Linear_Algebra-project.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# CompMech04-Linear Algebra Project\n",
    "# Practical Linear Algebra for Finite Element Analysis\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this project we will perform a linear-elastic finite element analysis (FEA) on a support structure made of 11 beams that are riveted in 7 locations to create a truss as shown in the image below. \n",
    "\n",
    "![Mesh image of truss](../images/mesh.png)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The triangular truss shown above can be modeled using a [direct stiffness method [1]](https://en.wikipedia.org/wiki/Direct_stiffness_method), that is detailed in the [extra-FEA_material](./extra-FEA_material.ipynb) notebook. The end result of converting this structure to a FE model. Is that each joint, labeled $n~1-7$, short for _node 1-7_ can move in the x- and y-directions, but causes a force modeled with Hooke's law. Each beam labeled $el~1-11$, short for _element 1-11_, contributes to the stiffness of the structure. We have 14 equations where the sum of the components of forces = 0, represented by the equation\n",
    "\n",
    "$\\mathbf{F-Ku}=\\mathbf{0}$\n",
    "\n",
    "Where, $\\mathbf{F}$ are externally applied forces, $\\mathbf{u}$ are x- and y- displacements of nodes, and $\\mathbf{K}$ is the stiffness matrix given in `fea_arrays.npz` as `K`, shown below\n",
    "\n",
    "_note: the array shown is 1000x(`K`). You can use units of MPa (N/mm^2), N, and mm. The array `K` is in 1/mm_\n",
    "\n",
    "$\\mathbf{K}=EA*$\n",
    "\n",
    "$  \\left[ \\begin{array}{cccccccccccccc}\n",
    " 4.2 & 1.4 & -0.8 & -1.4 & -3.3 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
    " 1.4 & 2.5 & -1.4 & -2.5 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
    " -0.8 & -1.4 & 5.0 & 0.0 & -0.8 & 1.4 & -3.3 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
    " -1.4 & -2.5 & 0.0 & 5.0 & 1.4 & -2.5 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
    " -3.3 & 0.0 & -0.8 & 1.4 & 8.3 & 0.0 & -0.8 & -1.4 & -3.3 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
    " 0.0 & 0.0 & 1.4 & -2.5 & 0.0 & 5.0 & -1.4 & -2.5 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
    " 0.0 & 0.0 & -3.3 & 0.0 & -0.8 & -1.4 & 8.3 & 0.0 & -0.8 & 1.4 & -3.3 & 0.0 & 0.0 & 0.0 \\\\\n",
    " 0.0 & 0.0 & 0.0 & 0.0 & -1.4 & -2.5 & 0.0 & 5.0 & 1.4 & -2.5 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
    " 0.0 & 0.0 & 0.0 & 0.0 & -3.3 & 0.0 & -0.8 & 1.4 & 8.3 & 0.0 & -0.8 & -1.4 & -3.3 & 0.0 \\\\\n",
    " 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 1.4 & -2.5 & 0.0 & 5.0 & -1.4 & -2.5 & 0.0 & 0.0 \\\\\n",
    " 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & -3.3 & 0.0 & -0.8 & -1.4 & 5.0 & 0.0 & -0.8 & 1.4 \\\\\n",
    " 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & -1.4 & -2.5 & 0.0 & 5.0 & 1.4 & -2.5 \\\\\n",
    " 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & -3.3 & 0.0 & -0.8 & 1.4 & 4.2 & -1.4 \\\\\n",
    " 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 1.4 & -2.5 & -1.4 & 2.5 \\\\\n",
    "\\end{array}\\right]~\\frac{1}{m}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.00416667,  0.00144338, -0.00083333, -0.00144338, -0.00333333,\n",
       "         0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "         0.        ,  0.        ,  0.        ,  0.        ],\n",
