AE-245 - Lista 02 - Q2.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Biblioteca\n",
    "import numpy as np\n",
    "import numpy.ma as ma\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Coordinate matrix\n",
    "coord = np.array([[1, 0, 0],[2, 2, 0],[3, 0,-0.5]])\n",
    "nnos = np.size(coord,0)\n",
    "\n",
    "# Incidence matrix\n",
    "inci = np.array([[1, 1, 2, 80e9, 2e-2*(4e-2)**3/12, 2e-2*4e-2],[2,2,3,80e9, 5e-3*(5e-3)**3/12, (5e-3)**2]])\n",
    "nel = np.size(inci,0)\n",
    "\n",
    "# Boundary conditions\n",
    "bc = np.array([[1,1,0],[1,2,0],[1,3,0],[3,1,0],[3,2,0]])\n",
    "\n",
    "# Mask stiffness matrix\n",
    "mask = np.zeros((8,8))\n",
    "for i in range(0, np.size(bc,0)):\n",
    "    if bc[i,1] == 1:\n",
    "        mask[3*bc[i,0]-3,3*bc[i,0]-3] = 1\n",
    "    elif bc[i,1] == 2:\n",
    "        mask[3*bc[i,0]-2,3*bc[i,0]-2] = 1\n",
    "    elif bc[i,1] == 3:\n",
    "        mask[3*bc[i,0]-1,3*bc[i,0]-1] = 1\n",
    "mask = ma.masked_equal(mask, 1)\n",
    "mask = ma.mask_rowcols(mask)\n",
    "mask = (mask==False)\n",
    "\n",
    "# Mask load vector\n",
    "maskv = np.zeros(8)\n",
    "for i in range(0, np.size(bc,0)):\n",
    "    if bc[i,1] == 1:\n",
    "        maskv[3*bc[i,0]-3] = 1\n",
    "    elif bc[i,1] == 2:\n",
    "        maskv[3*bc[i,0]-2] = 1\n",
    "    elif bc[i,1] == 3:\n",
    "        maskv[3*bc[i,0]-1] = 1\n",
    "maskv = ma.masked_equal(maskv, 1)\n",
    "maskv = (maskv==False)\n",
    "\n",
    "#  Load vector\n",
    "qx = 0\n",
    "qy = 10e3\n",
    "L = 2\n",
    "\n",
    "f = np.array([[qx*L/2],[qy*L/2], [qy*L**2/12], [qx*L/2],[qy*L/2], [-qy*L**2/12], [0],[0]])\n",
    "\n",
    "kg = np.zeros((3*(nnos-1)+2,3*(nnos-1)+2)) # global stiffness matrix pre-allocation\n",
    "\n",
    "# Global matrix assembly\n",
    "i = 0\n",
    "node1 = inci[i,1] # first node element\n",
    "node2 = inci[i,2] # second node element\n",
    "\n",
    "x1 = coord[int(node1) - 1, 1]\n",
    "x2 = coord[int(node2) - 1, 1]\n",
    "\n",
    "y1 = coord[int(node1) - 1, 2]\n",
    "y2 = coord[int(node2) - 1, 2]\n",
    "\n",
    "# local stiffness matrix\n",
    "inertia = inci[i,4]\n",
    "E = inci[i,3] \n",
    "A = inci[i,5]\n",
    "l = np.sqrt((x2 - x1)**2 + (y2 - y1)**2)\n",
    "\n",
    "ke = E/l**3*np.array([[A*l**2, 0, 0,-A*l**2, 0, 0], [0, 12*inertia, 6*l*inertia, 0,-12*inertia, 6*l*inertia], [0, 6*l*inertia, 4*l**2*inertia, 0, -6*l*inertia, 2*l**2*inertia], [-A*l**2, 0, 0,A*l**2, 0, 0], [0, -12*inertia, -6*l*inertia, 0, 12*inertia, -6*l*inertia], [0, 6*l*inertia, 2*l**2*inertia,0, -6*l*inertia, 4*l**2*inertia] ])\n",
    "\n",
    "# localization vector\n",
    "loc = [3*node1-3,3*node1-2, 3*node1-1,3*node2-3, 3*node2-2,3*node2-1]\n",
    "    \n",
    "# global stiffness matrix \n",
    "kg[[[int(loc[0])],[int(loc[1])],[int(loc[2])], [int(loc[3])], [int(loc[4])], [int(loc[5])] ], [int(loc[0]),int(loc[1]),int(loc[2]),int(loc[3]), int(loc[4]), int(loc[5])]] = kg[[[int(loc[0])],[int(loc[1])],[int(loc[2])], [int(loc[3])], [int(loc[4])], [int(loc[5])] ], [int(loc[0]),int(loc[1]),int(loc[2]),int(loc[3]), int(loc[4]), int(loc[5])]] + ke\n",
