " # Initialize global stiffness matrix and force vector\n",
+        "KG = np.zeros((num_dofs, num_dofs))\n",
+        "kt_global = np.zeros((num_dofs, num_dofs))\n",
+        "F_global = np.zeros(num_dofs)\n",
+        "  # Calculate Dof Matrix\n",
+        "for i, (node1, node2) in enumerate(connectivity):\n",
+        " dofs[i,:] = np.array([2 * node1, 2 * node1 + 1, 2 * node2, 2 * node2 + 1])\n",
+        " NodeDof[node1,0]=np.array([2 * node1])\n",
+        " NodeDof[node1,1]=np.array([2 * node1 + 1])\n",
+        " NodeDof[node2,0]=np.array([ 2 * node2])\n",
+        " NodeDof[node2,1]=np.array([2* node2+1])\n",
+        " print(NodeDof)\n",
+        "# Calculate element lengths and stiffness matrices\n",
+        "for i, (node1, node2) in enumerate(connectivity):\n",
+        " x1, y1 = coordinates[node1]\n",
+        " x2, y2 = coordinates[node2]\n",
+        "  L = np.sqrt((x2 - x1) ** 2 + (y2 - y1) ** 2)\n",
+        " c = (x2 - x1) / L\n",
+        " s = (y2 - y1) / L\n",
+        "  k_local = (E * A / L) * np.array([\n",
+        "  [c ** 2, c * s, -c ** 2, -c * s],\n",
+        "  [c * s, s ** 2, -c * s, -s ** 2],\n",
+        "  [-c ** 2, -c * s, c ** 2, c * s],\n",
+        "  [-c * s, -s ** 2, c * s, s ** 2]\n",
+        " ])\n",
+        "  # Assemble local stiffness matrix into global stiffness matrix\n",
+        "\n",
+        " KG[np.ix_(dofs[i,:], dofs[i,:])] += k_local\n",
+        " # print(k_local)\n",
+        " # print(np.ix_(dofs[i,:], dofs[i,:]) )\n",
+        " # print(K_global)\n",
+        " print(KG)\n",
+        "kt_global=KG*1\n",
+        "# Apply boundary conditions and applied loads\n",
+        "for node in range(num_nodes):\n",
+        " for i in range(2):\n",
+        "  if supports[node, i] == 1:\n",
+        "   fixed_dof = NodeDof[node,i]\n",
+        "   kt_global[fixed_dof, :] = 0\n",
+        "   kt_global[:, fixed_dof] = 0\n",
+        "   kt_global[fixed_dof, fixed_dof] = 1\n",
+        "   F_global[fixed_dof] = 0\n",
+        "  else:\n",
+        "   applied_force = applied_loads[node, i]\n",
+        "   F_global[2 * node + i] = applied_force\n",
+        " print(KG)\n",
+        "# Solve for displacements\n",
+        "displacement = np.linalg.solve(kt_global, F_global)\n",
+        "print(KG)\n",
+        "# Calculate reaction forces\n",
+        "reaction_forces = np.dot(KG, displacement)\n",
+        " print(KG)\n",
+        "print(\"Displacements (mm):\")\n",
+        "print(displacement * 1000)\n",
+        "print(\"Reaction Forces (N):\")\n",
+        "print(reaction_forces)\n",
+        "\n",
+        "\n"
+      ]
+    }
+  ]
+}