JuliaFEM.jl/notebooks/2015-06-25-shape-functions.ipynb

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  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sympy import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "xi = DeferredVector(\"xi\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Matrix([\n",
       "[          -xi[1] - xi[2] - xi[3] + 1],\n",
       "[                               xi[1]],\n",
       "[                               xi[2]],\n",
       "[                               xi[3]],\n",
       "[4*xi[1]*(-xi[1] - xi[2] - xi[3] + 1)],\n",
       "[                       4*xi[1]*xi[2]],\n",
       "[4*xi[2]*(-xi[1] - xi[2] - xi[3] + 1)],\n",
       "[4*xi[3]*(-xi[1] - xi[2] - xi[3] + 1)],\n",
       "[                       4*xi[1]*xi[3]],\n",
       "[                       4*xi[2]*xi[3]]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def c3d10():\n",
    "    N1 = 1 - xi[1] - xi[2] - xi[3]\n",
    "    N2 = xi[1]\n",
    "    N3 = xi[2]\n",
    "    N4 = xi[3]\n",
    "    N5 = 4*xi[1]*(1-xi[1]-xi[2]-xi[3])\n",
    "    N6 = 4*xi[1]*xi[2]\n",
    "    N7 = 4*xi[2]*(1-xi[1]-xi[2]-xi[3])\n",
    "    N8 = 4*xi[3]*(1-xi[1]-xi[2]-xi[3])\n",
    "    N9 = 4*xi[1]*xi[3]\n",
    "    N10 = 4*xi[2]*xi[3]\n",
    "    N = Matrix([N1, N2, N3, N4, N5, N6, N7, N8, N9, N10])\n",
    "    dN = Matrix([N.diff(xi[1]).T, N.diff(xi[2]).T, N.diff(xi[3]).T]).T\n",
    "    return N, dN\n",
    "\n",
    "N, dN = c3d10()\n",
    "N"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Matrix([\n",
       "[                              -1,                               -1,                               -1],\n",
       "[                               1,                                0,                                0],\n",
       "[                               0,                                1,                                0],\n",
       "[                               0,                                0,                                1],\n",
       "[-8*xi[1] - 4*xi[2] - 4*xi[3] + 4,                         -4*xi[1],                         -4*xi[1]],\n",
       "[                         4*xi[2],                          4*xi[1],                                0],\n",
       "[                        -4*xi[2], -4*xi[1] - 8*xi[2] - 4*xi[3] + 4,                         -4*xi[2]],\n",
       "[                        -4*xi[3],                         -4*xi[3], -4*xi[1] - 4*xi[2] - 8*xi[3] + 4],\n",
       "[                         4*xi[3],                                0,                          4*xi[1]],\n",
       "[                               0,                          4*xi[3],                          4*xi[2]]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dN"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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    "name": "ipython",
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