HW9_Calculations.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# HW9: Finite Elements (Rayleigh-Ritz) and Stability"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import *\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.ticker import AutoMinorLocator\n",
    "plt.rc('text',usetex=True)\n",
    "init_printing()\n",
    "plt.rcParams['ytick.right']=True\n",
    "plt.rcParams['xtick.top']=True\n",
    "plt.rcParams['ytick.direction']='in'\n",
    "plt.rcParams['ytick.labelsize']=26\n",
    "plt.rcParams['xtick.direction']='in'\n",
    "plt.rcParams['xtick.labelsize']=26\n",
    "plt.rcParams['xtick.minor.visible']=True\n",
    "plt.rcParams['ytick.minor.visible']=True\n",
    "plt.rcParams['xtick.major.size']=8\n",
    "plt.rcParams['xtick.minor.size']=4\n",
    "plt.rcParams['ytick.major.size']=8\n",
    "plt.rcParams['ytick.minor.size']=4\n",
    "plt.rcParams['lines.markersize']=np.sqrt(36)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Initialize the degrees of freedom"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "alph = zeros(6,1)\n",
    "for i in range(len(alph)):\n",
    "    alph[i] = Symbol('alpha_{}'.format(i+1),real=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}\\alpha_{1}\\\\\\alpha_{2}\\\\\\alpha_{3}\\\\\\alpha_{4}\\\\\\alpha_{5}\\\\\\alpha_{6}\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡α₁⎤\n",
       "⎢  ⎥\n",
       "⎢α₂⎥\n",
       "⎢  ⎥\n",
       "⎢α₃⎥\n",
       "⎢  ⎥\n",
       "⎢α₄⎥\n",
       "⎢  ⎥\n",
       "⎢α₅⎥\n",
       "⎢  ⎥\n",
       "⎣α₆⎦"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = Symbol('x',real=True)\n",
    "y = Symbol('y',real=True)\n",
    "\n",
    "a1 = Symbol('a_1',real=True)\n",
    "a2 = Symbol('a_2',real=True)\n",
    "a3 = Symbol('a_3',real=True)\n",
    "\n",
    "l = Symbol('l',real=True)\n",
    "w = Symbol('w',real=True)\n",
    "h = Symbol('h',real=True)\n",
    "\n",
    "N1_1 = a1 + a2*x + a3 *y #shape function for node 1 subscript (elem: no.)\n",
    "N3_1 = a1 + a2*x + a3 *y\n",
    "N1_2 = a1 + a2*x + a3 *y\n",
    "N1_3 = a1 + a2*x + a3 *y\n",
    "N3_3 = a1 + a2*x + a3 *y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Determine the shape functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Triangle 1\n",
    "sys1_1 = solve_linear_system(Matrix([[1.,0,l,1], [1.,0,0,0], [1,0.5*w,l,0]]),a1,a2,a3)\n",
    "sys2_1 = solve_linear_system(Matrix([[1.,0,l,0], [1.,0,0,0], [1,0.5*w,l,1]]),a1,a2,a3)\n",
    "\n",
    "# Triangle 2\n",
    "sys1_2 = solve_linear_system(Matrix([[1.,0.5*w,l,1], [1.,0,0,0], [1,w,0,0]]),a1,a2,a3)\n",
    "\n",
    "# Triangle 3\n",
    "sys1_3 = solve_linear_system(Matrix([[1.,0.5*w,l,1], [1.,w,0,0], [1,w,l,0]]),a1,a2,a3)\n",
    "sys2_3 = solve_linear_system(Matrix([[1.,0.5*w,l,0], [1.,w,0,0], [1,w,l,1]]),a1,a2,a3)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Triangle 1\n",
    "N1_1 = N1_1.subs(sys1_1)\n",
    "N3_1 = N3_1.subs(sys2_1)\n",
    "\n",
    "# Triangle 2\n",
    "N1_2 = N1_2.subs(sys1_2)\n",
    "\n",
    "# Triangle 3\n",
    "N1_3 = N1_3.subs(sys1_3)\n",
    "N3_3 = N3_3.subs(sys2_3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Look for the displacement field $u$ and $v$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\frac{2.0 x}{w}$$"