       "       [ 0.00144338,  0.0025    , -0.00144338, -0.0025    ,  0.        ,\n",
       "         0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "         0.        ,  0.        ,  0.        ,  0.        ],\n",
       "       [-0.00083333, -0.00144338,  0.005     ,  0.        , -0.00083333,\n",
       "         0.00144338, -0.00333333,  0.        ,  0.        ,  0.        ,\n",
       "         0.        ,  0.        ,  0.        ,  0.        ],\n",
       "       [-0.00144338, -0.0025    ,  0.        ,  0.005     ,  0.00144338,\n",
       "        -0.0025    ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "         0.        ,  0.        ,  0.        ,  0.        ],\n",
       "       [-0.00333333,  0.        , -0.00083333,  0.00144338,  0.00833333,\n",
       "         0.        , -0.00083333, -0.00144338, -0.00333333,  0.        ,\n",
       "         0.        ,  0.        ,  0.        ,  0.        ],\n",
       "       [ 0.        ,  0.        ,  0.00144338, -0.0025    ,  0.        ,\n",
       "         0.005     , -0.00144338, -0.0025    ,  0.        ,  0.        ,\n",
       "         0.        ,  0.        ,  0.        ,  0.        ],\n",
       "       [ 0.        ,  0.        , -0.00333333,  0.        , -0.00083333,\n",
       "        -0.00144338,  0.00833333,  0.        , -0.00083333,  0.00144338,\n",
       "        -0.00333333,  0.        ,  0.        ,  0.        ],\n",
       "       [ 0.        ,  0.        ,  0.        ,  0.        , -0.00144338,\n",
       "        -0.0025    ,  0.        ,  0.005     ,  0.00144338, -0.0025    ,\n",
       "         0.        ,  0.        ,  0.        ,  0.        ],\n",
       "       [ 0.        ,  0.        ,  0.        ,  0.        , -0.00333333,\n",
       "         0.        , -0.00083333,  0.00144338,  0.00833333,  0.        ,\n",
       "        -0.00083333, -0.00144338, -0.00333333,  0.        ],\n",
       "       [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "         0.        ,  0.00144338, -0.0025    ,  0.        ,  0.005     ,\n",
       "        -0.00144338, -0.0025    ,  0.        ,  0.        ],\n",
       "       [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "         0.        , -0.00333333,  0.        , -0.00083333, -0.00144338,\n",
       "         0.005     ,  0.        , -0.00083333,  0.00144338],\n",
       "       [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "         0.        ,  0.        ,  0.        , -0.00144338, -0.0025    ,\n",
       "         0.        ,  0.005     ,  0.00144338, -0.0025    ],\n",
       "       [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "         0.        ,  0.        ,  0.        , -0.00333333,  0.        ,\n",
       "        -0.00083333,  0.00144338,  0.00416667, -0.00144338],\n",
       "       [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "         0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "         0.00144338, -0.0025    , -0.00144338,  0.0025    ]])"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import rcParams\n",
    "rcParams['font.family'] = 'sans'\n",
    "rcParams['font.size'] = 16\n",
    "rcParams['lines.linewidth'] = 3\n",
    "fea_arrays = np.load('./fea_arrays.npz')\n",
    "K=fea_arrays['K']\n",
    "K"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this project we are solving the problem, $\\mathbf{F}=\\mathbf{Ku}$, where $\\mathbf{F}$ is measured in Newtons, $\\mathbf{K}$ `=E*A*K` is the stiffness in N/mm, `E` is Young's modulus measured in MPa (N/mm^2), and `A` is the cross-sectional area of the beam measured in mm^2. \n",
