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": 24,
   "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": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\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": "markdown",
   "metadata": {},
   "source": [
    "## 1a  the error would be a LinAlgError because K is ill conditioned"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1b the condition of k is so large because there are no proper boundary conditions which are necessary. This results in a very large K matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1c since the condition can only be found for the particular segments, the expected error would be 1x10^(-15)"
   ]
  },
  {
   "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": "markdown",
   "metadata": {},
   "source": [
    "# A:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def LUNaive(A):\n",
    "    '''LUNaive: naive LU decomposition\n",
    "    L,U = LUNaive(A): LU decomposition without pivoting.\n",
    "    solution method requires floating point numbers, \n",
    "    as such the dtype is changed to float\n",
    "    \n",
    "    Arguments:\n",
    "    ----------\n",
    "    A = coefficient matrix\n",
    "    returns:\n",
    "    ---------\n",
    "    L = Lower triangular matrix\n",
    "    U = Upper triangular matrix\n",
    "    '''\n",
    "    [m,n] = np.shape(A)\n",
    "    if m!=n: error('Matrix A must be square')\n",
    "    nb = n+1\n",
    "    # Gauss Elimination\n",
    "    U = A.astype(float)\n",
    "    L = np.eye(n)\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": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def solveLU(L,U,b):\n",
    "    '''solveLU: solve for x when LUx = b\n",
    "    x = solveLU(L,U,b): solves for x given the lower and upper \n",
    "    triangular matrix storage\n",
    "    uses forward substitution for \n",
    "    1. Ly = b\n",
    "    then backward substitution for\n",
    "    2. Ux = y\n",
    "    \n",
    "    Arguments:\n",
    "    ----------\n",
    "    L = Lower triangular matrix\n",
    "    U = Upper triangular matrix\n",
    "    b = output vector\n",
    "    \n",
    "    returns:\n",
    "    ---------\n",
    "    x = solution of LUx=b '''\n",
    "    n=len(b)\n",
    "    x=np.zeros(n)\n",
    "    y=np.zeros(n)\n",
    "        \n",
    "    # forward substitution\n",
    "    for k in range(0,n):\n",
    "        y[k] = b[k] - L[k,0:k]@y[0:k]\n",
    "    # backward substitution\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": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "L=((LUNaive(K[2:13,2:13]))[0])\n",
    "U=((LUNaive(K[2:13,2:13]))[1])\n",
    "\n",
    "F=np.array([[0],[0],[0],[0],[0],[-100],[0],[0],[0],[0],[0]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# B:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.01948557 -0.02125     0.00433013 -0.04        0.01082532 -0.05375\n",
      "  0.01732051 -0.04        0.00216506 -0.02125     0.02165064]\n"
     ]
    }
   ],
   "source": [
    "Emod_steel = 200e3\n",
    "a = 0.1 ### mm^2\n",
    "x1 = 1/Emod_steel*a\n",
    "b1 = F*x1\n",
    "\n",
    "U_Steel = solveLU(L,U,b1)\n",
    "print(U_Steel)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.05567306 -0.06071429  0.01237179 -0.11428571  0.03092948 -0.15357143\n",
      "  0.04948717 -0.11428571  0.0061859  -0.06071429  0.06185896]\n"
     ]
    }
   ],
   "source": [
    "Emod_alu = 70e3\n",
    "x2 = 1/Emod_alu*a\n",
    "b2 = F*x2\n",
    "\n",
    "U_Alu = solveLU(L,U,b2)\n",
    "print(U_Alu)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# C:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.          0.          0.01948557 -0.02125     0.00433013 -0.04\n",
      "  0.01082532 -0.05375     0.01732051 -0.04        0.00216506 -0.02125\n",
      "  0.02165064  0.        ]\n",
      "[ 0.          0.          0.05567306 -0.06071429  0.01237179 -0.11428571\n",
      "  0.03092948 -0.15357143  0.04948717 -0.11428571  0.0061859  -0.06071429\n",
      "  0.06185896  0.        ]\n"
     ]
    }
   ],
   "source": [
    "u_steel = np.zeros(len(K))\n",
    "u_steel[0] = 0\n",
    "u_steel[1] = 0\n",
    "u_steel[13] = 0\n",
    "u_steel[2:13]=U_Steel\n",
    "\n",
    "u_alu = np.zeros(len(K))\n",
    "u_alu[0] = 0\n",
    "u_alu[1] = 0\n",
    "u_alu[13] = 0\n",
    "u_alu[2:13]=U_Alu\n",
    "print(u_steel)\n",
    "print(u_alu)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "Force_steel = (K*Emod_steel*a)@u_steel\n",
    "Force_alu = (K*Emod_alu*a)@u_alu"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Steel Reaction Forces\n",
      "[-2.22044605e-16  5.00000000e-01  2.22044605e-16  1.11022302e-16\n",
      "  2.22044605e-16  1.66533454e-16  2.95238729e-16 -1.00000000e+00\n",
      "  4.44089210e-16  5.55111512e-17  5.55111512e-17  0.00000000e+00\n",
      "  0.00000000e+00  5.00000000e-01]\n",
      "Aluminum Reaction Forces\n",
      "[-3.33066907e-16  5.00000000e-01 -4.44089210e-16  1.38777878e-16\n",
      "  2.22044605e-16 -2.77555756e-17  5.12161182e-16 -1.00000000e+00\n",