      ],
      "text/plain": [
       "2.0⋅x\n",
       "─────\n",
       "  w  "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N3_1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Triangle 1\n",
    "u1_1 = N1_1*alph[0] + N3_1*alph[2]\n",
    "v1_1 = N1_1*alph[1] + N3_1*alph[3]\n",
    "\n",
    "# Triangle 2\n",
    "u1_2 = N1_2*alph[2]\n",
    "v1_2 = N1_2*alph[3]\n",
    "\n",
    "# Triangle 3\n",
    "u1_3 = N1_3*alph[2] + N3_3*alph[-2]\n",
    "v1_3 = N1_3 * alph[3] + N3_3*alph[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "eps_1 = Matrix([[u1_1.diff(x),0.5*(u1_1.diff(y) + v1_1.diff(x)) ], [0.5*(u1_1.diff(y) + v1_1.diff(x)), v1_1.diff(y)]])\n",
    "eps_2 = Matrix([[u1_2.diff(x),0.5*(u1_2.diff(y) + v1_2.diff(x)) ], [0.5*(u1_2.diff(y) + v1_2.diff(x)), v1_2.diff(y)]])\n",
    "eps_3 = Matrix([[u1_3.diff(x),0.5*(u1_3.diff(y) + v1_3.diff(x)) ], [0.5*(u1_3.diff(y) + v1_3.diff(x)), v1_3.diff(y)]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Material properties\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "mu = 1.e7/2\n",
    "nu = 0.\n",
    "lmbda = 0.\n",
    "P = 10.\n",
    "# l = w = 1\n",
    "# h = 0.01\n",
    "\n",
    "# A_i are the elemental volumes\n",
    "A3 = A1 = 1/4*w*l*h\n",
    "A2 = 2*A3\n",
    "# Defining the potential energy\n",
    "U = mu*trace(eps_1*eps_1)*A1 + mu*trace(eps_3*eps_3)*A3 + mu*trace(eps_2*eps_2)*A2 - P*alph[4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "eqns = []\n",
    "for i in range(len(alph)):\n",
    "    eqns.append(U.diff(alph[i]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'subs_list' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-12-681b1e1c984c>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0meqns\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msubs\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0msubs_list\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      2\u001b[0m \u001b[0meps_1\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mNameError\u001b[0m: name 'subs_list' is not defined"
     ]
    }
   ],
   "source": [
    "eqns[0].subs(subs_list)\n",
    "eps_1[0,0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "soln = solve(eqns,alph)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "alph_new = alph.subs(soln)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAbMAAADfCAMAAABLcs0gAAAAOVBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACXHtMAAAAEnRSTlMAMquJZkQiEEAwdrvNme9U3XwDrL/iAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAgAElEQVR4Ae1di3asoA513vdOTzu9/f+PvUlghwSjg4+ptue4VqeKEEKiqOxN6LrNt+vmGmylwI9t+f2xlck2r/dy31yFUQUe9/NZMxzO5+MhHT1Omtq44yQ1lvHZ3m7+uOse99PxUic2HA+U61fgZGkL9n29nk/d7U0Vfzt0jz9ydEv/9MzzHS/pef5+jvNnz2cfXXf76ud8mhKXCyqwkkwL/vQ0sRk33v+4Xkzvfetu76lLfC83X6OGXlJjIZvtce37jHQ7kP0nb2G5qAIr2bTg/G5PvHD/fD+f1AGn0730brdzum1cImty+3p0D9HvduTr+Xp+T31jNtTtdDoe6Zq7ni6Xs3RSp/td3ZnFSdEiybUQNd+TOpCX8tjy3eHS9X1G+d56faMVUroDJywqN1QB9HUt+Jhzox2+ZDtC4vP/d/KX9nMneoxe0Okd7vdPLo/E63vaLqnj+RBHc6fIEr5Y20u2BbvzncpePr4+5RL4c+gO6KwgTvpT6cKSJC5Df7yh5iMVflBbIE9O+vJ0JUQ+y9cQF4BQI+QOXbRt6NxNOamsuw1UkM7Sr2vBH70w9fzgzmdyFbX263SmrXeRDZZMFySuuw++Xb70rnuIz6pEFvWHsqRr6p2ebGSBq/iMDmT7ovqvX4fukt9MTmwv6KTiJHeRRFlwtZCnpGYSIVcD5IlwV/56v9+/SjchGejndOu