{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Eigenvalues and eigenvectors of stiffness matrices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy.utilities.codegen import codegen\n",
    "from sympy import *\n",
    "from sympy import init_printing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "init_printing()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "r, s, t, x, y, z = symbols('r s t x y z') \n",
    "k, m, n = symbols('k m n', integer=True)\n",
    "rho, nu, E = symbols('rho, nu, E')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Predefinition"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The constitutive model tensor in Voigt notation (plane stress) is\n",
    "$$C = \\frac{E}{(1 - \\nu^2)}\n",
    "\\begin{pmatrix}\n",
    "1 & \\nu & 0\\\\\n",
    "\\nu & 1 & 0\\\\\n",
    "0 & 0 & \\frac{1 - \\nu}{2)}\n",
    "\\end{pmatrix}$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{E}{1 - \\nu^{2}} & \\frac{E \\nu}{1 - \\nu^{2}} & 0\\\\\\frac{E \\nu}{1 - \\nu^{2}} & \\frac{E}{1 - \\nu^{2}} & 0\\\\0 & 0 & \\frac{E \\left(\\frac{1}{2} - \\frac{\\nu}{2}\\right)}{1 - \\nu^{2}}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡  E      E⋅ν             ⎤\n",
       "⎢──────  ──────      0    ⎥\n",
       "⎢     2       2           ⎥\n",
       "⎢1 - ν   1 - ν            ⎥\n",
       "⎢                         ⎥\n",
       "⎢ E⋅ν      E              ⎥\n",
       "⎢──────  ──────      0    ⎥\n",
       "⎢     2       2           ⎥\n",
       "⎢1 - ν   1 - ν            ⎥\n",
       "⎢                         ⎥\n",
       "⎢                  ⎛1   ν⎞⎥\n",
       "⎢                E⋅⎜─ - ─⎟⎥\n",
       "⎢                  ⎝2   2⎠⎥\n",
       "⎢  0       0     ─────────⎥\n",
       "⎢                       2 ⎥\n",
       "⎣                  1 - ν  ⎦"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "K_factor = E/(1 - nu**2)\n",
    "C = K_factor * Matrix([\n",
    "        [1, nu, 0],\n",
    "        [nu, 1, 0],\n",
    "         [0, 0, (1 - nu)/2]])\n",
    "\n",
    "C"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Interpolation functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The shape functions are"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{\\left(r + 1\\right) \\left(s + 1\\right)}{4}\\\\\\frac{\\left(1 - r\\right) \\left(s + 1\\right)}{4}\\\\\\frac{\\left(1 - r\\right) \\left(1 - s\\right)}{4}\\\\\\frac{\\left(1 - s\\right) \\left(r + 1\\right)}{4}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡(r + 1)⋅(s + 1)⎤\n",
       "⎢───────────────⎥\n",
       "⎢       4       ⎥\n",
       "⎢               ⎥\n",
       "⎢(1 - r)⋅(s + 1)⎥\n",
       "⎢───────────────⎥\n",
       "⎢       4       ⎥\n",
       "⎢               ⎥\n",