    "\n",
    "i = 1\n",
    "node1 = inci[i,1] # first node element\n",
    "node2 = inci[i,2] # second node element\n",
    "\n",
    "x1 = coord[int(node1) - 1, 1]\n",
    "x2 = coord[int(node2) - 1, 1]\n",
    "\n",
    "y1 = coord[int(node1) - 1, 2]\n",
    "y2 = coord[int(node2) - 1, 2]\n",
    "\n",
    "if (x2-x1) ==0:\n",
    "    if y2 > y1:\n",
    "        theta = 2*np.arctan(1)\n",
    "    else:\n",
    "        theta =-2*np.arctan(1)\n",
    "else:\n",
    "    theta = np.arctan((y2-y1)/(x2-x1))\n",
    "\n",
    "c = np.cos(theta)\n",
    "s = np.sin(theta)\n",
    "\n",
    "inertia = inci[i,4]\n",
    "E = inci[i,3] \n",
    "A = inci[i,5]\n",
    "l = np.sqrt((x2 - x1)**2 + (y2 - y1)**2)\n",
    "\n",
    "\n",
    "# local stiffness matrix\n",
    "ke = E*A/l*np.array([[c**2, c*s, -c**2, -c*s], [c*s, s**2, -c*s, -s**2], [-c**2, -c*s, c**2, c*s], [-c*s, -s**2, c*s, s**2]])\n",
    "\n",
    "# localization vector\n",
    "loc = [3*node1-3,3*node1-2,3*node2-3, 3*node2-2]\n",
    "\n",
    "# global stiffness matrix \n",
    "kg[[[int(loc[0])],[int(loc[1])],[int(loc[2])], [int(loc[3])]], [int(loc[0]),int(loc[1]),int(loc[2]),int(loc[3])]] = kg[[[int(loc[0])],[int(loc[1])],[int(loc[2])], [int(loc[3])]], [int(loc[0]),int(loc[1]),int(loc[2]),int(loc[3])]] +  ke\n",
    "\n",
    "\n",
    "kg_aux = kg[mask.data]\n",
    "kg_aux = np.reshape(kg_aux, (2*nnos-np.size(bc,1), 2*nnos-np.size(bc,1)))\n",
    "f_aux  = f[maskv.data]\n",
    "\n",
    "# displacement\n",
    "u = np.zeros((8, 1))\n",
    "u[maskv.data] = np.linalg.solve(kg_aux, f_aux)\n",
    "u_ = u[[0,1,3,4,6,7]]\n",
    "u_ = np.reshape(u_,(nnos,2))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "factor = 1.1\n",
    "new_coord = coord[:,1:3] + factor*u_\n",
    "\n",
    "fig, ax = plt.subplots(figsize = (12, 7))\n",
    "\n",
    "# original truss\n",
    "for i in range(0, np.size(inci,0)):\n",
    "    x1 = coord[int(inci[i,1]-1), 1]\n",
    "    x2 = coord[int(inci[i,2]-1), 1]\n",
    "    \n",
    "    y1 = coord[int(inci[i,1]-1), 2]\n",
    "    y2 = coord[int(inci[i,2]-1), 2]\n",
    "    \n",
    "    plt.plot([x1,x2], [y1,y2], 'bo-')\n",
    "    \n",
    "    s  = \"{}\".format(i+1)\n",
    "    plt.text((x1+x2)/2, (y1+y2)/2 + 0.05, s, fontsize = 15)\n",
    "    \n",
    "# deformed truss\n",
    "for i in range(0, np.size(inci,0)):\n",
    "    x1 = new_coord[int(inci[i,1]-1), 0]\n",
    "    x2 = new_coord[int(inci[i,2]-1), 0]\n",
    "    \n",
    "    y1 = new_coord[int(inci[i,1]-1), 1]\n",
    "    y2 = new_coord[int(inci[i,2]-1), 1]\n",
    "    \n",
    "    plt.plot([x1,x2], [y1,y2], 'ro--')    \n",
    "    \n",
    "fig.savefig('fem2_2.png',dpi=300)                              # salvar figura como png (dpi = número de pixels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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
}