0u4DQIuTyUJ85Yb5ckjVQASqi/7YFpwk3C/vpzN3UoRjciB3bpSZ3eAe8SukPfV0Xy9WJLOz6fj4lH3zSv/P5nl7TcJmduV8Un10efP99XA7yX4pqHVzUSKIDmDf7LNVMtoa8oHx3Sz673Mlct/fuxpfSH7qExelcAEJVyO2uLyilbaIMyjlhuQIWpZvNUGxBlsDFrzmf7Jxn+ay7f5HX0naQu+VTb3DxWZ3otNDWS+qnepsuWe4bj9fb8UG3yulww+uJivNFpTzMi/vsg7x6+ErqsDzeBsqfOtL9TAL+pGspZebfIjQp1d1Tf8bnJgvjQrQN1Za6h5Sn6Xeezw7Hw/Er9/mpCR/UqORF4zNKjLb8jp9PsY3zdsBThp5jVzb7LfcAWocvKsWKeVPjL2+325ned2gz8uTOveMJlOq73i7k0yMpeefTditCk5DHtfYZtc0pMyIsCR7MoA9tq8DY/jyf8d18kW6d+zN+lJGRDvkFg69tTYzqxhMsnSs+u8p3KFv7Rn0bP0q6fL+oOF/0/Y22D/6R2ypfsLfHJfk6yeNaBsp3/L7C9aPP4LyVUBFyleuHz9I2QdiBdZONbRTVRsmXqV8Ys3x2lcvwlDs1fSRzg7SH8i8m6VT+/bzYy/oP+sYrPVwO147fIdgs0tuK46gY6vBFRV65JZLPDiRc3kWzPMk0UJ4fSNy19/oDFZqEHE6n0/tX3eBKmUFhudndQIZ8qSHX8/+zfNbJtzt9TEl3KO/R5TmaVKgSrSL0TLI2essH17fD4fCe3t343eDMLqR71tZRFRWpat783sj3HH0mdJA3Vp7y8evgWV96oSeEQgily1vuLGEQOlAbP1AnbfN8dn2/3/llOXWH9IlJtk7b9fTn6529YBMrjY738gijjOQb3j7k04N9dD9JX0XfxizW1eGLSjm0GDVfqDzf5JA3Vv7yfn6cT8FXDoRCCPn17YvejGYJEzXpZ6A2MRfytPyf57MWya15+D1gyQbzLpHRK/sSob1aUsJn7y4fyIjk7X3WffJdMX/DkMV8CUHJlwgN6qGk6+Rrdgc++7ZB0thmW6fiG7Rdjx34rHub2jm0N2//OdM7+CQ99+AzHW2epPkvyfwEG41auQefESwTqfZXpPU/M543exc+e67mvxzGAo0+S7DNv9/vsYDxT7Tb6LOo6L+0jSyw2Gc04j1luxJuZkdBppSVvEpYMiUHqE8pR5t+0atAlGZqjXdjXSKtbXmYxQ7q2fNuv9ln589Qnoz7KIUjUzIsi0JGsXgsKrFAeKAqD1ZZPQr1QwYuM+Ei5XDsC0NYKuVj6lNW5v3tQQOZ/N1eKqmUopEpoEBFaJRmG1ZGWJ2CoS6h1qYqMYmYpeVjvtlnaWjd1sP7N6kIFA5QMrhipnbI5qgYhGo+HhjIV9YFj+lmFElYF1qEBeiBwFWGsJTE8y/dSoUyhVZDmTd5BlFqqaQW2kU0KZsGmaZhQ/QQpwtUdFpDGE7yfzXLxcJCNofZb/bZNUR53qWfA4UDQAwjKEwTkA0wSCfY1+34WcaqMKpXqB+JdaFFWIAecHlHWEry02+hTEEolBET0U+ppBYa8rAcdQoyS8OG6SEEctedv9cawqz6xSwNdMdmn52PmfhraQ1dupkuh0ThgJmURUFqJYSQ6SLCnqD78qHkMGiv1I/EuihFeuWFW8DYqtOC7uoyZgmhUIafZ0TPGeGXKE3KCNU0sSxkasOG6SHQxchKELcSxSDM5ihmAUgn9cY/zT47Uv/NsJajNVxTp54pHHSy4HcxFUP6UgVusvaF+pFYF0q4YJX1IFFBQFjy5IqIMmWUedCFXyrpCVWalBGqaazDJHpI1sXIom6ZLpzelWpyGLMkCqjUOvTT7DOG4Ll3crQGpTWybbkK9dkQFYNeoMp7Y/aZUj8y60LZHyxRDxL7IhOWnBYxZaooI2NjWkkgNPOwvFBLncKtwfrw28oIPSTTsLwsS7PCBeByFLMYk7Km0dbqM3mcJYqUoTUw95M2fqlgCkcx01MqhmNdSNGvM1gXSrhg2XrgqSAhucIJLcow4k0cAtZvnF8SCa1kLqKHVFwTY0hWMG0Hc30grfrf6jMGwK9fHT82DK0hVwAKh5qpgYrBekC9TP1Q1oW+dnAmHLSyLyBUlene5F2shV9imsZV66Yy16CHqLCwthX7RmaUkd+49ZbWkN5BOFWedblvBItijD3B9oD2oH5QkrAuQCYZK2+1YFm6QWjx2YcMQaOSOUIhEw2jyubTQyDMGVLVv4efwXqad1rvM36KXo/8/uVoDQn6AoUDlAywKMbYE1y5ap+pH2BdgEwyVn6AXFGEQhnqGNJLZQO/ZEgoFEXDoOgiBZ0h2RyyNYCJrT6DyOp/yydgVcQcwhQmafnuK4SuKnNUWAuWuNBn3Tt//szdohGBubK03CuEripzVJj0ZNqWeGepz+RzNRb9L3W6BQLaXl/IYp91/Ijb0bbkvm9uxssqaTLmcp81N3S9jLdrdx0w2/dMKd822sCP9Nn544Nn8WIz4FRrCIQY5YLAof+l1PdcGgN6/EyfucYYcKo5BEKIcjmp0YEp1TD8HklYJY199p+v/64i69uEnG82AoIBp5r5ndSzFsStWW9Taksi7f8295lFj8l6Bf5FHAIHWot9CTVNEQ0Y+7bgVMb4UHIMme6jXCZiAtfSr5ZTFRvTYXpO/d6NfTZ9PvWKOlr0mMQW+Bc4M3DqEgGBX1UTMsNTLRVSy9POqD05dsIYMm0RN3wwAW6X1qFa39SC02EauD//LUdbP88cekxWL9EBMF6IMWJjDn6upFuKB/sLOKVD/3kOHDuDR/N5UzEpU4S4Fbjd5pfS+ceUwhQse/qb9rf2mULU0l4D/9KxWN6B1tkoj/NZppgljKGAU3rtJ59Z2UWMwOUINiACMZhU4HYeAuaPCYLXLZpsS02ONpB1X+Hfxj5z6DHPkc19nrRMLK84ddRYm5vOawgEKelkq5iqCEtVn6WICVKR5jdospzAT7oscPSt/zf2mUOPFf4VuCTfZ4pTR2ZxkQPotkBHKAZ1slVMVYSlwme8jyACyO/QZM6ADRlx/I3/N/aZR48RHSBBHLZvTLEjenbRB1g6433mZSO6gi/iUOgCt6Nv5GpDNJmek/kdtafT6xO29plFjxWnzs1O3Y++PATGqLBrDYGQSlrZ+g5SFWGhuM8K3E6JWm2IJuMFKdDp9Ulb+8yhx9TcFAMrtTtZHqB1YAt6NjlUFyEQMlzuZGcxdRGWCp8BbrdItofljQ6Tow2Ysgt3t/ZZ59DjHB1A2qQ4M33cKruuam0VxiC/f2tJJzuLqYqwQPgMcLtDn2M0mTho7mqp9Hrt4eY+W7N5M0MgwGeTVJkcbWCS9NHMv8pnYH6Mtrh/EuMg/TPDKdOjDQzLmnqGfXZjSvOv2L5v5LZ5NPoFdmUe6Kbjjeu2qYG1tEqFM6INrFKvCPldfWMJuLuehUJJs6YThpJmJP4yn31TCIQ50QZmOGegyG/z2UAzf1XyJJ99z6z9v7mWpmtrks+aJP7L9GoLLPDZDiIWFCJUYKcBNl2dM3qdiNLqcr3jUBnDCesVkIRJEQuSiIk+M9ELmPI6IWBBmZrvdS90EGGCOBZGPkgRDwy9SiUwYE0fmNU2JWBBFJ0gSpsZsSBS2mvLc+Nkflz7l/1En6Xhbq5VppOCQQEGBtc7ELCgTM3n0qpgoYPMiVhgiFBFJpRpCVjw6ogFhhNmW80myNukiAWpzESflegFErGgMCjSGHyZ10/SFc1IkFWZmk/nMMRX6CBzIxYoEUplAieR64J+Sh19pVx0gmQRH8UAipaWGcpK1UJqFkDXLMpywkyr81n5V8zSTJmc6DONXpAiFhQGRfKZzusndZRRkQIWcAfwgogFhQjV8xk/z3iayQgtRKMTGNaHpolJ4TNtmaGs1C3MXC4riztuDVigGpocxiwNEQtEJZkzOIGTqtELUsSC9oAFqS9VTCWbolA2ZkYsMEQotQjuM2rgk4AFnUYnMKwPTXM+4wMJxWAoK8oZyc/UrIyRZThhLAAXgMkxLWIBC+m6ifxGRC8oCzFlBkW6z0jgUMACWsdv/YgFlgilFik+ex6w4NURCwonjI2dfeY4JsUsDRELWEj73NyUu0QvSBELCoMCPnsasMDP3V8pYoGjdRSfMVDdFrAgYn1UQvcQsSB5YdrzrEQvSBELCoMi+6wxYAGuOCxWoUwQfaqzdjioKBwDBA2VWXzWHrDABmNIhsm/6M5oMjn1IVdVVE5PVLBoGDahIWJBUmqaz0z0AolYAAYFzIR5/ZZRETEwVHtQNkiZxREL1LyZDkJObw5YEMcQIK0gFC2DomMtfB5SIczRELFgjs9M9AJBqsCgAAMD8/odoyJgYKgpQAdBIIAlEQvUvFhKA7B1Cy3kZ0QsmOOzVEZ+9xexAD4zSi7fXVXoqLCWiAWpPdP6RmuD3UUs0LEVq+XS/VWFjgrjT8m2bb7P/kUsaLNwY66miAVJ1gKf7S1iQWScxrH9qKhLW0uOE+oOmu+yqd9nrpbdHAyHMVhtqvq2gQoqSy+5zypRmx36MAaHHM+V1HkWxSBEvFwzNMdq3nfi5x38Cp+5pr/R2oFpUvbTKAYx/GallRzNo+62+Gv22Wc/nZPqwxjQipXvPKZGgJp8Uo/YzcFvYb6S4/vorqEiNnFnnNQrDSQfEQ/aYsN8ZaW7xyHZ0hQXxoAGVM4ZoEkzxLwUB31T6RrxsrZJ+8ixYaCCSqmd9Y08Qe+ebJ2AZ0W9gT4jnsBQGAMOtn+TZc5l8dxKCkqj+zTw28DHk+bQydqVBb//cGc+4/UmTggRUrBhsUsahsa4rDEVP3SSnwkRZywrTWLLMzqdFC2dTsbwmxHNH6E8qErbhoEKkgL6uzOfsV4yPZN3FBvmgzwMXbDhlCgnXBgDWpDmKBB/vjGslFJ6JHoBR+m9vdNlQJ9MBqDbMFBBaars7c5n9z9uMh7C9JOycp8pNly1Qw49B0ujGGSEmbJoaZ9TCmMw0IDIrg4ghC5xk4Pd+YymSRinCeo9M4yBzogfxs6tybPPHIhsz28YqMCqQfv78xndDHhxpLXceUhnZhgD9dlT7Nwj0vsLVLBrn934HUHieoiaFvUGrKpvEVVD+NAD2ohiYKWgtM8potA3DkHW//rGwOJidbqvzvTwl+7QYMN8LhmtPYxB7mMhZQxZZvHqsxBEJrU0A+fecttZ33ggKvhRBh/oB6i32AdQOJDsyGgeEc8v55DyDDtXlwxA1hsGKqjaujOfVdotOpwYxUB9NlDphoEKKo3YZxM4qVXpfR+WxfFa9BwYB0HRLQMVQIf8fyIntSq978NVh3WfDjh/ny1+cd9IrxX0UFxp2zRQQdWGX+2zdipTZZX+4axZhH0xq6T8ap+tF8Vg20AFlad/t8+qxv6Sw6199pODFGx1CWzts63a/ZPr3a/PmsMizHo9UEKVdV6YaDPQvtRmkIfq9Hccbu8zEwrBNlh4teCAjC1IcebFh+vtaUHGtnnirNvCRJcDIQ2efID7Mmsfbe+zEgrBtk3mrIIDMrYgxeNqfAZTPi8oY5q2Qt53iZDlMqG2ZTNMnMjpB9v7rIRCsNpLWAQdy2f7ISQA4BRZ4dwHGShj8wABhgsOUK7AsjLj/EatEuZgS7rj9j7TUAh2Nn8KiwCfDUce8EEGej4bLkh8LEFWXaVIFC9hzNjkMLU1BxkwHl9rl322LSdVQyFYIkYKi5B9VqIbUKs9pcMHGah9NlIQhCpbKfFGlGVV7jOTw9TWPJF2LUcZOdtzUhEKwRExMIdfcM7RBSlu96+TDivi3sjOHimYCVWuUsuyUp/5HFobFDSm/LbdzfvGEgrBxg5IYRHQN+boBmKURHejBSYyfRGW8pyO/DxrKBixP7ysKEeXYgCg8u/9v7nPSigES8SASRKfoHVBirpvRFiEZFK8vHguSBhCgAvoPRvm2LJv3NxnJhSCJWJIWATcZ4hu8IzSUeyc77OGgrZSd7uoz8IczUEGnMx1Djb3mQmFYIkYAn0pB6Ql8gDbA3aeUNBW6kwKWfFCFitCc67WloPNfTag5LyPVrXzgNQpyaOyVkTmpuiU8u7VZ92ssAjh2MV0o0iJUVntQQZm1j5WbLc+23VYhAlBBsaMP/Pcfn2257AIwaj0TPvPKbZjn81pTlzGBXIOAZcwMRa2ferf4DMfyDkEXMLE7b0Ta8A++62cVLTYB3J2gAuyhIk4ubf/P5CTiqm7NKR7uueJs2RWwJwukc1dAjmnoO/0GQdcx3ojTLQZdrP/8/pGieku9tMJ7XwEmBOJZY684NEpkHMKHKLT2q0XwkSbYT/7P85nUaj0ZM40NolRRWNiHmpJkSJkXNkCLporTNSz+9r5aT4LQ6Unk2bchoGZjxTUJZu6BHLm4V5MazdYZkncl3MGtPlpPotCpeemic8UEo3a61g7BsuM8u447Yf5jAh0avjkng/yYnoRMT6jxGjLcbDklMcyo9y7TftZPmNUXX2m6OfMOfIhlrlbRxnFfpbP4lDpuTmD7yDa3Ea0U/PvdOdn+YyNKIGRLPoJyyaftc+RD7FMCNvz/x/ns/Pb1/GRQ4bQ57OuQKMwp02sLO/nyA+inVWp3R3+OJ/tzoLfr9A/n32/zZfWyD7blpOKFvyUmWjQd7v/23NSt2v7T615r33ja2afhdBmmFj5cwezzopGe/KZmYkmi/Lm2MSjAYWj2Wfn+7nQwTM0k2CYENoME4uFeC/XMkrr8SVeebQnn5WZaDL7jMcpODYxW0rDEgNqyQGFMR+MTQSL3mmUWLlsPn8IbbpECHE2Ry3zCHxO1BoHe/JZmYkms88Qm3gkoHCZD0a2ACFRwEsAowrNgN4fQpslEUKsbUstW846KxrtyWc6Ew2zz1Js4uGAwmY+mPEZTZTpzjm0fhWAGBPMHA6DRDEKfGZymFq2nHW2T5/pTDTMPiuxiRGWWKEWGSk288GMz7r7F3ktbT6/TjDzOIzFO+Ezk8PUsuXMin36DDPRyqK8iE08uBivzgczPjscD8ev/FxSvCbBMD951tkufVZmomH2Gc/q5Bm00wIK86PsIs8xHlBm2Lo/Wy3CYXY+62yXPisz0WT2WYlNPC2gcIoAhycP3kE8DGOnuhVb8B76xjjHv77RW6szM9Fk9hnHkODYxFMDCsvL3THHNM7QDD3+HHQ9iMOoz8IcW846K9bi98adcFLNTDSZ3YXYxFMDCl/f73f+ph4LQDyIw6jPwhxbzjorPtsnJ3XWx6uau7Ru+t6oEP1Sny53zRJ7+j4z7Zoz+ywcwjAym3ZHhWw666yov1Of7XL22bazzl7vM37FXrRtO8UrVH07lbw1X3Sf7WnJ0tD+PyvRL9u7js/cpDwyx7MFa3sWu9KqZdFklV7GoYRaA1bifkoLoQ2VaUiPYkNGaU9FhcoESntBahZ3D6ziMz8pj5AQjKp7DUaOaJm4jv/mbrUGLKcBF3tWXYjOmdiDz8qX85EykdKlBO8Vs1hEYRWf+Ul5NE7+bMFarxkdnT4ftJLq/K3WgCXJJ9p8kVQSuJkVEqXZ8wP7kTKR0r54MYtd36HnswjkTYLaJ+XRRUUb8OXr6XJJr1y0gI960+HH3e342V8ppF1AmRaYVMVvwcWQEk0tLL2CV6rgZlq6iheJdJiGYs8AUdAZjZio2JupOKQ0hNJ/Y5Y0GUvO1T6LQV7O2j4pr1qw9vLx9SktoeEgXazP48fcCTxUK3wj8X8GqJ8LEGQmTQuUVuUfMw8QMutWUM5gEqKgAAY3U6E+rRbKI886vl21MMeLVEnkEBqC6orSEGZyWLOYZXtrn8Ugb5IzSIivJuVlSBj48iUvG3hirfCigbHbFB5OuARKCcZYxAQBRQPT5AgXI6PKYKbW30WTEKUFBjdToT4NikIogxBpnWUqoDUkc1hlsjivdBGmtVmzmGV72Wd2vDEGeZMUaW1BflV05yflddWCtZfD5cGfNmNBS+kNqrw3QnsA1A0CoIGBl3VyoOgJmdm8pRXhJERZVZfsn2JDWqFIGxYq8QeBAvHkRREWzVSE0smQ0NDWZsxilu3tjTdGIG8Smq5QRX5zovsnt3tXLVh7OV5vRLEfC1rqhBQ8hJIZoJ4gwMDLQzLlyiutiCYhpmaogFahdFUy4pce2VqDFzYoS1s9kCN1D6JT3TeGIO/ESXm6+KldsDYt03kTDJJbJnfeHeuxq314B1cc7RqAukXA8ETAItP4jKYWhpMQ7dxCumNuvPodI0X3aiSkEkr4+u12JoCVt7iFw7LQ6qEc+iZAABX1jYdsSK4qBHknTspTnyV8mdtwox5DOo18FQ7hxx4rzgD1FAEBAF3JND381yOehAiOFhuEt0ah1MzHBVflUAsDWZ3XMMrBL2JJF/qtfBaDvDl3uj312aoyyk5Cg6sFa/nJzC2YHu00A9RTBIRBTUnB+pbIrYgnIVagdoxZB0IPdB/ml+byDlIJG1KwaBjnGOkbI5AXPknFMvKLRPufum5Gg6sFa/k9/04v8w1BS5Mw2BcA9RQBIbzMOiXR9NtrRW8SYm6GluAlGR7UH/UW1KqFvtGjjPKmCd7rIuR22d7qPqNXwADkFe3bJ+VVC9be6ENTvs+mRjsFQD1FQAgvk/4wb78VwSREP7eQ7p338+N86kMxtdALtZQ/bF6AkHdm2d7aZ+Ximr83ccHaXkUwRe/EgoRXyNQLYYFepegTDc2yva/wWdcfhiqqNexFIwINxUazvEKmzhAYrbn15LiGdtnel/jMDmi2qvwv36gF7LD7S3y25oK1oy35a066ZXtf47OdEJR+j0sdzvoan623YO3vMfuSlvivDPbZPubAL2nT31W2mgP/U4IH/KV6pmvzRX3j33Xhf3NrF/usOcBAapgyiea2M+IqhaQmVOC5gUit/7uHfD4ZpdXlesexLpHWtijM4iaC2Ax2v9lnJqiAK8/AszI+Mi8CRI6U0ZEsCpPISjHr4go5IxcJyodcpYjUxI9pkfX+9jjQRrKG6SgITOB0CkhXtmEDLJJQl1BrW5maZfzLOhVp9lkJKmDrEvRbCRsgW3DFA5EGCpOI80BUYYoIOUOpFHxeDwTVCrlKjtQEoVDmTZ59lFoqqYU+JVhBJv/PDRtikThd0D6nNYThJP9Xs7TMLmn2WQkqYOtKy9uC8YFBcxA5JKdiN4JKGSZRGbgtTJFEztAiLEAPuPwgV6kwrMq4XRrBFxPRT6mkFhqSqRzpCjJLwwZZJCS86ML60+a1hrB0Lv0Ws1gio81h9pt9pkEFLF8hBxgAYQM+A5GD6ynMC+FFOIIVtFemSCJnlCK98gLUM1fJaUEXP/d9aYNQKMPPM57QopXQcamBlVIylRGqaSIUMrVhYyySpIuRRT4jKcqwgjCbo5gFE1Sl3vin2WcaVMDyFXKAgUzYoBoKMhdHGrBMIr3PClMkkTOUSsEq64E0vANXyWohPhG0hwvAJEaZBzvm63S4YdTOC1UylRGqaSzSyORujBJGWCSZYGVkUbdMF45SAaGgyWHM0jD9t9lnCCrg+Apm9djEV1CfGSKHY34YJpGaQpe3zeQMpVKwufQgkTQyV8lpMcqwIhEykqaVBEIzmcoLjUIisD5M/R5hkYShERzDKvvM1VbMYkzKmkZbq89KUAHLjsgETBA2yqU9LdJAZoqAnJF6rsyF0YOKpBGxJjyvQm96BsgpeAG/4T6howRCK5nSMCgqBp2vYFAbXRO4DUV4+NPqsxJUwLIjcgUgbKjPpkUaAFNEyRn62sEq42Ayr0J99ib9ZgsdJaZiaIdAD0Jy/+GqiopJZysY1rZi32iCClh2hHByO7YJMz7gMxA5bKTnHsmCcuOSAlOEkoScAcrJWHmrBdesG4RCGfK6MA5RyRyhkImGUWVPWSTPFQxzNIRGaL3P+Cl6PfL7l2NHpIn8IGyAbAEixxgvgm0MU3SZKUI0GYkQzQsuMRN8rPwQR0OFQhki8qaXygY6ypBQKIqGQdFFCjpDsjlkawiN0OoziKz+t3wCVkXMIUxhkpbvvkLoqjJHhbUgjwt9Nm95WzgmGhHAudn/XyF0VZmjwqQne9L2pT7bZYCBJ23e8ek+Hy9QdrHP1l/elgcu/qbNtpffF55uy332tIqJGdx074llf2R2H5SgoQlb+cwDSgZ0mhzywEtqaLJm6eNjRg/N1bIzUK5fgRMGzadepRv5rAKUCug0OeRBJckZZVwXHkUAAAU1SURBVPwgwMeKHuNF67NxuaACW7Bo3jCW7wpWc5nsuRfuO0CJvvz4W0yqwyhuc92VpOZyIWZW9GiXwznDcs8iHBTNJ3J4V7jP1oh0QN/XPBxIYxbyC4xZceGoDgkI4KGpVJhs+DxUgsPHUI7+98AvxmoyJj0CdPfLDVWAuqzmOuaPk6P/l/tsjUgHCoDl2VvAmPlThnHhuA4e6ffQFD59GiId0HhWFJzFAHEQBmXGgG4L4CV7ewAOsowvrOYmKIHJMbS73GdyYYIcgfHSXF2CZqpEPlcApTRcn0GnFMWAM6SSwIXjOqRokUSlMMQA4HwYm/b4GNcoG/TgAwiDMsPCPICXJPkKiqx0ln+N5iYoQTk/uLfcZ6tEOiDOhgw36wWXfAZcOK5DgO8ImuoAnA9j03SHBkEJEF1AzFXsnC+9y0HiL/BJD3QrgGehZ1TgZNkMRnN0vpL36c9yn4Xh7HO90lgFhSNlEvqsZzTkQTITpydceDhkvpalHZh5jUgHKizfZyNAt6pgoGdNkx0oNpChtNYXi4+W+2yNSAeqm06f11YILhzW4aMLONPwAQHno9h0qtOhxSkJv7Bz9tkiYVnWUG0mKAFqH/m/3Gf8KOuFs08gRXoqKZAbqVGhzz2fJcA7rMMXdXgygPOZ2HQVSMA8XBcD3SE2bYMSREaq0hb7bJVIB6oUQh4AY064cFxHBVyzDNwaAM6XYNMqDO8gS4RBMQvya6NRgUkY3V3ss26NSAeqYg55gFYAF47qGAO+AZwvwaZ7PlsiTH0WYtM2KIGaYnhnuc/WiHSg+uWXXmDMwIXDOuroAiQEpgFwDgB8EZ4MZZYIg2IxNm2DEqgphneW+2xY9owzC0MeqGlmVN0rsqawJ7JMUIKeGv2EnfkM3I2+ok0pwXBDU7kw05rCxmXZoAShKj5xbz6bOFzqG/NTjyYOjO/NZ39jyAMXlKDhutudz1qIRw3t+klZnkCjvabszmd/X8gDH5Sg56F+wv581tfxX4q3QIvPbn8+y8ac3L80asA3Nts7qTpq8VlV5N/hxhZYwWc7iFwwwHvKtrUEwmFzR28CUdqwhHwmVgYkq6HiEyIXzPSZiWLA1FflXzwPXGDWQHHqF66FYN7TIhfEvCcQOX5b5IKZPitRDGRaKfgXoE7wZ/9A4IIyRZ9dpuMDNHaaQaQ5kQs87wlCoc1vi1ww02clioFELgD/AuPx4HHInaR0kAR4lSn6dBbjcIVrMTdygeFLQSi0ER/ST6mEavZaRSQplwaZpWXbRS6Y6TONYpAiF4B/ASuBx8E+q6gTdg2U4jMlbsyNXGD4UnohQBt+nvF8E62kp5WSpAxfQ9O4ESpTW7Zh5IKZPtMoBilyQXvgAlpqiCxQLw1TuBYzIxdYvpTaFz6jCn9V5IKZPkMUA1q6ga9C3hoDF9Dyf/2lYZRrMTNygeNLBT77XZEL5vmsRDFIkQvAvyhX9tPABZ5zkYkbCAjgKCR64AkgNn5Cumro17FCijYMMf+eyAXJZ/KFL+3S1o/ulCgGKXIB+BdqpcbABXpLZK6FBgTQNwRWAwcVASSc9s/59dYHq6T7NZELPtNYDPPRZUuEeW70081EMRAqKfgX8Bl4HGMxAqQSmBdcC0r8F7lgJCBg8lRa+empl3wGE8VA5tmDfwHqBHgcYzwM5zNwLRAQ4F/kAm/wdY/+RS6Ybk/0LmHJ7wAQ39uG80L9yjhIfHpeKsZB5pWOS60qc1QYf0m+fPuWSl7eir1U0BS5YLmy33FhLNfyh0hoM+b/AdqHXOHrG+JJAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}\\frac{8.0 \\cdot 10^{-6} l^{3} \\left(256.0 l^{6} + 192.0 l^{4} w^{2} + 24.0 l^{2} w^{4} - w^{6}\\right)}{h w \\left(512.0 l^{8} + 640.0 l^{6} w^{2} + 176.0 l^{4} w^{4} + 24.0 l^{2} w^{6} + w^{8}\\right)}\\\\\\frac{6.4 \\cdot 10^{-5} l^{6} \\left(16.0 l^{2} + 5.0 w^{2}\\right)}{h \\left(512.0 l^{8} + 640.0 l^{6} w^{2} + 176.0 l^{4} w^{4} + 24.0 l^{2} w^{6} + w^{8}\\right)}\\\\\\frac{3.2 \\cdot 10^{-5} l^{3} \\left(2.0 l^{2} + w^{2}\\right)}{h w \\left(16.0 l^{4} + 16.0 l^{2} w^{2} + w^{4}\\right)}\\\\\\frac{4.0 \\cdot 10^{-6} l^{2} w^{2}}{h \\left(32.0 l^{4} + 8.0 l^{2} w^{2} + w^{4}\\right)}\\\\\\frac{8.0 \\cdot 10^{-6} l \\left(256.0 l^{8} + 256.0 l^{6} w^{2} + 104.0 l^{4} w^{4} + 19.0 l^{2} w^{6} + w^{8}\\right)}{h w \\left(512.0 l^{8} + 640.0 l^{6} w^{2} + 176.0 l^{4} w^{4} + 24.0 l^{2} w^{6} + w^{8}\\right)}\\\\- \\frac{8.0 \\cdot 10^{-6} l^{2} \\left(128.0 l^{6} + 56.0 l^{4} w^{2} + 16.0 l^{2} w^{4} + w^{6}\\right)}{h \\left(512.0 l^{8} + 640.0 l^{6} w^{2} + 176.0 l^{4} w^{4} + 24.0 l^{2} w^{6} + w^{8}\\right)}\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡              3 ⎛       6          4  2         2  4    6⎞       ⎤\n",