       "⎢(1 - r)⋅(1 - s)⎥\n",
       "⎢───────────────⎥\n",
       "⎢       4       ⎥\n",
       "⎢               ⎥\n",
       "⎢(1 - s)⋅(r + 1)⎥\n",
       "⎢───────────────⎥\n",
       "⎣       4       ⎦"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N = S(1)/4*Matrix([(1 + r)*(1 + s),\n",
    "         (1 - r)*(1 + s),\n",
    "         (1 - r)*(1 - s),\n",
    "         (1 + r)*(1 - s)])\n",
    "N"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Thus, the interpolation matrix renders"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Derivatives interpolation matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAoEAAABNCAYAAADZ5r5eAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAUMUlEQVR4Ae1dTY7cNhpNG8YsB44DzAHau1n65wRxbmDHJ/DkBm7MCYzODZJezsqxb2DnBIF9A/sAA8RpzHIW43mvLMVqNquKFD9Jj+RHgF2iRFLve99T9VekKJ18+vTpq5bSycnJXdhzAbvutWSX21IPA67BenzVMlLXYRvedT+24UdVK26qAsvFNVwoP6DdbeRbue29vjNQyoBrsJRBb2/BgOvQgsXt+3A/bu+DHhDcoNCQP+3JL2shASN/75AZBL6oBbPjbIsB12Bb/qzVGtdhrZ67itv9eJUPL81jALHd+z3x3W4aeDoS+DNO8T44zYeg7EVnwBlwBpwBZ8AZcAacgToYOAfMcHb0AfY9IvxpEPgTf3lwZ0pCZMmOfx/qfkDbVyntvI4zYMWAa9CKSe9nLgOuwbnMebsWGHD963sRsRkH+K4k+O0f2LELAm9cOZJYQAc/oeprdP4jPt8gcxrWkzOwGgOuwdWo9hPtYcA1uIcY390FA67/Ntw8HQnMsegUlc8gAg4xMgh8nNPY66YxMPDLEddLZE7V30F+kTNii/qtJtegiGc71qlrcCUNdqyxlRiedRrXf0BbjTq9EdiQWjxDRQYmXDjyBzLF4MmegV/RJUdcz4Yh3ecov4TQnG/8CAEXrkF7zc3psVedugbnqGVem141No+tdVq5/q/zXJ1Os4NABCCcR75EUPIY+QTbvBfw4XUu0vewT+Rn6S3arwk+OGd/Co7/vNcS2wx6WK5m1fYSnlpCg0vg7KHPXnXqGlxP3b1qbD2G88/k+r/OWa06zQ4CYXq40uQj9nFKWCnxWYG1J06xx3j9Dfv5WJ9btRtYgN81WECecdNedVqDBulq/y40FvxG3an5sRb9r+muKr8L5waB9xn1InP07iVGqJJXFS/lEWA5ReaClZ04sc1p05pHF/eNrnI0kGnf8c9H2/5LH7sGNXy8T4et61RSg5SEfxdqXBilKMT9KKv/Ut4L2lf5XXgz12AEfNeWG+f2sUR94OIzDZtYpYyLfxzl4yjrvtTtfYGuwX2SWHd/zzpV1SAV4N+F614HS51N2Y/K+l/KH4f6rfm7cM5I4CEu/JgNA+PQ/ziaMu11DAy/me70bWdgAwZcpxuQ3tkpXWOdObxSc6vVqQeB2oobRwS1UTq63hlwnfaugOXtd40tz7GfoZyB6nSaPB2M4c7de+YOcYQhYq4W3pvQB+8jiM2bk7jbOP4k0phvIzn4HEILbJHzbrlrHO2LYRh/cYxva4nVkdsHH9HHXD6fepFcou5T+P7K/aalvrbCERJciivsr5JyczpN4d3C167DFKZ3dVxje6hK+H9r8p0bnt5C/2GfDZSr1WlyEHhMcClORB98rtC1BFHxsTN8HArfQJKdLLBln3TBBrDnEpzwDGPANz3bGERV9V5n2gQj7k0NmbNd6msrHCH2UlxhfzWUyWVrOk3h3cLXrsMUpnf3N7rG0qi6Vss1do2SxXbU/F1YNB2MfwCvF2O1sGNlbImm8fEwY8A3bTIGhrHHx0zrdbOt6mtVXMbCcJ2CUGVfK2NL1KJrzDWWKJVNq1Wp09lBIL5YOHr3EJ+xQGVTTyhjyyCGD4S+H6nP0bR3w6+8yOG+dqn6WhXXAuroXqfKvlbGlqFF15j/v82Qy2ZVq9TprCAQXywM/B5sRvWBEytjOwD72iEEeXwUz8fhS3x3fLDtexSeXmvQ4Q5VX6viWkIivetU2dfK2HK06Brz/7c5etmqbq06nRUEgmS+0ozvsVVMythy+eKo3wN8mT9jxvYF8rcQ25XFErmdNlRf1dequJZyfc86Vfa1MrZcLbrGchlbp35LGrNgrDqdJi8MGdlBMHIX25KLEpSxjfzlfCLY42KK6GKanH5arKvqa1VcS2qgV50q+1oZ2xwtusbmsLZsm9Y0ZsFWjTqdMxL4BIa+siBs0gdvqLTocwlsE5i+KcSAqq9VcQm5rhkoyr5WxtaMAFYwRNmPythWcE0bp8gaCUTkz6Ffvp/XNA3RM0e9ZqelsM0G5A0XY0DV16q4FnNExx0r+1oZW8eSyTZd2Y/K2LKJ7rxB8kggnM7FILcQsMlNBStj61xf5uar+loVl7kDvEM+Dsa/C10HizLgGluUXu98wkDOSOBDtLsDcYYjgefY9xbBIVezbpWUsW3FSavnVfW1Kq5WdbClXcq+Vsa2pc9qO7eyH5Wx1ebnzfHytRRc6PEW+R4CueRVpwj8TtHmPfLXw3QuNjWSMjYFhsAPfX4Bv3ElU9VJ1dequKbObkkHU7vW3lb2tTK2tf0Unq8m/Sv7URlb6PMWy3N0jDa7W/sQA5wkTwdPyRs7GPZdoMwHR0skZWxbEwRu7iJzJPefyJzSqjqp+loV1+js1nQw2rXFp7KvlbFt4avxnLXpX9mPythGf7f6aaXj2SOBrRLbg10QD4P2c/wKuNODvW5jnAHXQZwX39sHA67/PvzcupVzdIw2ZSOBrZPq9jkDzoAz4Aw4A86AM9A6AzdbN3Bt+4YI+zuc9/Vwbk678hV7Zxh5k1tZPWD0D2dAggG/fiTcYALCfWlCo3eyIQM9aNiDwGUExvvuGAR+h8DvDYTEBTRcSONBIEjw5AwcYcCvnyMEVXTYfVmRsxxqlIGmNbxpEIjgiKNk58iXyAyUeI/aCwROyauUUV8mwR4Ger8gc779DQNAgsOn33tHIjZIrWlsAwpXO2Wv10+LGu3Vl6tdLDNO1KLOZtCQ3KQXDW8aBMIbvyI/R5C0e2XcINK3+OQIWnWjZiNm4Of07zgdnCw6r7gIA01pbBGGRDrt+PppTqMd+1LkaorCaE5nUSuNdvai4VmPiLHgGIESR8tOQfSf7wzGNkcEWX5pcY4N+3iIc+9GAS0wgKtHyM8s+uqpj8Y11rIrTa8fZaI60Gg3vnSdKTNQhK1pDW8WBMIlj5FjgdJv2M/n2XGquLoE3JwS5uv11Ke0b1dHbj7gJjWWT8PBFlI6qOj6OUhqxsFmNVqJL6X0n6Gb3KrN6iyXiJz6lWiYJs3W8ZZBIKPrWOJoINO+45+P6v5lEBgLbjdHTEEj8yZX3od5C9svkVseYdynodo1VqQlcR3IXj9FpO9v3LJGJX0prv/9Sik70rLOypg53FpSw4RspeObh+1f5ijAj6N8Hw+cgeRXlzACyABQMggENt5n+UN1pM4A3LLGZtBxpYmyDpSvnyskGhRa16iqL5X1byCra120rrNrBhvuUNUwTbTS8Q1DvnK6GocuxxGZadsxMPxmutO3nYFMBlxjmYR59dUZcI2uTnmXJ3Sdden2NKO3CgJHdOOI4Fj2T2fAmgHXmDWj3p81A65Ra0a9vxgDrrMYK53v43TwX5H/jfy/FbkYR/tipxx/tfweO6i8D8Pun47hwxAu39ccTWjPe/Vi927w4r2N408iDT+gT970ezCVYjvYuebBJjVWSrWFDtAH9cjHTaT+U7lE3afQ6btD+C2wHepf8FizGi31pWvMVK3N6mwfSxb6KdUwsVngiNlogO0v6Jdx31cMAv+D/Dfk1UYF8c/gEkbglNEVLeM/lhqfE7g3wKOxxxJ4OYvVAVePsJ+P0/kxdjxlH9oWYUs5h1KdVjVWyrGFDsgtcNwrxRK2t8AW9qlcblmjpb50jdkpt2Wd7WPJQj+lGiY2CxwxGw2w/Rf9Mu5bL/CLGMLFE2PANz08jgRKLq6YAk3ZRgAn+9BoZWwp3CbU6UJjCTwcrKKsA2VsB0lNP9iNRlV9qYorXUJJNbvRWRIbMyspa2UuttVG/yKc84HQ9yP7OcLwboigI4fr2QWncATvIT5jwe6mhihjMySmeY2VcqWsA2VspbxP2nehUVVfquKa6MNqswudWZEV60dZKyXYNgsCEeT9DKI/DuB3nGObwdL3yE93Oyr+M9jyQNEEZWyWfLWusVKulHWgjK2U92n7HjSq6ktVXFN9WG33oDMrrmL9KGulFNtmQeBANEf9HsCIZ8zYvkD+FoI9eAP50Fb9g6/Fey4KUhmbNWUta6yUK2UdKGMr5T1s37pGVX2piivUh1W5dZ1Z8RTrR1krRdg2eVj0yDCCPd5gHl0MMdap8RMB7V3gllzYooxtCV+3qrFSrpR1oIytlPdY+5Y1qupLVVwxfVjta1lnVhzF+lHWigW2rUcCY5y3sO8JLrhXhobwpl6r/qyxGZrpXa3IgLIOlLGt6KImTqXqS1VcTTi9MSOUtVKMbdORwMaEsjMHkTmHZvl+XrM0/ILjqGlRWgJbESBvvAkDyjpQxraJsyo+qaovVXFV7OpmoStrxQqbjwQayhdO4cKWWwja5KaClbEZusC7OsKAsg6UsR2h1Q8HDKj6UhVXQJ8XBRhQ1oolNh8JtBXbQ3R3Bw4KRwLPse8tgkOuiN4qKWPbipMez6usA2VsPWqlxGZVX6riKuHa2y7DgLJWzLDxLRJcxPAW+R6ClOpX5SLYoj0XsIUroTZNwHIKAO+Rvwae4ulcK2MGjv6F/v6uhm1qo5Ivp7ha2lbVKDk+hM21cVyFShwd8uVxS5apMfAj/z24jPXr9KqkwUMWp+BU1PBoUy421N/dtoa45OTm2Entn4MTf4AdfOMIp2U3TQPJ4zt9L1B+AcKtFnfMsm3CER/SzQCVSQLbZyif/05wSvhyiq2lbUWNjvzuw+baGBna/6nG0T5f7rdg2SMTfqS/B5dlYdneJxxLf4en4lTT8NR7pdhaHAnkWzrOEXDdmRLl218YgGiq4KgWnF+Y9a21GHBtHGfaOTrMkfNzmB+Lo7VwXAtOC5+wD9j750igLwyxYtX7cQacAWfAGXAGnAFnoCIGsqaDh+jxO9j3erCR0658NdoZRt7kVsQOGDf5AFfnOPHvw8k/bD0VvAkJjZ20R/27juMi7lELcSaO73UNHedobg3X4Vzm6mm39PUzZySQK1+ZGdj8iE8uxBjvL8OmJziN/Lwe+OGDnnmvoqc2GOhG/67jo4LtRgtHmdhTwTW0hxjb3a5DWz5lelvj+kkeCQQYBnq/IHMu+Q0CHAY3X+HT770jEVcTuToDZxwpJU/jApGrtbxUDQOd6t91HFFop1qIMJG0yzWURFN+JddhPmcVtlj8+rmRSgqCPY788TEnnP4dp4NTm/dWj+9DJlcvkf9ApiM9VcxAp/p3HUc026kWIkwk7XINJdGUX8l1mM9ZhS0Wv36Sg8AJeXxI4W4UcLKvaBO/aB4hPyvqRKQxbQGUS1ygj5G5+pqPhSFns1NL/MwmQaehuf51TPuCZAkdf+m9ma0utDDXW66hucxlt3MdZlOm32Ct6ycrCAQojmjxtWjqD5Xms4m2SlwQwmngMX3EhmnQPHZc+LklRznQZXBWpP8cfvfVrUHHm2mjIi1sxhGE5Rrad3UZ7a9Eh1tqMIdpNZyrXD83cxhCXQaBigHN+HYBDp3yV9EtXByciv0NASsXr6yZ6Lj7OD8fRMpg8KVK0Dx8YShwdNAfwjhl9X+Q0HkHJXUspA1ZLQhx5Bqad+3ltJLUoZAGD3IpjnOV60fiYdFwBKdQTzcI2A4KROWg86PiCcfhDDgDzoAz4AzUzQBiCn9YdN0udPTOgDPgDDgDzoAz4AyUMXCjrLm3dgacAWfAGXAGnAFnwBmokYHkewIxfPjpmIGYzuX08t6EPjjHzXv2wsR7527j+JPwAMp8NM3B5+xZYIucN3tXKY6l+KEhpdiyyZjZoBQn2lNLvyJPF+ccQnOJg0+P3bdZiusQAKtjVraX2mqFI+SlFFfY39yyBQ7naPeM2b3/L1rmx8q2Uh1a4Qivo1JcYX9LlS1wtsCh3xO4lMIM+4XQ/J5JQz69K2fAGXAGnAFnoFcGEFPY3BOIjmQfGq2CTQVHTOzK2KZ4VXGq4ppyZ7WtaqsKLhUcMX+rYFPBEXKkiivEmVJWtUUVV8ipMs6lsM2+JxCAODr1EJ+p024h34uVVbCp4IgRrYxtilcVpyquKXdW26q2quBSwRHztwo2FRwhR6q4QpwpZVVbVHGFnCrjXBLbrCAQgBj48fVxckkFmwqOmIOUsU3xquJUxTXlzmpb1VYVXCo4Yv5WwaaCI+RIFVeIM6WsaosqrpBTZZxLY5sVBIJAzic/D4kUKatgU8ERc4sytileVZyquKbcWW2r2qqCSwVHzN8q2FRwhByp4gpxppRVbVHFFXKqjHNRbNlBIKLSu2DvQ8igQlkFmwqOmE+UsU3xquJUxTXlzmpb1VYVXCo4Yv5WwaaCI+RIFVeIM6WsaosqrpBTZZxrYMsOAkHgEzxO41VIZGGZr6Kz6HMJbHNMs8ZhxQ9tscY2h5+UNqo4VXGlcJpbR9VWFVwqOGJ+VcGmgiPkSBVXiDOlrGqLKq6QU2Wci2NLfk4gWUNUymHJn0IGS8sIKvmsNubZaSlsuYCWwGHBD+1YAlsuPyn1VXGq4krhNLeOqq0quFRwxPyqgk0FR8iRKq4QZ0pZ1RZVXCGnyjjXwpY8EghAXAxyCwGJ3FSwCjYVHKHQWVbGNsWrilMV15Q7q21VW1VwqeCI+VsFmwqOkCNVXCHOlLKqLaq4Qk6Vca6JLWckkG/6uANw4UjgOfa9RXD4c0jyimUVbCo4YtQrY5viVcWpimvKndW2qq0quFRwxPytgk0FR8iRKq4QZ0pZ1RZVXCGnyjhXwzZ9Y0hIEMuvENxFX9mGwO8Ux98jfz1MV7K+RFLBpoIj5hRlbFO8qjhVcU25s9pWtVUFlwqOmL9VsKngCDlSxRXiTCmr2qKKK+RUGWcJNrRlnMZ47VpC7HZyE3s5vXt27ejnHe9i+9Ep7w0cg8MLlF+gM4uFHbHTZe1TwaaCI0aeMrYpXlWcqrim3Fltq9qqgksFR8zfKthUcIQcqeIKcaaUVW1RxRVyqozTANs57OXtfNH0fxtaptfdDhQIAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{s}{4} + \\frac{1}{4} & 0 & - \\frac{s}{4} - \\frac{1}{4} & 0 & \\frac{s}{4} - \\frac{1}{4} & 0 & \\frac{1}{4} - \\frac{s}{4} & 0\\\\0 & \\frac{r}{4} + \\frac{1}{4} & 0 & \\frac{1}{4} - \\frac{r}{4} & 0 & \\frac{r}{4} - \\frac{1}{4} & 0 & - \\frac{r}{4} - \\frac{1}{4}\\\\\\frac{r}{4} + \\frac{1}{4} & \\frac{s}{4} + \\frac{1}{4} & \\frac{1}{4} - \\frac{r}{4} & - \\frac{s}{4} - \\frac{1}{4} & \\frac{r}{4} - \\frac{1}{4} & \\frac{s}{4} - \\frac{1}{4} & - \\frac{r}{4} - \\frac{1}{4} & \\frac{1}{4} - \\frac{s}{4}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡s   1           s   1           s   1          1   s          ⎤\n",