    "\n",
    "There are three constraints on the motion of the joints:\n",
    "\n",
    "i. node 1 displacement in the x-direction is 0 = `u[0]`\n",
    "\n",
    "ii. node 1 displacement in the y-direction is 0 = `u[1]`\n",
    "\n",
    "iii. node 7 displacement in the y-direction is 0 = `u[13]`\n",
    "\n",
    "We can satisfy these constraints by leaving out the first, second, and last rows and columns from our linear algebra description. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. Calculate the condition of `K` and the condition of `K[2:13,2:13]`. \n",
    "\n",
    "a. What error would you expect when you solve for `u` in `K*u = F`? \n",
    "\n",
    "b. Why is the condition of `K` so large?\n",
    "\n",
    "c. What error would you expect when you solve for `u[2:13]` in `K[2:13,2:13]*u=F[2:13]`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The condition of the K matrix is 1.458 x 10^17\n",
      "The condition of K[2:13,2:13] is 52.24\n"
     ]
    }
   ],
   "source": [
    "#1\n",
    "ck = K[2:13,2:13]\n",
    "condK = np.linalg.cond(K)\n",
    "condK_213 = np.linalg.cond(ck)\n",
    "print('The condition of the K matrix is',np.around(condK*(10**-17),3),'x 10^17')\n",
    "print('The condition of K[2:13,2:13] is',np.around(condK_213,2))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The expected error when solving for u is: 10 ^ 1\n"
     ]
    }
   ],
   "source": [
    "#1a\n",
    "print('The expected error when solving for u is: 10 ^',(17-16))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#1b\n",
    "The condition of K is so large because of the complexity of the matrix.  The condition of a matrix is related to accuracy of the matrix, and with a large and complex matrix it leaves a substantial amount of room for error.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The expected error when solving for u[2:13,2:13] based on the condition of K[2:13,2:13] is 10 ^ -15\n"
     ]
    }
   ],
   "source": [
    "#1c\n",
    "print('The expected error when solving for u[2:13,2:13] based on the condition of K[2:13,2:13] is 10 ^',(1-16))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. Apply a 100-N downward force to the central top node (n 4)\n",
    "\n",
    "a. Create the LU matrix for K[2:13,2:13]\n",
    "\n",
    "b. Use cross-sectional area of $0.1~mm^2$ and steel and almuminum moduli, $E=200~GPa~and~E=70~GPa,$ respectively. Solve the forward and backward substitution methods for \n",
    "\n",
    "* $\\mathbf{Ly}=\\mathbf{F}\\frac{1}{EA}$\n",
    "\n",
    "* $\\mathbf{Uu}=\\mathbf{y}$\n",
    "\n",
    "_your array `F` is zeros, except for `F[5]=-100`, to create a -100 N load at node 4._\n",
    "\n",
    "c. Plug in the values for $\\mathbf{u}$ into the full equation, $\\mathbf{Ku}=\\mathbf{F}$, to solve for the reaction forces\n",
    "\n",
    "d. Create a plot of the undeformed and deformed structure with the displacements and forces plotted as vectors (via `quiver`). Your result for aluminum should match the following result from [extra-FEA_material](./extra-FEA_material.ipynb). _note: The scale factor is applied to displacements $\\mathbf{u}$, not forces._\n",
    "\n",
    "![Deformed structure with loads applied](../images/deformed_truss.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {},
   "outputs": [],
   "source": [