       "⎢      8.0e-6⋅l ⋅⎝256.0⋅l  + 192.0⋅l ⋅w  + 24.0⋅l ⋅w  - w ⎠       ⎥\n",
       "⎢  ────────────────────────────────────────────────────────────   ⎥\n",
       "⎢      ⎛       8          6  2          4  4         2  6    8⎞   ⎥\n",
       "⎢  h⋅w⋅⎝512.0⋅l  + 640.0⋅l ⋅w  + 176.0⋅l ⋅w  + 24.0⋅l ⋅w  + w ⎠   ⎥\n",
       "⎢                                                                 ⎥\n",
       "⎢                          6 ⎛      2        2⎞                   ⎥\n",
       "⎢                  6.4e-5⋅l ⋅⎝16.0⋅l  + 5.0⋅w ⎠                   ⎥\n",
       "⎢   ──────────────────────────────────────────────────────────    ⎥\n",
       "⎢     ⎛       8          6  2          4  4         2  6    8⎞    ⎥\n",
       "⎢   h⋅⎝512.0⋅l  + 640.0⋅l ⋅w  + 176.0⋅l ⋅w  + 24.0⋅l ⋅w  + w ⎠    ⎥\n",
       "⎢                                                                 ⎥\n",
       "⎢                             3 ⎛     2    2⎞                     ⎥\n",
       "⎢                     3.2e-5⋅l ⋅⎝2.0⋅l  + w ⎠                     ⎥\n",
       "⎢                 ───────────────────────────────                 ⎥\n",
       "⎢                     ⎛      4         2  2    4⎞                 ⎥\n",
       "⎢                 h⋅w⋅⎝16.0⋅l  + 16.0⋅l ⋅w  + w ⎠                 ⎥\n",
       "⎢                                                                 ⎥\n",
       "⎢                                  2  2                           ⎥\n",
       "⎢                          4.0e-6⋅l ⋅w                            ⎥\n",
       "⎢                  ────────────────────────────                   ⎥\n",
       "⎢                    ⎛      4        2  2    4⎞                   ⎥\n",
       "⎢                  h⋅⎝32.0⋅l  + 8.0⋅l ⋅w  + w ⎠                   ⎥\n",
       "⎢                                                                 ⎥\n",
       "⎢         ⎛       8          6  2          4  4         2  6    8⎞⎥\n",
       "⎢8.0e-6⋅l⋅⎝256.0⋅l  + 256.0⋅l ⋅w  + 104.0⋅l ⋅w  + 19.0⋅l ⋅w  + w ⎠⎥\n",
       "⎢─────────────────────────────────────────────────────────────────⎥\n",
       "⎢       ⎛       8          6  2          4  4         2  6    8⎞  ⎥\n",
       "⎢   h⋅w⋅⎝512.0⋅l  + 640.0⋅l ⋅w  + 176.0⋅l ⋅w  + 24.0⋅l ⋅w  + w ⎠  ⎥\n",
       "⎢                                                                 ⎥\n",
       "⎢              2 ⎛       6         4  2         2  4    6⎞        ⎥\n",
       "⎢     -8.0e-6⋅l ⋅⎝128.0⋅l  + 56.0⋅l ⋅w  + 16.0⋅l ⋅w  + w ⎠        ⎥\n",
       "⎢   ──────────────────────────────────────────────────────────    ⎥\n",
       "⎢     ⎛       8          6  2          4  4         2  6    8⎞    ⎥\n",
       "⎣   h⋅⎝512.0⋅l  + 640.0⋅l ⋅w  + 176.0⋅l ⋅w  + 24.0⋅l ⋅w  + w ⎠    ⎦"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alph_new"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "subs_list = [(l,1), (w,1), (h,0.01)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}278.492239467849\\\\99.3348115299335\\\\290.909090909091\\\\9.75609756097561\\\\376.053215077605\\\\-118.847006651885\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡278.492239467849 ⎤\n",
