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{
"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": 32,
"metadata": {},
"outputs": [],
"source": [
"from __future__ import print_function\n",
"import numpy as np\n",
"import pandas as pd\n",
"import random\n",
"import ipywidgets as widgets\n",
"import matplotlib.pyplot as plt\n",
"from ipywidgets import interact, interactive, fixed, interact_manual\n",
"fea_arrays = np.load('./fea_arrays.npz')\n",
"K=fea_arrays['K']\n",
"def LUNaive(A):\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\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {},
"outputs": [],
"source": [
"def solveLU(L,U,b):\n",
" \n",
" n=len(b)\n",
" x=np.zeros(n)\n",
" y=np.zeros(n)\n",
" \n",
" \n",
" for k in range(0,n):\n",
" y[k] = b[k] - L[k,0:k]@y[0:k]\n",
" \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": "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": 34,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The condition of K is: 1.4577532625238035e+17\n",
"CThe condition of K[2:13,2:13] is: 52.23542514351006\n",
"\n",
"The expected error of u: 14.577532625238035\n",
"The condition of K is large because it ill-conditioned, meaning small changes easily affect the input\n",
"The expected error of u[2:13]: 5.223542514351006e-15\n"
]
}
],
"source": [
"condition1 = np.linalg.cond(K)\n",
"condition2 = np.linalg.cond(K[2:13,2:13])\n",
"print('The condition of K is:', condition1)\n",
"print('CThe condition of K[2:13,2:13] is: ', condition2)\n",
"print()\n",
"error1 = condition1*1e-16\n",
"error2 = condition2*1e-16\n",
"print('The expected error of u:',error1)\n",
"print('The condition of K is large because it ill-conditioned, meaning small changes easily affect the input')\n",
"print('The expected error of u[2:13]:',error2)"
]
},
{
"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": 35,
"metadata": {},
"outputs": [],
"source": [
"L,U = LUNaive(K[2:13,2:13])"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {},
"outputs": [],
"source": [
"A = 1e-7\n",
"Est = 200e9\n",
"Eal = 70e9\n",
"F = np.zeros(11)\n",
"F[5] = -100\n",
"ust = solveLU(L,U,F/Est/A)\n",
"ual = solveLU(L,U,F/Eal/A)"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {},
"outputs": [],
"source": [
"u1 = np.zeros(14)\n",
"for i in range(len(ust)):\n",
" u1[i+2] = ust[i]\n",
"u2 = np.zeros(14)\n",
"for i in range(len(ual)):\n",
" u2[i+2] = ual[i]\n",
"\n",
"Fst = K*Est*A@u1\n",
"Fal = K*Eal*A@u2\n",
"\n",
"u1 = u1*1000\n",
"u2 = u2*1000"
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Steel\n",
"\n",
" Displacements:\n",
" ---------------\n",
" u_1x : 0.00 mm\n",
" u_1y : 0.00 mm\n",
" u_2x : 1948.56 mm\n",
" u_2y : -2125.00 mm\n",
" u_3x : 433.01 mm\n",
" u_3y : -4000.00 mm\n",
" u_4x : 1082.53 mm\n",
" u_4y : -5375.00 mm\n",
" u_5x : 1732.05 mm\n",
" u_5y : -4000.00 mm\n",
" u_6x : 216.51 mm\n",
" u_6y : -2125.00 mm\n",
" u_7x : 2165.06 mm\n",
" u_7y : 0.00 mm\n",
"\n",
" Forces:\n",
" ---------------\n",
" F_1x : 0.00 N\n",
" F_1y : 50.00 N\n",
" F_2x : -0.00 N\n",