    "def LUNaive(A):\n",
    "    [m,n] = np.shape(A)\n",
    "    if m!=n: error('Matrix A must be square')\n",
    "    nb = n+1\n",
    "    U = A.astype(float)\n",
    "    L = np.eye(n)\n",
    "    for k in range(0,n-1):\n",
    "        for i in range(k+1,n):\n",
    "            if U[k,k] != 0.0:\n",
    "                factor = U[i,k]/U[k,k]\n",
    "                L[i,k]=factor\n",
    "                U[i,:] = U[i,:] - factor*U[k,:]\n",
    "    return L,U"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "metadata": {},
   "outputs": [],
   "source": [
    "def solveLU(L,U,b):\n",
    "    n=len(b)\n",
    "    x=np.zeros(n)\n",
    "    y=np.zeros(n)\n",
    "    for k in range(0,n):\n",
    "        y[k] = b[k] - L[k,0:k]@y[0:k]\n",
    "    for k in range(n-1,-1,-1):\n",
    "        x[k] = (y[k] - U[k,k+1:n]@x[k+1:n])/U[k,k]\n",
    "    return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "metadata": {},
   "outputs": [],
   "source": [
    "L, U = LUNaive(K[2:13,2:13])\n",
    "\n",
    "A = 0.1 #mm^2\n",
    "\n",
    "E_alum = 70 #Gpa\n",
    "E_steel = 200 #Gpa\n",
    "\n",
    "F = np.zeros(11)\n",
    "F[5] = -100 #N\n",
    "\n",
    "F_alum = F/(E_alum*A)\n",
    "F_steel = F/(E_steel*A)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "metadata": {},
   "outputs": [],
   "source": [
    "b_steel = F*(1/E_steel/A)\n",
    "b_alum = F*(1/E_alum/A)\n",
    "\n",
    "u_steel_1 = solveLU(L,U,b_steel)*1e-3\n",
    "u_alum_1 = solveLU(L,U,b_alum)*1e-3\n",
    "\n",
    "F_steel_1 = E_steel*A*K[2:13,2:13]@u_steel_1*1e3\n",
    "F_alum_1 = E_alum*A*K[2:13,2:13]@u_alum_1*1e3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Steel Displacement:\n",
      "2.0 mm\n",
      "-2.0 mm\n",
      "0.0 mm\n",
      "-4.0 mm\n",
      "1.0 mm\n",
      "-5.0 mm\n",
      "2.0 mm\n",
      "-4.0 mm\n",
      "0.0 mm\n",
      "-2.0 mm\n",
      "2.0 mm\n",
      "Aluminum Displacement:\n",
      "6.0 mm\n",
      "-6.0 mm\n",
      "1.0 mm\n",
      "-11.0 mm\n",
      "3.0 mm\n",
      "-15.0 mm\n",
      "5.0 mm\n",
      "-11.0 mm\n",
      "1.0 mm\n",
      "-6.0 mm\n",
      "6.0 mm\n"
     ]
    }
   ],
   "source": [
    "   print('Steel Displacement:')\n",
    "for i in range(len(u_steel_1)):\n",
    "    print(np.around(u_steel_1[i]),'mm')\n",
    "print('Aluminum Displacement:')\n",
    "for i in range(len(u_alum_1)):\n",
    "    print(np.around(u_alum_1[i]),'mm')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Steel Forces:\n",
      "0.0 N\n",
      "-5e-15 N\n",
      "-1.4e-14 N\n",
      "3.1e-14 N\n",
      "-1.4e-14 N\n",
      "-99.99999999999993 N\n",
      "1.4e-14 N\n",
      "1.4e-14 N\n",
      "-2.6e-14 N\n",
      "-5.6e-14 N\n",
      "1.4e-14 N\n",
      "Aluminum Forces:\n",
      "1.4e-14 N\n",
      "-4e-14 N\n",
      "1.4e-14 N\n",
      "8.7e-14 N\n",
      "1.7e-14 N\n",
      "-100.00000000000011 N\n",
      "-4.2e-14 N\n",
      "9.7e-14 N\n",
      "2.4e-14 N\n",
      "-5.6e-14 N\n",
      "1.4e-14 N\n"
     ]
    }
   ],
   "source": [
    "print('Steel Forces:')\n",
    "for i in range(len(F_steel_1)):\n",
    "    print(np.around(F_steel_1[i],15),'N')\n",
    "print('Aluminum Forces:')\n",
    "for i in range(len(F_alum_1)):\n",
    "    print(np.around(F_alum_1[i],15),'N')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "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": [
    "#2d\n",
    "L=300 # mm\n",