       "⎢─ + ─    0    - ─ - ─     0     ─ - ─    0     ─ - ─      0   ⎥\n",
       "⎢4   4           4   4           4   4          4   4          ⎥\n",
       "⎢                                                              ⎥\n",
       "⎢       r   1            1   r          r   1             r   1⎥\n",
       "⎢  0    ─ + ─     0      ─ - ─     0    ─ - ─     0     - ─ - ─⎥\n",
       "⎢       4   4            4   4          4   4             4   4⎥\n",
       "⎢                                                              ⎥\n",
       "⎢r   1  s   1   1   r     s   1  r   1  s   1    r   1   1   s ⎥\n",
       "⎢─ + ─  ─ + ─   ─ - ─   - ─ - ─  ─ - ─  ─ - ─  - ─ - ─   ─ - ─ ⎥\n",
       "⎣4   4  4   4   4   4     4   4  4   4  4   4    4   4   4   4 ⎦"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dHdr = zeros(2,4)\n",
    "for i in range(4):\n",
    "    dHdr[0,i] = diff(N[i],r)\n",
    "    dHdr[1,i] = diff(N[i],s)\n",
    "\n",
    "jaco = eye(2)  # Jacobian matrix, identity for now\n",
    "dHdx = jaco*dHdr\n",
    "\n",
    "B = zeros(3,8)\n",
    "for i in range(4):\n",
    "    B[0, 2*i] = dHdx[0, i]\n",
    "    B[1, 2*i+1] = dHdx[1, i]\n",
    "    B[2, 2*i] = dHdx[1, i]\n",
    "    B[2, 2*i+1] = dHdx[0, i]\n",
    "    \n",
    "B"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Being the stiffness matrix integrand\n",
    "$$K_\\text{int} = B^T C B$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "K_int = B.T*C*B"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Analytic integration"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The stiffness matrix is obtained integrating the product of the interpolator-derivatives (displacement-to-strains) matrix with the constitutive tensor and itself, i.e.\n",
    "$$\\begin{align*}\n",
    "K &= \\int\\limits_{-1}^{1}\\int\\limits_{-1}^{1} K_\\text{int} dr\\, ds\\\\\n",
    " &= \\int\\limits_{-1}^{1}\\int\\limits_{-1}^{1} B^T C\\, B\\, dr\\, ds \\enspace .\n",
    "\\end{align*}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{1}{2} - \\frac{\\nu}{6} & \\frac{\\nu}{8} + \\frac{1}{8} & - \\frac{\\nu}{12} - \\frac{1}{4} & \\frac{3 \\nu}{8} - \\frac{1}{8} & \\frac{\\nu}{12} - \\frac{1}{4} & - \\frac{\\nu}{8} - \\frac{1}{8} & \\frac{\\nu}{6} & \\frac{1}{8} - \\frac{3 \\nu}{8}\\\\\\frac{\\nu}{8} + \\frac{1}{8} & \\frac{1}{2} - \\frac{\\nu}{6} & \\frac{1}{8} - \\frac{3 \\nu}{8} & \\frac{\\nu}{6} & - \\frac{\\nu}{8} - \\frac{1}{8} & \\frac{\\nu}{12} - \\frac{1}{4} & \\frac{3 \\nu}{8} - \\frac{1}{8} & - \\frac{\\nu}{12} - \\frac{1}{4}\\\\- \\frac{\\nu}{12} - \\frac{1}{4} & \\frac{1}{8} - \\frac{3 \\nu}{8} & \\frac{1}{2} - \\frac{\\nu}{6} & - \\frac{\\nu}{8} - \\frac{1}{8} & \\frac{\\nu}{6} & \\frac{3 \\nu}{8} - \\frac{1}{8} & \\frac{\\nu}{12} - \\frac{1}{4} & \\frac{\\nu}{8} + \\frac{1}{8}\\\\\\frac{3 \\nu}{8} - \\frac{1}{8} & \\frac{\\nu}{6} & - \\frac{\\nu}{8} - \\frac{1}{8} & \\frac{1}{2} - \\frac{\\nu}{6} & \\frac{1}{8} - \\frac{3 \\nu}{8} & - \\frac{\\nu}{12} - \\frac{1}{4} & \\frac{\\nu}{8} + \\frac{1}{8} & \\frac{\\nu}{12} - \\frac{1}{4}\\\\\\frac{\\nu}{12} - \\frac{1}{4} & - \\frac{\\nu}{8} - \\frac{1}{8} & \\frac{\\nu}{6} & \\frac{1}{8} - \\frac{3 \\nu}{8} & \\frac{1}{2} - \\frac{\\nu}{6} & \\frac{\\nu}{8} + \\frac{1}{8} & - \\frac{\\nu}{12} - \\frac{1}{4} & \\frac{3 \\nu}{8} - \\frac{1}{8}\\\\- \\frac{\\nu}{8} - \\frac{1}{8} & \\frac{\\nu}{12} - \\frac{1}{4} & \\frac{3 \\nu}{8} - \\frac{1}{8} & - \\frac{\\nu}{12} - \\frac{1}{4} & \\frac{\\nu}{8} + \\frac{1}{8} & \\frac{1}{2} - \\frac{\\nu}{6} & \\frac{1}{8} - \\frac{3 \\nu}{8} & \\frac{\\nu}{6}\\\\\\frac{\\nu}{6} & \\frac{3 \\nu}{8} - \\frac{1}{8} & \\frac{\\nu}{12} - \\frac{1}{4} & \\frac{\\nu}{8} + \\frac{1}{8} & - \\frac{\\nu}{12} - \\frac{1}{4} & \\frac{1}{8} - \\frac{3 \\nu}{8} & \\frac{1}{2} - \\frac{\\nu}{6} & - \\frac{\\nu}{8} - \\frac{1}{8}\\\\\\frac{1}{8} - \\frac{3 \\nu}{8} & - \\frac{\\nu}{12} - \\frac{1}{4} & \\frac{\\nu}{8} + \\frac{1}{8} & \\frac{\\nu}{12} - \\frac{1}{4} & \\frac{3 \\nu}{8} - \\frac{1}{8} & \\frac{\\nu}{6} & - \\frac{\\nu}{8} - \\frac{1}{8} & \\frac{1}{2} - \\frac{\\nu}{6}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡ 1   ν     ν   1      ν    1  3⋅ν   1    ν    1     ν   1      ν      1   3⋅ν\n",
       "⎢ ─ - ─     ─ + ─    - ── - ─  ─── - ─    ── - ─   - ─ - ─      ─      ─ - ───\n",
       "⎢ 2   6     8   8      12   4   8    8    12   4     8   8      6      8    8 \n",
       "⎢                                                                             \n",
       "⎢ ν   1     1   ν    1   3⋅ν      ν        ν   1    ν    1   3⋅ν   1     ν    \n",
       "⎢ ─ + ─     ─ - ─    ─ - ───      ─      - ─ - ─    ── - ─   ─── - ─   - ── - \n",
       "⎢ 8   8     2   6    8    8       6        8   8    12   4    8    8     12   \n",
       "⎢                                                                             \n",
       "⎢  ν    1  1   3⋅ν    1   ν      ν   1      ν      3⋅ν   1    ν    1    ν   1 \n",
       "⎢- ── - ─  ─ - ───    ─ - ─    - ─ - ─      ─      ─── - ─    ── - ─    ─ + ─ \n",
       "⎢  12   4  8    8     2   6      8   8      6       8    8    12   4    8   8 \n",
       "⎢                                                                             \n",
       "⎢3⋅ν   1      ν        ν   1    1   ν    1   3⋅ν     ν    1   ν   1     ν    1\n",