      "  0.00000000e+00 -3.88578059e-16  0.00000000e+00  0.00000000e+00\n",
      "  0.00000000e+00  5.00000000e-01]\n"
     ]
    }
   ],
   "source": [
    "print('Steel Reaction Forces')\n",
    "print(Force_steel)\n",
    "print('Aluminum Reaction Forces')\n",
    "print(Force_alu)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# D:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x864 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],[3,1,0],[4,1.5,3**0.5/2],[5,2,0],[6,2.5,3**0.5/2],[7,3,0]])\n",
    "nodes[:,1:3]*=300\n",
    "elementss = np.array([[1,1,2],[2,2,3],[3,1,3],[4,2,4],[5,3,4],[6,3,5],[7,4,5],[8,4,6],[9,5,6],[10,5,7],[11,6,7]])\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",
    "plt.figure(figsize=(15,12))\n",
    "plt.plot(r[ix],r[iy],'-',color='b')\n",
    "plt.plot(r[ix]+u_steel[ix]*500,r[iy]+u_steel[iy]*500,'-',color='g')\n",
    "plt.quiver(r[ix],r[iy],u_steel[ix],u_steel[iy],color='orange',scale=1,label='displacements')\n",
    "plt.quiver(r[ix],r[iy],Force_steel[ix],Force_steel[iy],color='red',label='applied forces')\n",
    "plt.title('Steel Deformation and Forces')\n",
    "plt.xlabel('x (mm)')\n",
    "plt.ylabel('y (mm)')\n",
    "plt.axis(300*np.array([-0.5,3.5,-1,1.5]))\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(15,12))\n",
    "plt.plot(r[ix],r[iy],'-',color='b')\n",
    "plt.plot(r[ix]+u_alu[ix]*500,r[iy]+u_alu[iy]*500,'-',color='g')\n",
    "plt.quiver(r[ix],r[iy],u_alu[ix],u_alu[iy],color='orange',scale=1,label='displacements')\n",
    "plt.quiver(r[ix],r[iy],Force_alu[ix],Force_alu[iy],color='red',label='applied forces')\n",
    "plt.title('Aluminum Deformation and Forces')\n",
    "plt.xlabel('x (mm)')\n",
    "plt.ylabel('y (mm)')\n",
    "plt.axis(300*np.array([-0.5,3.5,-1,1.5]))\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": "markdown",
   "metadata": {},
   "source": [
    "# A:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " the minimum aluminum cross-sectional area is  7.679000000000899\n"
     ]
    }
   ],
   "source": [
    "y_val = 100\n",
    "area_hold = 0.1;\n",
    "while (y_val>0.2):\n",
    "    area_hold = area_hold + 0.001\n",
    "    F_new_alu = F*(1/(Emod_alu*area_hold))\n",
    "    u_int_alu = solveLU(L, U, F_new_alu)\n",
    "    y_val = max(abs(u_int_alu))\n",
    "alu_val = area_hold \n",
    "print(' the minimum aluminum cross-sectional area is ', alu_val)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# B:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " the minimum steel cross-sectional area is  2.687999999999815\n"
     ]
    }
   ],
   "source": [
    "y_val = 100\n",
    "area_hold = 0.1;\n",
    "while (y_val>0.2):\n",
    "    area_hold = area_hold + 0.001\n",
    "    F_new_steel = F*(1/(Emod_steel*area_hold))\n",
    "    u_int_steel = solveLU(L, U, F_new_steel)\n",
    "    y_val = max(abs(u_int_steel))\n",
    "steel_val = area_hold \n",
    "print(' the minimum steel cross-sectional area is ', steel_val)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# C:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The weight of the aluminum truss is: 0.069 N\n",
      "The weight of the steel truss is: 0.068 N\n"
     ]
    }
   ],
   "source": [
    "#densities\n",
    "d_steel= 7700*(1/1000)**3 \n",
    "d_alu= 2710*(1/1000)**3 \n",
    "#length\n",
    "leng=300\n",
    "#volume\n",
    "Vol_steel= steel_val*leng*11\n",
    "Vol_alu= alu_val*leng*11\n",
    "#wenght\n",
    "steel_weight= d_steel*Vol_steel\n",
    "alu_weight= d_alu*Vol_alu\n",
    "print('The weight of the aluminum truss is: {:.3f} N'.format(alu_weight))\n",
    "\n",
    "print('The weight of the steel truss is: {:.3f} N'.format(steel_weight))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# D:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The aluminum truss is $0.1061.\n",
      "The steel truss is $0.032512.\n",
      "Steel is the cheaper\n"
     ]
    }
   ],
   "source": [
    "alu_price= 1545/1000\n",
    "steel_price= 476/1000 \n",
    "alu_cost= alu_price*alu_weight\n",
    "steel_cost= steel_price*steel_weight\n",
    "print('The aluminum truss is ${:.5}.'.format(alu_cost))\n",
    "print('The steel truss is ${:.5}.'.format(steel_cost))\n",
    "print('Steel is the cheaper')"
   ]
  },
  {
   "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": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random as random\n",
    "import pandas as pd\n",
    "\n",
    "steel_data = pd.read_csv('../data/steel_price.csv')\n",
    "alu_data = pd.read_csv('../data/al_price.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "year_alu = alu_data['Year'].values\n",
    "price_alu = alu_data['dollars/MT'].values\n",
    "year_steel = steel_data['Year'].values\n",
    "price_steel = steel_data['dollars/MT'].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "203"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(year_alu)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "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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