" F_2y : 0.00 N\n",
" F_3x : 0.00 N\n",
" F_3y : 0.00 N\n",
" F_4x : 0.00 N\n",
" F_4y : -100.00 N\n",
" F_5x : -0.00 N\n",
" F_5y : 0.00 N\n",
" F_6x : 0.00 N\n",
" F_6y : 0.00 N\n",
" F_7x : 0.00 N\n",
" F_7y : 50.00 N\n",
"\n",
"d)\n"
]
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"print('Steel\\n')\n",
"\n",
"xy={0:'x',1:'y'}\n",
"print(' Displacements:\\n ---------------')\n",
"for i in range(len(u1)):\n",
" print(' u_{}{} : {:.2f} mm'.format(int(i/2)+1,xy[i%2],u1[i]))\n",
"print()\n",
"print(' Forces:\\n ---------------')\n",
"for i in range(len(Fst)):\n",
" print(' F_{}{} : {:.2f} N'.format(int(i/2)+1,xy[i%2],Fst[i]))\n",
" \n",
"print()\n",
"\n",
"print('d)')\n",
"l = 300\n",
"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]*=l\n",
"elems = 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",
"r = np.block([n[1:3] for n in nodes])\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",
"for n in nodes:\n",
" if n[2]>0.8*l: offset=0.1\n",
" else: offset=-l/5\n",
" plt.text(n[1]-l/3,n[2]+offset,'n {}'.format(int(n[0])),color='b') \n",
"s = 5\n",
"plt.plot(r[ix]+u1[ix]*s,r[iy]+u1[iy]*s,'-',color=(1,0,0,1))\n",
"plt.quiver(r[ix],r[iy],Fst[ix],Fst[iy],color=(1,0,0,1),label='Applied Forces')\n",
"plt.quiver(r[ix],r[iy],u1[ix],u1[iy],color=(0,0,1,1),label='displacements')\n",
"plt.axis(l*np.array([-0.5,3.5,-1,1.5]))\n",
"plt.legend(bbox_to_anchor=(1,0.5))\n",
"plt.title('Steel : Deformation Scale = {:.1f}x'.format(s),size=20)\n",
"plt.xlabel('x (mm)',size=15)\n",
"plt.ylabel('y (mm)',size=15);"
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Aluminum\n",
"\n",
" The displacements:\n",
" ---------------\n",
" u1x : 0.00 mm\n",
" u1y : 0.00 mm\n",
" u2x : 5567.31 mm\n",
" u2y : -6071.43 mm\n",
" u3x : 1237.18 mm\n",
" u3y : -11428.57 mm\n",
" u4x : 3092.95 mm\n",
" u4y : -15357.14 mm\n",
" u5x : 4948.72 mm\n",
" u5y : -11428.57 mm\n",
" u6x : 618.59 mm\n",
" u6y : -6071.43 mm\n",
" u7x : 6185.90 mm\n",
" u7y : 0.00 mm\n",
"\n",
" The Forces:\n",
" ---------------\n",
" F1x : 0.00 N\n",
" F1y : 50.00 N\n",
" F2x : -0.00 N\n",
" F2y : -0.00 N\n",
" F3x : 0.00 N\n",
" F3y : 0.00 N\n",
" F4x : 0.00 N\n",
" F4y : -100.00 N\n",
" F5x : 0.00 N\n",
" F5y : 0.00 N\n",
" F6x : 0.00 N\n",
" F6y : -0.00 N\n",
" F7x : 0.00 N\n",
" F7y : 50.00 N\n"
]
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"print('Aluminum\\n')\n",
"\n",
"xy={0:'x',1:'y'}\n",
"print(' The displacements:\\n ---------------')\n",
"for i in range(len(u2)):\n",
" print(' u{}{} : {:.2f} mm'.format(int(i/2)+1,xy[i%2],u2[i]))\n",
"print()\n",
"print(' The Forces:\\n ---------------')\n",
"for i in range(len(Fal)):\n",
" print(' F{}{} : {:.2f} N'.format(int(i/2)+1,xy[i%2],Fal[i]))\n",
"\n",
"l = 300\n",
"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]*=l\n",
"elems = 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",
"r = np.block([n[1:3] for n in nodes])\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",
"for n in nodes:\n",
" if n[2]>0.8*l: offset=0.1\n",
" else: offset=-l/5\n",