    "nodes = np.array([[1,0,0],[2,0.5,3**0.5/2],\n",
    "                  [3,1,0],[4,1.5,3**0.5/2],\n",
    "                  [5,2,0],[6,2.5,3**0.5/2],\n",
    "                  [7,3,0]])\n",
    "\n",
    "nodes[:,1:3]*=L\n",
    "\n",
    "elems = np.array([[1,1,2],[2,2,3],\n",
    "                  [3,1,3],[4,2,4],\n",
    "                  [5,3,4],[6,3,5],\n",
    "                  [7,4,5],[8,4,6],\n",
    "                  [9,5,6],[10,5,7],\n",
    "                  [11,6,7]])\n",
    "\n",
    "ix = 2*np.block([[np.arange(0,5)],[np.arange(1,6)],\n",
    "                 [np.arange(2,7)],[np.arange(0,5)]])\n",
    "\n",
    "iy = ix+1\n",
    "\n",
    "r = np.block([n[1:3] for n in nodes])\n",
    "\n",
    "plt.figure(figsize=(10,10))\n",
    "plt.plot(r[ix],r[iy],'-',color='k')\n",
    "plt.plot(r[ix],r[iy],'o',color='b')\n",
    "plt.plot(r[0],r[1],'^',color='r',markersize=20)\n",
    "plt.plot(r[0],r[1],'>',color='k',markersize=20)\n",
    "plt.plot(r[-2],r[-1],'^',color='r',markersize=20)\n",
    "\n",
    "\n",
    "for k in nodes:\n",
    "    if k[2]>0.8*L: offset=0.1\n",
    "    else: offset=-L/5\n",
    "    plt.text(k[1]-L/3,k[2]+offset,'n {}'.format(int(k[0])),color='r')\n",
    "\n",
    "\n",
    "for i in elems:\n",
    "    n_1=nodes[i[1]-1]\n",
    "    n_2=nodes[i[2]-1]\n",
    "    \n",
    "    x=np.mean([n_2[1],n_1[1]])\n",
    "    y=np.mean([n_2[2],n_1[2]])\n",
    "   \n",
    "    plt.text(x-L/5,y-L/10,int(i[0]),color='green')\n",
    "    \n",
    "plt.title('Undeformed truss structure')\n",
    "plt.xlabel('x (mm)')\n",
    "plt.ylabel('y (mm)')\n",
    "plt.axis(L*np.array([-0.5,3.5,-1,1.5]));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "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": [
    "nodes = np.array([[1,0,0],[2,0.5,3**0.5/2],\n",
    "                  [3,1,0],[4,1.5,3**0.5/2],\n",
    "                  [5,2,0],[6,2.5,3**0.5/2],\n",
    "                  [7,3,0]])\n",
    "\n",
    "nodes[:,1:3]*=l\n",
    "\n",
    "elems = np.array([[1,1,2],[2,2,3],\n",
    "                  [3,1,3],[4,2,4],\n",
    "                  [5,3,4],[6,3,5],\n",
    "                  [7,4,5],[8,4,6],\n",
    "                  [9,5,6],[10,5,7],\n",
    "                  [11,6,7]])\n",
    "\n",
    "ix = 2*np.block([[np.arange(0,5)],[np.arange(1,6)],[np.arange(2,7)],[np.arange(0,5)]])\n",
    "iy = ix+1\n",
    "\n",
    "r = np.block([n[1:3] for n in nodes])\n",
    "\n",
    "scale = 5\n",
    "\n",
    "u_s = np.zeros(2*len(nodes))\n",
    "u_a = np.zeros(2*len(nodes))\n",
    "\n",
    "u_s[2:13] = u_steel_1\n",
    "u_a[2:13] = u_alum_1\n",
    "\n",
    "F_s = np.zeros(2*len(nodes))\n",
    "F_a = np.zeros(2*len(nodes))\n",
    "\n",
    "F_s[2:13] = F_steel_1\n",
    "F_a[2:13] = F_alum_1\n",
    "\n",
    "plt.figure(figsize=(10,10))\n",
    "plt.plot(r[ix],r[iy],'-',color=(0,0,0,1))\n",
    "plt.plot(r[ix]+u_s[ix]*s,r[iy]+u_s[iy]*s,'-',color=(1,0,0,1))\n",
    "plt.quiver(r[ix],r[iy],F_s[ix],F_s[iy],color=(1,0,0,1),label='Applied Forces Steel')\n",
    "plt.quiver(r[ix],r[iy],u_s[ix],u_s[iy],color=(0,0,1,1),label='Displacements Steel')\n",
    "plt.axis(l*np.array([-0.5,3.5,-0.5,2]))\n",
    "plt.xlabel('x (mm)')\n",
    "plt.ylabel('y (mm)')\n",
    "plt.title('Steel: Deformation scale = {:.1f}x'.format(scale))\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 182,
   "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": [
    "plt.figure(figsize=(10,10))\n",
    "plt.plot(r[ix],r[iy],'-',color=(0,0,0,1))\n",
    "plt.plot(r[ix]+u_a[ix]*s,r[iy]+u_a[iy]*s,'-',color=(1,0,0,1))\n",
    "plt.quiver(r[ix],r[iy],F_a[ix],F_a[iy],color=(1,0,0,1),label='Applied Forces Steel')\n",
    "plt.quiver(r[ix],r[iy],u_a[ix],u_a[iy],color=(0,0,1,1),label='Displacements Steel')\n",
    "plt.axis(l*np.array([-0.5,3.5,-0.5,2]))\n",
    "plt.xlabel('x (mm)')\n",
    "plt.ylabel('y (mm)')\n",
    "plt.title('Steel: Deformation scale = {:.1f}x'.format(scale))\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. Determine cross-sectional area\n",
    "\n",
    "a. Using aluminum, what is the minimum cross-sectional area to keep total y-deflections $<0.2~mm$?\n",
    "\n",
    "b. Using steel, what is the minimum cross-sectional area to keep total y-deflections $<0.2~mm$?\n",
    "\n",
    "c. What are the weights of the aluminum and steel trusses with the chosed cross-sectional areas?\n",
    "\n",
    "d. The current price (2020/03) of [aluminum](https://tradingeconomics.com/commodity/aluminum) is 1545 dollars/Tonne and [steel](https://tradingeconomics.com/commodity/steel) is 476 dollars/Tonne [2]. Which material is cheaper to  create the truss?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Aluminum: minimum cross ssectional area =  7.68 mm^2\n",
      "Steel: minimum cross ssectional area =  2.7 mm^2\n"
     ]
    }
   ],
   "source": [
    "#3a/b\n",
    "A1 = np.linspace(0.1,10,1000)\n",
    "\n",
    "for i in range (0, 1000):\n",
    "    F_al = F*(1/(E_alum*10**3)/A1[i])\n",
    "    u_al = solveLU(L,U,F_al)\n",
    "    u_al_1 = u_al[1::2]\n",
    "    if min(u_al_1)>-0.2:\n",
    "        print('Aluminum: minimum cross ssectional area = ',np.around(A1[i],2),'mm^2')\n",
    "        AcsAl = A1[i]\n",
    "        break\n",
    "for i in range (0, 1000):\n",
    "    F_st_1 = F*(1/(E_steel*10**3)/A1[i])\n",
    "    u_st_1 = solveLU(L,U,F_st_1)\n",
    "    u_st_2 = u_st_1[1::2]\n",
    "    if min(u_st_2)>-0.2:\n",
    "        print('Steel: minimum cross ssectional area = ',np.around(A1[i],2),'mm^2')\n",
    "        AcsSt = A1[i]\n",
    "        break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Aluminum truss: 68.44 g\n",
      "Steel truss: 68.96 g\n"
     ]
    }
   ],
   "source": [
    "#3c\n",
    "n_beam = 11\n",
    "L = 300\n",
    "V_al = n_beam*AcsAl*L\n",
    "V_st = n_beam*AcsSt*L\n",
    "rho_al = 0.0027\n",
    "rho_st = 0.00775\n",
    "mass_al = V_al*rho_al\n",
    "mass_st = V_st*rho_st\n",
    "print('Aluminum truss:',np.around(mass_al,2),'g')\n",
    "print('Steel truss:',np.around(mass_st,2),'g')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Steel is cheaper than aluminum\n",
      "Steel vs Aluminum\n",
      "0.03 $ vs 0.11 $\n"
     ]
    }
   ],
   "source": [
    "#3d\n",
    "al_price = 1545\n",
    "st_price = 476\n",
    "cost_al = mass_al*al_price/(1000**2)\n",
    "cost_st = mass_st*st_price/(1000**2)\n",
    "print('Steel is cheaper than aluminum')\n",
    "print('Steel vs Aluminum')\n",
    "print(np.around(cost_st,2),'$', 'vs',np.around(cost_al,2),'$')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4. Future Predictions using past data\n",
    "\n",
    "The data from the price of aluminum and steel are in the data files `../data/al_prices.csv` and `../data/steel_price.csv`. If you're going to produce these supports for 5 years, how would you use the price history of steel and aluminum to compare how much manufacturing will cost?\n",
