run_fem_frame.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Just run the below cell and enter the correct inputs in the required simple format** <br><br>\n",
    "You will get the complete analysis along with the External and Reaction force diagram as shown in the output cell<br><br>\n",
    "*In case you are stuck, please follow the example cell* <br><br>\n",
    "**Note:** Make sure you have *fem_frame_complete_analysis.ipynb* file in the same folder as *run_fem_frame.ipynb* file"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Enter total number of nodes: 3\n",
      "\n",
      "Enter (x,y) coordinates of node-1 (Example: 2,-3.7): 0,0\n",
      "Enter support type at node-1 ---> write 'P/p' for Planar and 'I/i' for Inclined: p\n",
      "Enter constraint type at node-1 ---> write 'f' for Fixed, 'fr' for Free, 'h' for hinged and 'r' for Roller support: f\n",
      "\n",
      "Enter (x,y) coordinates of node-2 (Example: 2,-3.7): 6,0\n",
      "Enter support type at node-2 ---> write 'P/p' for Planar and 'I/i' for Inclined: p\n",
      "Enter constraint type at node-2 ---> write 'f' for Fixed, 'fr' for Free, 'h' for hinged and 'r' for Roller support: h\n",
      "Enter external force Mz at node-2 (Example: 0.75): -4\n",
      "\n",
      "Enter (x,y) coordinates of node-3 (Example: 2,-3.7): 3,4\n",
      "Enter support type at node-3 ---> write 'P/p' for Planar and 'I/i' for Inclined: p\n",
      "Enter constraint type at node-3 ---> write 'f' for Fixed, 'fr' for Free, 'h' for hinged and 'r' for Roller support: fr\n",
      "Enter external force (Fx,Fy,Mz) at node-3 (Example: 1.2,-2,4.76 or 0,2.75,0): 3,-4,-6\n",
      "\n",
      "Enter total number of elements: 2\n",
      "\n",
      "Enter (From_node, To_node) for element-1 (Example: 2,3): 1,3\n",
      "Enter Young's modulus of element-1 (Example: 2.27e10 if E = 2.27*10^10 or 2.7e10*(2**(0.5)) if E = 2.7*sqrt(2)*10^10): 1.5e2\n",
      "Enter area of element-1 (Example: 2.27e-3 if A = 2.27*10^-3 or 2.7*(2**(0.5)) if A = 2.7*sqrt(2)): 1e-2\n",
      "Enter Izz of element-1 (Example: 2.27e-3 if I = 2.27*10^-3 or 2.7*(2**(0.5)) if I = 2.7*sqrt(2)): 2.7e-2*sqrt(2)\n",
      "\n",
      "Enter (From_node, To_node) for element-2 (Example: 2,3): 2,3\n",
      "Enter Young's modulus of element-2 (Example: 2.27e10 if E = 2.27*10^10 or 2.7e10*(2**(0.5)) if E = 2.7*sqrt(2)*10^10): 1\n",
      "Enter area of element-2 (Example: 2.27e-3 if A = 2.27*10^-3 or 2.7*(2**(0.5)) if A = 2.7*sqrt(2)): 2e-4\n",
      "Enter Izz of element-2 (Example: 2.27e-3 if I = 2.27*10^-3 or 2.7*(2**(0.5)) if I = 2.7*sqrt(2)): 3e-1\n",
      "\n",
      "LOCAL STIFFNESS MATRIX k1:\n",
      "\n",
      "[[ 0.4599 -0.1199 -1.0997 -0.4599  0.1199 -1.0997]\n",
      " [-0.1199  0.3899  0.8248  0.1199 -0.3899  0.8248]\n",
      " [-1.0997  0.8248  4.5821  1.0997 -0.8248  2.291 ]\n",
      " [-0.4599  0.1199  1.0997  0.4599 -0.1199  1.0997]\n",
      " [ 0.1199 -0.3899 -0.8248 -0.1199  0.3899 -0.8248]\n",
      " [-1.0997  0.8248  2.291   1.0997 -0.8248  4.5821]]\n",
      "\n",
      "LOCAL STIFFNESS MATRIX k2:\n",
      "\n",
      "[[ 0.0184  0.0138 -0.0576 -0.0184 -0.0138 -0.0576]\n",
      " [ 0.0138  0.0104 -0.0432 -0.0138 -0.0104 -0.0432]\n",
      " [-0.0576 -0.0432  0.24    0.0576  0.0432  0.12  ]\n",
      " [-0.0184 -0.0138  0.0576  0.0184  0.0138  0.0576]\n",
      " [-0.0138 -0.0104  0.0432  0.0138  0.0104  0.0432]\n",
      " [-0.0576 -0.0432  0.12    0.0576  0.0432  0.24  ]]\n",
      "\n",
      "GLOBAL STIFFNESS MATRIX K:\n",
      "\n",
      "[[ 0.4599 -0.1199 -1.0997  0.      0.      0.     -0.4599  0.1199 -1.0997]\n",
      " [-0.1199  0.3899  0.8248  0.      0.      0.      0.1199 -0.3899  0.8248]\n",
      " [-1.0997  0.8248  4.5821  0.      0.      0.      1.0997 -0.8248  2.291 ]\n",
      " [ 0.      0.      0.      0.0184  0.0138 -0.0576 -0.0184 -0.0138 -0.0576]\n",
      " [ 0.      0.      0.      0.0138  0.0104 -0.0432 -0.0138 -0.0104 -0.0432]\n",
      " [ 0.      0.      0.     -0.0576 -0.0432  0.24    0.0576  0.0432  0.12  ]\n",
      " [-0.4599  0.1199  1.0997 -0.0184 -0.0138  0.0576  0.4783 -0.1061  1.1573]\n",