" plt.text(n[1]-l/3,n[2]+offset,'n {}'.format(int(n[0])),color='b') \n",
"s = 5\n",
"plt.plot(r[ix]+u2[ix]*s,r[iy]+u2[iy]*s,'-',color=(1,0,0,1))\n",
"plt.quiver(r[ix],r[iy],Fal[ix],Fal[iy],color=(1,0,0,1),label='applied forces')\n",
"plt.quiver(r[ix],r[iy],u2[ix],u2[iy],color=(0,0,1,1),label='displacements')\n",
"plt.axis(l*np.array([-0.5,3.5,-1,1.5]))\n",
"plt.legend(bbox_to_anchor=(1,0.5))\n",
"plt.title('Aluminum : Deformation scale = {:.1f}x'.format(s),size=20)\n",
"plt.xlabel('x (mm)',size=15)\n",
"plt.ylabel('y (mm)',size=15);"
]
},
{
"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": 45,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The minimum cross-sectional area for aluminum: 7.9e-06 m^2\n",
" The aluminum displacements:\n",
" -----------------------\n",
" u1y : 0.00 mm\n",
" u2y : -76.85 mm\n",
" u3y : -144.67 mm\n",
" u4y : -194.39 mm\n",
" u5y : -144.67 mm\n",
" u6y : -76.85 mm\n",
" u7y : 0.00 mm\n",
"\n",
"The minimum cross-sectional area for steel: 2.8e-06 m^2\n",
"The steel Displacements:\n",
" --------------------\n",
" u1y : 0.00 mm\n",
" u2y : -75.89 mm\n",
" u3y : -142.86 mm\n",
" u4y : -191.96 mm\n",
" u5y : -142.86 mm\n",
" u6y : -75.89 mm\n",
" u7y : 0.00 mm\n"
]
}
],
"source": [
"Aal = 0.0000079\n",
"F = np.zeros(11)\n",
"F[5] = -100\n",
"\n",
"ual = solveLU(L,U,F/Eal/Aal)\n",
"u2 = np.zeros(14) \n",
"for i in range(len(ual)):\n",
" u2[i+2] = ual[i]\n",
"Fal = K*Eal*Aal@u2\n",
"\n",
"print('The minimum cross-sectional area for aluminum:', Aal,'m^2')\n",
"xy={0:'x',1:'y'}\n",
"print(' The aluminum displacements:\\n -----------------------')\n",
"for i in range(len(u2)):\n",
" if (i % 2) != 0:\n",
" print(' u{}{} : {:.2f} mm'.format(int(i/2)+1,xy[i%2],u2[i]*1000))\n",
"\n",
"print()\n",
"\n",
"Ast = 0.0000028\n",
"F = np.zeros(11)\n",
"F[5] = -100\n",
"\n",
"ust = solveLU(L,U,F/Est/Ast)\n",
"u1 = np.zeros(14)\n",
"for i in range(len(ust)):\n",
" u1[i+2] = ust[i]\n",
"Fst = K*Est*Ast@u1\n",
"\n",
"\n",
"print('The minimum cross-sectional area for steel:', Ast,'m^2')\n",
"xy={0:'x',1:'y'}\n",
"print('The steel Displacements:\\n --------------------')\n",
"for i in range(len(u1)):\n",
" if (i % 2) != 0:\n",
" print(' u{}{} : {:.2f} mm'.format(int(i/2)+1,xy[i%2],u1[i]*1000))"
]
},
{
"cell_type": "code",
"execution_count": 46,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The mass for steel : 0.0776 kg\n",
"The mass for aluminum: 0.0771 kg\n",
"The cost of Steel : $ 0.04\n",
"The cost of Aluminum: $ 0.12\n",
" The steel truss is cheaper.\n"
]
}
],
"source": [
"rhost = 7700 \n",
"rhoal = 2710 \n",
"l = 0.3 \n",
"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]*=l\n",
"elems = 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",
"for i in range(0,len(elems)):\n",
" n1 = elems[i][1] - 1\n",
" n2 = elems[i][2] - 1 \n",
" ix1 = nodes[n1][1]\n",
" iy1 = nodes[n1][2] \n",
" ix2 = nodes[n2][1]\n",
" iy2 = nodes[n2][2]\n",
" l += ((iy2-iy1)**2 + (ix2-ix1)**2)**0.5\n",
"\n",
"mst = Ast*l*rhost\n",
"mal = Aal*l*rhoal\n",