    "\n",
    "a. Separate the aluminum and steel data points into training and testing data (70-30%-split)\n",
    "\n",
    "b. Fit the training data to polynomial functions of order n. _Choose the highest order._\n",
    "\n",
    "c. Plot the error between your model and the training data and the error between your model and you testing data as a function of the polynomial function order, n. [Create the training-testing curves](../notebooks/03_Linear-regression-algebra.ipynb)\n",
    "\n",
    "d. Choose a polynomial function to predict the price of aluminum and steel in the year 2025. \n",
    "\n",
    "e. Based upon your price model would you change your answer in __3.b__?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import random as random\n",
    "aluminum = pd.read_csv('../data/al_price.csv')\n",
    "steel = pd.read_csv('../data/steel_price.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 194,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#4a/b/c\n",
    "#steel\n",
    "x_steel = steel['Year'].values\n",
    "y_steel = steel['dollars/MT'].values\n",
    "\n",
    "\n",
    "np.random.seed(103)\n",
    "i_rand = np.random.randint(0,len(x_steel),size=len(x_steel))\n",
    "\n",
    "\n",
    "train_per=0.7\n",
    "\n",
    "x_train_steel = x_steel[i_rand[:int(len(x_steel)*train_per)]]\n",
    "y_train_steel = y_steel[i_rand[:int(len(x_steel)*train_per)]]\n",
    "\n",
    "\n",
    "\n",
    "x_test_steel = x_steel[i_rand[int(len(x_steel)*train_per):]]\n",
    "y_test_steel = y_steel[i_rand[int(len(x_steel)*train_per):]]\n",
    "\n",
    "Z_train_steel = np.block([[x_train_steel**0]]).T\n",
    "Z_test_steel = np.block([[x_test_steel**0]]).T\n",
    "\n",
    "\n",
    "max_N=12\n",
    "SSE_train_steel = np.zeros(max_N)\n",
    "SSE_test_steel = np.zeros(max_N)\n",
    "for i in range(1,max_N):\n",
    "    Z_train_steel =np.hstack((Z_train_steel,x_train_steel.reshape(-1,1)**i))\n",
    "    Z_test_steel = np.hstack((Z_test_steel,x_test_steel.reshape(-1,1)**i))\n",
    "    \n",
    "    A_s = np.linalg.solve(Z_train_steel.T@Z_train_steel,Z_train_steel.T@y_train_steel)\n",
    "    \n",
    "    SSE_train_steel[i] = np.sum((y_train_steel-Z_train_steel@A_s)**2)/len(y_train_steel)\n",
    "    SSE_test_steel[i] = np.sum((y_test_steel-Z_test_steel@A_s)**2)/len(y_test_steel)\n",
    "\n",
    "\n",
    "plt.figure(figsize=(20,10))\n",
    "plt.semilogy(np.arange(2,max_N,1),SSE_train_steel[2:],'o-',label='Training Data')\n",
    "plt.semilogy(np.arange(2,max_N,1),SSE_test_steel[2:],'s-',label='Testing Data')\n",
    "plt.title('Steel Error in Testing-Training vs. Order')\n",
    "plt.xlabel('Polynomial Order [m=2->10]')\n",
    "plt.ylabel('Error')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#aluminum\n",
    "x_alum = aluminum['Year'].values\n",
    "y_alum = aluminum['dollars/MT'].values\n",
    "\n",
    "\n",
    "np.random.seed(103)\n",
    "i_rand = np.random.randint(0,len(x_alum),size=len(x_alum))\n",
    "\n",
    "\n",
    "train_per=0.7\n",
    "\n",
    "x_train_alum = x_alum[i_rand[:int(len(x_alum)*train_per)]]\n",
    "y_train_alum = y_alum[i_rand[:int(len(x_alum)*train_per)]]\n",
    "\n",
    "\n",
    "\n",
    "x_test_alum = x_alum[i_rand[int(len(x_alum)*train_per):]]\n",
    "y_test_alum = y_alum[i_rand[int(len(x_alum)*train_per):]]\n",
    "\n",
    "Z_train_alum = np.block([[x_train_alum**0]]).T\n",