       "⎢                 ⎥\n",
       "⎢99.3348115299335 ⎥\n",
       "⎢                 ⎥\n",
       "⎢290.909090909091 ⎥\n",
       "⎢                 ⎥\n",
       "⎢9.75609756097561 ⎥\n",
       "⎢                 ⎥\n",
       "⎢376.053215077605 ⎥\n",
       "⎢                 ⎥\n",
       "⎣-118.847006651885⎦"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alph_new = alph_new.subs(subs_list)\n",
    "alph_new * 10**6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.tri as tri"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "u = np.array([alph_new],float).flatten()\n",
    "u_def = u * 5.e2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "xnodes = np.array([0., 1., 1., 0.5, 0.])\n",
    "ynodes = np.array([0., 0., 1., 1, 1])\n",
    "conn = [[0,3,4], [0,1,3], [1,2,3]]\n",
    "triangles = tri.Triangulation(xnodes, ynodes, triangles = conn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "xnodes_def = np.array([0.,1.,1+u_def[-2],0.5+u_def[-4],u_def[0]])\n",
    "ynodes_def = np.array([0.,0.,1+u_def[-1],1+u_def[-3],1+u_def[1]])\n",
    "triangles_def = tri.Triangulation(xnodes_def, ynodes_def, triangles = conn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax = plt.subplots(1,1,figsize=(10,10))\n",
    "ax.triplot(triangles,'r-',lw=3,label=r'$\\Omega_0$: Undeformed')\n",
    "ax.triplot(triangles_def,'b--',lw=3,label=r'$\\Omega$: Deformed')\n",
    "# ax.grid(which='major')\n",
    "ax.text(0.15,0.65,r'$e = 1$',fontsize=26,transform=ax.transAxes,bbox=dict(facecolor='wheat',edgecolor='k'))\n",
    "ax.text(0.4,0.55,r'$e = 2$',fontsize=26,transform=ax.transAxes,bbox=dict(facecolor='wheat',edgecolor='k'))\n",
    "ax.text(0.7,0.6,r'$e = 3$',fontsize=26,transform=ax.transAxes,bbox=dict(facecolor='wheat',edgecolor='k'))\n",
    "ax.tick_params(pad=10)\n",
    "ax.xaxis.set_minor_locator(AutoMinorLocator(20))\n",
    "ax.yaxis.set_minor_locator(AutoMinorLocator(20))\n",
    "h,l = ax.get_legend_handles_labels()\n",
    "ax.legend(loc='lower center',handles = [h[0],h[2]],labels = [l[0],l[2]],fontsize=30,ncol=4,fancybox=False,facecolor='wheat',edgecolor='k',shadow=True)\n",
    "fig.tight_layout()\n",
    "fig.savefig(r'plotP1.eps')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "alph_subs = {alph[i]:alph_new[i] for i in range(len(alph))}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculate the strains in the elements\n",
    "\n",
    "# Element 1:\n",
    "eps1 = eps_1.subs(alph_subs).subs(subs_list)\n",
    "\n",
    "# Element 2:\n",
    "eps2 = eps_2.subs(alph_subs).subs(subs_list)\n",
    "\n",
    "# Element 3:\n",
    "eps3 = eps_3.subs(alph_subs).subs(subs_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "eps1*10**6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "eps2*10**6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "eps3*10**6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "eps1*10**7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "eps2*10**7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "eps3*10**7"
   ]
  }
 ],
 "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": "3.6.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}