"print('The mass for steel :', round(mst,4),'kg')\n",
"print('The mass for aluminum:', round(mal,4),'kg')\n",
"\n",
"pricest = 476/1000 \n",
"priceal = 1545/1000 \n",
"\n",
"costst = mst*pricest\n",
"costal = mal*priceal\n",
"\n",
"print('The cost of Steel : $',round(costst,2))\n",
"print('The cost of Aluminum: $',round(costal,2))\n",
"print(' The steel truss is 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": 55,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 720x720 with 2 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"steel = pd.read_csv('../data/steel_price.csv')\n",
"aluminum = pd.read_csv('../data/al_price.csv')\n",
"ts = steel['Year']\n",
"Ps = steel['dollars/MT']\n",
"ta = aluminum['Year']\n",
"Pa = aluminum['dollars/MT']\n",
"\n",
"\n",
"np.random.seed(100)\n",
"srandom = random.sample(range(0,len(ts)),len(ts))\n",
"arandom = random.sample(range(0,len(ta)),len(ta))\n",
"trainper=0.7\n",
"np.random.seed(100)\n",
"\n",
"tstrain = np.sort(ts[srandom[:int(len(ts)*trainper)]])\n",
"Pstrain = np.sort(Ps[srandom[:int(len(ts)*trainper)]])\n",
"tstest = np.sort(ts[srandom[int(len(ts)*trainper):]])\n",
"Pstest = np.sort(Ps[srandom[int(len(ts)*trainper):]])\n",
"\n",
"tatrain = np.sort(ta[srandom[:int(len(ta)*trainper)]])\n",
"Patrain = np.sort(Pa[srandom[:int(len(ta)*trainper)]])\n",
"tatest = np.sort(ta[arandom[int(len(ta)*trainper):]])\n",
"Patest = np.sort(Pa[arandom[int(len(ta)*trainper):]])\n",
"\n",
"\n",
"maxn = 46\n",
"Zstrain = np.block([[tstrain**0]]).T\n",
"for i in range(1,maxn+1):\n",
" Zstrain = np.hstack((Zstrain,tstrain.reshape(-1,1)**i))\n",
"astrain = np.linalg.solve(Zstrain.T@Zstrain,Zstrain.T@Pstrain)\n",
"\n",
"\n",
"Zatrain = np.block([[tatrain**0]]).T\n",
"for i in range(1,maxn+1):\n",
" Zatrain = np.hstack((Zatrain,tatrain.reshape(-1,1)**i))\n",
"aatrain = np.linalg.solve(Zatrain.T@Zatrain,Zatrain.T@Patrain)\n",
"\n",
"\n",
"f, axes = plt.subplots(2, 1,figsize=(10,10));\n",
"axes[0].plot(tstrain,Pstrain,'o',label='Steel');\n",
"axes[0].set_ylabel('Price (usd)',size=20);\n",
"axes[0].plot(tstrain,Zstrain@astrain,label='Order Fit: {}'.format(maxn),lw=3);\n",
"axes[0].legend(prop={'size':15});\n",
"\n",
"axes[1].plot(tatrain,Patrain,'o',label='Aluminum');\n",
"axes[1].set_ylabel('Price (usd)',size=20);\n",
"axes[1].plot(tatrain,Zatrain@aatrain,label='Order Fit {}'.format(maxn),lw=3);\n",
"axes[1].legend(prop={'size':15});\n",
"\n",
"plt.xlabel('Time (years)',size=20);"
]
},
{
"cell_type": "code",
"execution_count": 57,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The error of steel\n",
"---- n = 1 ----\n",
"The coefficient of determination for this fit is: 0.613\n",
"The correlation coefficient this fit is: 0.783\n",
"\n",
"---- n = 2 ----\n",
"The coefficient of determination for this fit is: 0.746\n",
"The correlation coefficient this fit is: 0.864\n",
"\n",
"---- n = 3 ----\n",
"The coefficient of determination for this fit is: 0.746\n",
"The correlation coefficient this fit is: 0.864\n",
"\n",
"---- n = 4 ----\n",
"The coefficient of determination for this fit is: 0.746\n",