    "Z_test_alum = np.block([[x_test_alum**0]]).T\n",
    "\n",
    "\n",
    "max_N=15\n",
    "SSE_train_alum = np.zeros(max_N)\n",
    "SSE_test_alum = np.zeros(max_N)\n",
    "for i in range(1,max_N):\n",
    "    Z_train_alum =np.hstack((Z_train_alum,x_train_alum.reshape(-1,1)**i))\n",
    "    Z_test_alum = np.hstack((Z_test_alum,x_test_alum.reshape(-1,1)**i))\n",
    "    \n",
    "    A_al = np.linalg.solve(Z_train_alum.T@Z_train_alum,Z_train_alum.T@y_train_alum)\n",
    "    \n",
    "    SSE_train_alum[i] = np.sum((y_train_alum-Z_train_alum@A_al)**2)/len(y_train_alum)\n",
    "    SSE_test_alum[i] = np.sum((y_test_alum-Z_test_alum@A_al)**2)/len(y_test_alum)\n",
    "\n",
    "\n",
    "plt.figure(figsize=(20,10))\n",
    "plt.semilogy(np.arange(2,max_N,1),SSE_train_alum[2:],'o-',label='Training Data')\n",
    "plt.semilogy(np.arange(2,max_N,1),SSE_test_alum[2:],'s-',label='Testing Data')\n",
    "plt.title('Alum Error in Testing-Training vs. Order')\n",
    "plt.xlabel('Polynomial Order [m=2->10]')\n",
    "plt.ylabel('Error')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 196,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#4d\n",
    "#steel\n",
    "Z_steel=np.block([[x_steel**0],[x_steel**1],\n",
    "              [x_steel**2],[x_steel**3],\n",
    "              [x_steel**4],[x_steel**5],\n",
    "              [x_steel**6],[x_steel**7],\n",
    "              [x_steel**8],[x_steel**9],\n",
    "              [x_steel**10],[x_steel**11]]).T\n",
    "A_steel = np.linalg.solve(Z_steel[:189].T@Z_steel[:189],Z_steel[:189].T@y_steel)\n",
    "\n",
    "xfunction_s = np.linspace(np.min(x_steel),2025,len(y_steel))\n",
    "yfunction_s = np.poly1d(np.flip(A_steel))\n",
    "\n",
    "plt.figure(figsize=(8,8))\n",
    "plt.plot(x_steel,y_steel,'k',label='Data')\n",
    "plt.plot(xfunction_s, yfunction_s(xfunction_s), label='11th Order Polynomial Fit')\n",
    "plt.xlabel('Year')\n",
    "plt.ylabel('Price ($/ton)')\n",
    "plt.title('Predicted Price of Steel vs Year')\n",
    "plt.legend();\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#alum\n",
    "Z_alum=np.block([[x_alum**0],[x_alum**1],\n",
    "              [x_alum**2],[x_alum**3],\n",
    "              [x_alum**4],[x_alum**5],\n",
    "              [x_alum**6],[x_alum**7],\n",
    "              [x_alum**8],[x_alum**9],\n",
    "              [x_alum**10],[x_alum**11],\n",
    "                 [x_alum**12],[x_alum**13],[x_alum**14]]).T\n",
    "A_alum = np.linalg.solve(Z_alum[:203].T@Z_alum[:203],Z_alum[:203].T@y_alum)\n",
    "\n",
    "xfunction_al = np.linspace(np.min(x_alum),2025,len(y_alum))\n",
    "yfunction_al = np.poly1d(np.flip(A_alum))\n",
    "\n",
    "plt.figure(figsize=(8,8))\n",
    "plt.plot(x_alum,y_alum,'k',label='Data')\n",
    "plt.plot(xfunction_al, yfunction_al(xfunction_al), label='14th Order Polynomial Fit')\n",
    "plt.xlabel('Year')\n",
    "plt.ylabel('Price ($/ton)')\n",
    "plt.title('Predicted Price of Aluminum vs Year')\n",
    "plt.legend();\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you were to build a truss 5 years from now, aluminum would be the cheaper option."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# References\n",
    "\n",
    "1. <https://en.wikipedia.org/wiki/Direct_stiffness_method>\n",
    "\n",
    "2. Aluminum and steel price history on <https://tradingeconomics.com>"
   ]
  },
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