FEM 2D Truss.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import numpy.ma as ma\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Input"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "E = 80e9 # youngs modulus\n",
    "A = 1e-4 # section area"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Coordinate matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "coord = np.array([[1, 0, 0],[2, 1.2,0.3],[3, 2.4,0],[4,1.2,0.8]])\n",
    "nnos = np.size(coord,0)  # number of nodes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Incidence matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "inci = np.array([[1, 1, 2],[2,2,3],[3,3,4],[4,4,1],[5,2,4]])\n",
    "nel = np.size(inci,0) # number of elements"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Boundary conditions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "#   bc=[node | degree of freedom | value]\n",
    "#\n",
    "#   Degree of freedom 1 --> x\n",
    "#   Degree of freedom 2 --> y\n",
    "\n",
    "bc = np.array([[1,1,0],[1,2,0],[3,2,0]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Mask stiffness matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "mask = np.zeros((2*nnos,2*nnos))\n",
    "for i in range(0, np.size(bc,0)):\n",
    "    if bc[i,1] == 1:\n",
    "        mask[2*bc[i,0]-2,2*bc[i,0]-2] = 1\n",
    "    elif bc[i,1] == 2:\n",
    "        mask[2*bc[i,0]-1,2*bc[i,0]-1] = 1\n",
    "mask = ma.masked_equal(mask, 1)\n",
    "mask = ma.mask_rowcols(mask)\n",
    "mask = (mask==False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Mask load vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "maskv = np.zeros(2*nnos)\n",
    "for i in range(0, np.size(bc,0)):\n",
    "    if bc[i,1] == 1:\n",
    "        maskv[2*bc[i,0]-2] = 1\n",
    "    elif bc[i,1] == 2:\n",
    "        maskv[2*bc[i,0]-1] = 1\n",
    "maskv = ma.masked_equal(maskv, 1)\n",
    "maskv = (maskv==False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#  Load vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "#   F = [node | degree of freedom | value]\n",
    "#\n",
    "#   Degree of freedom 1 --> Fx\n",
    "#   Degree of freedom 2 --> Fy\n",
    "\n",
    "load = np.array([[4,1,-30e3],[4,2,20e3]])\n",
    "\n",
    "f = np.zeros((2*nnos,1)) # global force vector pre-allocation\n",
    "\n",
    "for i in range(0,np.size(load,0)):\n",
    "    if load[i,1] == 1:\n",
    "        f[int(2*load[i,0]-2)] = load[i,2]\n",
    "    elif load[i,1] == 2:\n",
    "        f[int(2*load[i,0]-1)] = load[i,2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Global matrix assembly"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False, False,  True,  True,  True, False,  True,  True])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kg = np.zeros((2*nnos,2*nnos)) # global stiffness matrix pre-allocation\n",
    "for i in range(0,nel):\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",
    "    l = np.sqrt((x2 - x1)**2 + (y2 - y1)**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",
    "    # 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",
    "\n",
    "    # localization vector\n",
    "    loc = [2*node1-2,2*node1-1,2*node2-2,2*node2-1]\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",
    "kg_aux = kg[mask.data]\n",
    "kg_aux = np.reshape(kg_aux, (2*nnos-np.size(bc,0), 2*nnos-np.size(bc,0)))\n",
    "f_aux  = f[maskv.data]\n",
    "maskv.data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Displacement"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "u = np.zeros((2*nnos, 1))\n",
    "u[maskv.data] = np.linalg.solve(kg_aux, f_aux)\n",
    "u_ = np.reshape(u,(nnos,2))\n",
    "displacement_x = u_[:,0]\n",
    "displacement_y = u_[:,1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Post-processing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "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 = 5\n",
    "new_coord = coord[:,1:3] + factor*u_\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], 'r--')    \n",
    "    \n",
    "# load applied\n",
    "for i in range(0, np.size(load,0)):\n",
    "    node = load[i,0]\n",
    "    X = coord[int(node - 1), 1]\n",
    "    Y = coord[int(node - 1), 2]\n",
    "    U = 0\n",
    "    V = 0\n",
    "    if load[i,1] == 1:\n",
    "        if load[i,2] > 0:\n",
    "            U = 1\n",
    "        else:\n",
    "            U = -1\n",
    "    elif load[i,1] == 2:\n",
    "        if load[i,2] > 0:\n",
    "            V = 1\n",
    "        else:\n",
    "            V = -1\n",
    "    ax.quiver(X, Y, U, V)\n",
    "    \n",
    "fig.savefig('fem1a.png',dpi=300)                              # save figure (dpi = number of pixels)\n",
    "\n",
    "plt.title('Treliça', fontsize = 20)\n",
    "plt.xlabel('Deslocamento horizontal', fontsize = 15)\n",
    "plt.ylabel('Deslocamento vertical', fontsize = 15)\n",
    "    \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Stress"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Normal force in element     1 = 49477.27 N.\n",
      "Normal force in element     2 = 49477.27 N.\n",
      "Normal force in element     3 = 57688.82 N.\n",
      "Normal force in element     4 = 21633.31 N.\n",
      "Normal force in element     5 = 24000.00 N.\n"
     ]
    }
   ],
   "source": [
    "stress = np.zeros((nel, 1))\n",
    "\n",
    "for i in range(0,nel):\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",
    "    l = np.sqrt((x2 - x1)**2 + (y2 - y1)**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",
    "\n",
    "    c = np.cos(theta)\n",
    "    s = np.sin(theta)\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 = [2*node1-2, 2*node1-1, 2*node2-2, 2*node2-1]\n",
    "\n",
    "    d = u[[int(loc[0]),int(loc[1]),int(loc[2]), int(loc[3])]]\n",
    "\n",
    "    elforce = np.matmul(ke,d)\n",
    "\n",
    "    stress[i] = np.sqrt(elforce[1]**2 + elforce[2]**2)/A\n",
    "    \n",
    "    force_element = np.sqrt(elforce[1]**2 + elforce[2]**2)\n",
    "    \n",
    "    print(\"Normal force in element {0:5d} = {1:8.2f} N.\".format(i + 1, force_element[0]))\n",
    "\n",
    "    if ((x2-x1)*elforce[3])<0:\n",
    "            stress[i]=-stress[i]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Reaction forces"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 3.00000000e+04]\n",
      " [-5.82076609e-11]\n",
      " [-2.00000000e+04]]\n"
     ]
    }
   ],
   "source": [
    "F = np.matmul(kg,u)\n",
    "maskv = (maskv==False)\n",
    "print(F[maskv.mask])"
   ]
  }
 ],
 "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
}