      " [ 0.1199 -0.3899 -0.8248 -0.0138 -0.0104  0.0432 -0.1061  0.4003 -0.7816]\n",
      " [-1.0997  0.8248  2.291  -0.0576 -0.0432  0.12    1.1573 -0.7816  4.8221]]\n",
      "\n",
      "TRANSFORMED GLOBAL STIFFNESS MATRIX K:\n",
      "\n",
      "[[ 0.4599 -0.1199 -1.0997  0.      0.      0.     -0.4599  0.1199 -1.0997]\n",
      " [-0.1199  0.3899  0.8248  0.      0.      0.      0.1199 -0.3899  0.8248]\n",
      " [-1.0997  0.8248  4.5821  0.      0.      0.      1.0997 -0.8248  2.291 ]\n",
      " [ 0.      0.      0.      0.0184  0.0138 -0.0576 -0.0184 -0.0138 -0.0576]\n",
      " [ 0.      0.      0.      0.0138  0.0104 -0.0432 -0.0138 -0.0104 -0.0432]\n",
      " [ 0.      0.      0.     -0.0576 -0.0432  0.24    0.0576  0.0432  0.12  ]\n",
      " [-0.4599  0.1199  1.0997 -0.0184 -0.0138  0.0576  0.4783 -0.1061  1.1573]\n",
      " [ 0.1199 -0.3899 -0.8248 -0.0138 -0.0104  0.0432 -0.1061  0.4003 -0.7816]\n",
      " [-1.0997  0.8248  2.291  -0.0576 -0.0432  0.12    1.1573 -0.7816  4.8221]]\n",
      "\n",
      "DISPLACEMENT MATRIX Q:\n",
      "\n",
      "[[  0.    ]\n",
      " [  0.    ]\n",
      " [  0.    ]\n",
      " [  0.    ]\n",
      " [  0.    ]\n",
      " [-13.7474]\n",
      " [ 34.3609]\n",
      " [-25.2507]\n",
      " [-13.2415]]\n",
      "\n",
      "REACTION FORCE R:\n",
      "\n",
      "[[-4.2693]\n",
      " [ 3.046 ]\n",
      " [28.2759]\n",
      " [ 1.2693]\n",
      " [ 0.954 ]\n",
      " [ 0.    ]\n",
      " [ 0.    ]\n",
      " [ 0.    ]\n",
      " [ 0.    ]]\n",
      "\n",
      "\n",
      "External Forces\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x648 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Reaction Forces\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x648 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Analysis ends here!\n"
     ]
    }
   ],
   "source": [
    "%run fem_frame_complete_analysis.ipynb"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Done\n"
     ]
    }
   ],
   "source": [
    "'''\n",
    "Enter total number of nodes: 3\n",
    "\n",
    "Enter (x,y) coordinates of node-1 (Example: 2,-3.7): 0,0\n",
    "Enter support type at node-1 ---> write 'P/p' for Planar and 'I/i' for Inclined: p\n",
    "Enter constraint type at node-1 ---> write 'f' for Fixed, 'fr' for Free, 'h' for hinged and 'r' for Roller support: f\n",
    "\n",
    "Enter (x,y) coordinates of node-2 (Example: 2,-3.7): 6,0\n",
    "Enter support type at node-2 ---> write 'P/p' for Planar and 'I/i' for Inclined: p\n",
    "Enter constraint type at node-2 ---> write 'f' for Fixed, 'fr' for Free, 'h' for hinged and 'r' for Roller support: h\n",
    "Enter external force Mz at node-2 (Example: 0.75): -3\n",
    "\n",
    "Enter (x,y) coordinates of node-3 (Example: 2,-3.7): 3,4\n",
    "Enter support type at node-3 ---> write 'P/p' for Planar and 'I/i' for Inclined: p\n",
    "Enter constraint type at node-3 ---> write 'f' for Fixed, 'fr' for Free, 'h' for hinged and 'r' for Roller support: fr\n",
    "Enter external force (Fx,Fy,Mz) at node-3 (Example: 1.2,-2,4.76 or 0,2.75,0): 3,-6,4\n",
    "\n",
    "Enter total number of elements: 2\n",
    "\n",
    "Enter (From_node, To_node) for element-1 (Example: 2,3): 1,3\n",
    "Enter Young's modulus of element-1 (Example: 2.27e10 if E = 2.27*10^10 or 2.7e10*(2**(0.5)) if E = 2.7*sqrt(2)*10^10): 1\n",
    "Enter area of element-1 (Example: 2.27e-3 if A = 2.27*10^-3 or 2.7*(2**(0.5)) if A = 2.7*sqrt(2)): 1\n",
    "Enter Izz of element-1 (Example: 2.27e-3 if I = 2.27*10^-3 or 2.7*(2**(0.5)) if I = 2.7*sqrt(2)): 1\n",
    "\n",
    "Enter (From_node, To_node) for element-2 (Example: 2,3): 2,3\n",
    "Enter Young's modulus of element-2 (Example: 2.27e10 if E = 2.27*10^10 or 2.7e10*(2**(0.5)) if E = 2.7*sqrt(2)*10^10): 1\n",
    "Enter area of element-2 (Example: 2.27e-3 if A = 2.27*10^-3 or 2.7*(2**(0.5)) if A = 2.7*sqrt(2)): 1\n",
    "Enter Izz of element-2 (Example: 2.27e-3 if I = 2.27*10^-3 or 2.7*(2**(0.5)) if I = 2.7*sqrt(2)): 2.7*(2**(0.5))\n",
    "'''\n",
    "print(\"Done\")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}