       "⎢─── - ─      ─      - ─ - ─    ─ - ─    ─ - ───   - ── - ─   ─ + ─     ── - ─\n",
       "⎢ 8    8      6        8   8    2   6    8    8      12   4   8   8     12   4\n",
       "⎢                                                                             \n",
       "⎢ ν    1     ν   1      ν      1   3⋅ν    1   ν     ν   1      ν    1  3⋅ν   1\n",
       "⎢ ── - ─   - ─ - ─      ─      ─ - ───    ─ - ─     ─ + ─    - ── - ─  ─── - ─\n",
       "⎢ 12   4     8   8      6      8    8     2   6     8   8      12   4   8    8\n",
       "⎢                                                                             \n",
       "⎢  ν   1    ν    1   3⋅ν   1     ν    1   ν   1     1   ν    1   3⋅ν      ν   \n",
       "⎢- ─ - ─    ── - ─   ─── - ─   - ── - ─   ─ + ─     ─ - ─    ─ - ───      ─   \n",
       "⎢  8   8    12   4    8    8     12   4   8   8     2   6    8    8       6   \n",
       "⎢                                                                             \n",
       "⎢   ν      3⋅ν   1    ν    1    ν   1      ν    1  1   3⋅ν    1   ν      ν   1\n",
       "⎢   ─      ─── - ─    ── - ─    ─ + ─    - ── - ─  ─ - ───    ─ - ─    - ─ - ─\n",
       "⎢   6       8    8    12   4    8   8      12   4  8    8     2   6      8   8\n",
       "⎢                                                                             \n",
       "⎢1   3⋅ν     ν    1   ν   1     ν    1   3⋅ν   1      ν        ν   1    1   ν \n",
       "⎢─ - ───   - ── - ─   ─ + ─     ── - ─   ─── - ─      ─      - ─ - ─    ─ - ─ \n",
       "⎣8    8      12   4   8   8     12   4    8    8      6        8   8    2   6 \n",
       "\n",
       " ⎤\n",
       " ⎥\n",
       " ⎥\n",
       " ⎥\n",
       "1⎥\n",
       "─⎥\n",
       "4⎥\n",
       " ⎥\n",
       " ⎥\n",
       " ⎥\n",
       " ⎥\n",
       " ⎥\n",
       " ⎥\n",
       " ⎥\n",
       " ⎥\n",
       " ⎥\n",
       " ⎥\n",
       " ⎥\n",
       " ⎥\n",
       " ⎥\n",
       " ⎥\n",
       " ⎥\n",
       " ⎥\n",
       " ⎥\n",
       " ⎥\n",
       " ⎥\n",
       " ⎥\n",
       " ⎥\n",
       " ⎥\n",
       " ⎥\n",
       " ⎦"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "K = zeros(8,8)\n",
    "for i in range(8):\n",
    "    for j in range(8):\n",
    "        K[i,j] = integrate(K_int[i,j], (r,-1,1), (s,-1,1))\n",
    "\n",
    "simplify(K/K_factor)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can check some numerical vales for $E=1$ Pa and $\\nu=1/3$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "K_num = K.subs([(E, 1), (nu, S(1)/3)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left[ \\left( 0, \\  3, \\  \\left[ \\left[\\begin{matrix}1\\\\0\\\\1\\\\1\\\\0\\\\1\\\\0\\\\0\\end{matrix}\\right], \\  \\left[\\begin{matrix}1\\\\0\\\\1\\\\0\\\\1\\\\0\\\\1\\\\0\\end{matrix}\\right], \\  \\left[\\begin{matrix}-1\\\\1\\\\-1\\\\0\\\\0\\\\0\\\\0\\\\1\\end{matrix}\\right]\\right]\\right), \\  \\left( \\frac{1}{2}, \\  2, \\  \\left[ \\left[\\begin{matrix}-1\\\\0\\\\1\\\\0\\\\-1\\\\0\\\\1\\\\0\\end{matrix}\\right], \\  \\left[\\begin{matrix}0\\\\-1\\\\0\\\\1\\\\0\\\\-1\\\\0\\\\1\\end{matrix}\\right]\\right]\\right), \\  \\left( \\frac{3}{4}, \\  2, \\  \\left[ \\left[\\begin{matrix}0\\\\-1\\\\-1\\\\0\\\\0\\\\1\\\\1\\\\0\\end{matrix}\\right], \\  \\left[\\begin{matrix}1\\\\0\\\\0\\\\-1\\\\-1\\\\0\\\\0\\\\1\\end{matrix}\\right]\\right]\\right), \\  \\left( \\frac{3}{2}, \\  1, \\  \\left[ \\left[\\begin{matrix}-1\\\\-1\\\\1\\\\-1\\\\1\\\\1\\\\-1\\\\1\\end{matrix}\\right]\\right]\\right)\\right]$"
      ],
      "text/plain": [
       "⎡⎛      ⎡⎡1⎤  ⎡1⎤  ⎡-1⎤⎤⎞  ⎛        ⎡⎡-1⎤  ⎡0 ⎤⎤⎞  ⎛        ⎡⎡0 ⎤  ⎡1 ⎤⎤⎞  ⎛  \n",
       "⎢⎜      ⎢⎢ ⎥  ⎢ ⎥  ⎢  ⎥⎥⎟  ⎜        ⎢⎢  ⎥  ⎢  ⎥⎥⎟  ⎜        ⎢⎢  ⎥  ⎢  ⎥⎥⎟  ⎜  \n",
       "⎢⎜      ⎢⎢0⎥  ⎢0⎥  ⎢1 ⎥⎥⎟  ⎜        ⎢⎢0 ⎥  ⎢-1⎥⎥⎟  ⎜        ⎢⎢-1⎥  ⎢0 ⎥⎥⎟  ⎜  \n",
       "⎢⎜      ⎢⎢ ⎥  ⎢ ⎥  ⎢  ⎥⎥⎟  ⎜        ⎢⎢  ⎥  ⎢  ⎥⎥⎟  ⎜        ⎢⎢  ⎥  ⎢  ⎥⎥⎟  ⎜  \n",
       "⎢⎜      ⎢⎢1⎥  ⎢1⎥  ⎢-1⎥⎥⎟  ⎜        ⎢⎢1 ⎥  ⎢0 ⎥⎥⎟  ⎜        ⎢⎢-1⎥  ⎢0 ⎥⎥⎟  ⎜  \n",
       "⎢⎜      ⎢⎢ ⎥  ⎢ ⎥  ⎢  ⎥⎥⎟  ⎜        ⎢⎢  ⎥  ⎢  ⎥⎥⎟  ⎜        ⎢⎢  ⎥  ⎢  ⎥⎥⎟  ⎜  \n",
       "⎢⎜      ⎢⎢1⎥  ⎢0⎥  ⎢0 ⎥⎥⎟  ⎜        ⎢⎢0 ⎥  ⎢1 ⎥⎥⎟  ⎜        ⎢⎢0 ⎥  ⎢-1⎥⎥⎟  ⎜  \n",
       "⎢⎜0, 3, ⎢⎢ ⎥, ⎢ ⎥, ⎢  ⎥⎥⎟, ⎜1/2, 2, ⎢⎢  ⎥, ⎢  ⎥⎥⎟, ⎜3/4, 2, ⎢⎢  ⎥, ⎢  ⎥⎥⎟, ⎜3/\n",
       "⎢⎜      ⎢⎢0⎥  ⎢1⎥  ⎢0 ⎥⎥⎟  ⎜        ⎢⎢-1⎥  ⎢0 ⎥⎥⎟  ⎜        ⎢⎢0 ⎥  ⎢-1⎥⎥⎟  ⎜  \n",
       "⎢⎜      ⎢⎢ ⎥  ⎢ ⎥  ⎢  ⎥⎥⎟  ⎜        ⎢⎢  ⎥  ⎢  ⎥⎥⎟  ⎜        ⎢⎢  ⎥  ⎢  ⎥⎥⎟  ⎜  \n",
       "⎢⎜      ⎢⎢1⎥  ⎢0⎥  ⎢0 ⎥⎥⎟  ⎜        ⎢⎢0 ⎥  ⎢-1⎥⎥⎟  ⎜        ⎢⎢1 ⎥  ⎢0 ⎥⎥⎟  ⎜  \n",
       "⎢⎜      ⎢⎢ ⎥  ⎢ ⎥  ⎢  ⎥⎥⎟  ⎜        ⎢⎢  ⎥  ⎢  ⎥⎥⎟  ⎜        ⎢⎢  ⎥  ⎢  ⎥⎥⎟  ⎜  \n",
       "⎢⎜      ⎢⎢0⎥  ⎢1⎥  ⎢0 ⎥⎥⎟  ⎜        ⎢⎢1 ⎥  ⎢0 ⎥⎥⎟  ⎜        ⎢⎢1 ⎥  ⎢0 ⎥⎥⎟  ⎜  \n",
       "⎢⎜      ⎢⎢ ⎥  ⎢ ⎥  ⎢  ⎥⎥⎟  ⎜        ⎢⎢  ⎥  ⎢  ⎥⎥⎟  ⎜        ⎢⎢  ⎥  ⎢  ⎥⎥⎟  ⎜  \n",
       "⎣⎝      ⎣⎣0⎦  ⎣0⎦  ⎣1 ⎦⎦⎠  ⎝        ⎣⎣0 ⎦  ⎣1 ⎦⎦⎠  ⎝        ⎣⎣0 ⎦  ⎣1 ⎦⎦⎠  ⎝  \n",
       "\n",
       "      ⎡⎡-1⎤⎤⎞⎤\n",
       "      ⎢⎢  ⎥⎥⎟⎥\n",
       "      ⎢⎢-1⎥⎥⎟⎥\n",
       "      ⎢⎢  ⎥⎥⎟⎥\n",
       "      ⎢⎢1 ⎥⎥⎟⎥\n",
       "      ⎢⎢  ⎥⎥⎟⎥\n",
       "      ⎢⎢-1⎥⎥⎟⎥\n",
       "2, 1, ⎢⎢  ⎥⎥⎟⎥\n",
       "      ⎢⎢1 ⎥⎥⎟⎥\n",
       "      ⎢⎢  ⎥⎥⎟⎥\n",
       "      ⎢⎢1 ⎥⎥⎟⎥\n",
       "      ⎢⎢  ⎥⎥⎟⎥\n",
       "      ⎢⎢-1⎥⎥⎟⎥\n",
       "      ⎢⎢  ⎥⎥⎟⎥\n",
       "      ⎣⎣1 ⎦⎦⎠⎦"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "K_num.eigenvects()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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