"The correlation coefficient this fit is: 0.864\n",
"\n",
"---- n = 5 ----\n",
"The coefficient of determination for this fit is: 0.746\n",
"The correlation coefficient this fit is: 0.864\n",
"\n",
"---- n = 6 ----\n",
"The coefficient of determination for this fit is: 0.746\n",
"The correlation coefficient this fit is: 0.863\n",
"\n",
"---- n = 7 ----\n",
"The coefficient of determination for this fit is: 0.745\n",
"The correlation coefficient this fit is: 0.863\n",
"\n",
"---- n = 8 ----\n",
"The coefficient of determination for this fit is: 0.745\n",
"The correlation coefficient this fit is: 0.863\n",
"\n",
"---- n = 9 ----\n",
"The coefficient of determination for this fit is: 0.750\n",
"The correlation coefficient this fit is: 0.866\n",
"\n",
"---- n = 10 ----\n",
"The coefficient of determination for this fit is: 0.750\n",
"The correlation coefficient this fit is: 0.866\n",
"\n",
"---- n = 11 ----\n",
"The coefficient of determination for this fit is: 0.748\n",
"The correlation coefficient this fit is: 0.865\n",
"\n",
"---- n = 12 ----\n",
"The coefficient of determination for this fit is: 0.767\n",
"The correlation coefficient this fit is: 0.876\n",
"\n",
"---- n = 13 ----\n",
"The coefficient of determination for this fit is: 0.607\n",
"The correlation coefficient this fit is: 0.779\n",
"\n",
"---- n = 14 ----\n",
"The coefficient of determination for this fit is: 0.674\n",
"The correlation coefficient this fit is: 0.821\n",
"\n",
"---- n = 15 ----\n",
"The coefficient of determination for this fit is: 0.728\n",
"The correlation coefficient this fit is: 0.853\n",
"\n",
"---- n = 16 ----\n",
"The coefficient of determination for this fit is: -0.819\n",
"The correlation coefficient this fit is: nan\n",
"\n",
"---- n = 17 ----\n",
"The coefficient of determination for this fit is: 0.857\n",
"The correlation coefficient this fit is: 0.926\n",
"\n",
"---- n = 18 ----\n",
"The coefficient of determination for this fit is: 0.669\n",
"The correlation coefficient this fit is: 0.818\n",
"\n",
"---- n = 19 ----\n",
"The coefficient of determination for this fit is: 0.815\n",
"The correlation coefficient this fit is: 0.903\n",
"\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/opt/conda/lib/python3.7/site-packages/ipykernel_launcher.py:17: RuntimeWarning: invalid value encountered in double_scalars\n"
]
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"Zs = np.block([[tstrain**0]]).T\n",
"Zstest = np.block([[tstest**0]]).T\n",
"Zstrain = np.block([[tstrain**0]]).T\n",
"maxn = 20\n",
"SSEstest=np.zeros(maxn)\n",
"SSEstrain=np.zeros(maxn)\n",
"print('The error of steel')\n",
"for i in range(1,maxn):\n",
" Zs = np.hstack((Zs,tstrain.reshape(-1,1)**i))\n",
" Zstest=np.hstack((Zstest,tstest.reshape(-1,1)**i))\n",
" As = np.linalg.solve(Zs.T@Zs,Zs.T@Pstrain)\n",
" Sts=np.std(Pstrain)\n",
" Srs=np.std(Pstrain-Zs@As)\n",
" r2s=1-Srs/Sts\n",
" print('---- n = {:d} ----'.format(i))\n",
" print('The coefficient of determination for this fit is: {:.3f}'.format(r2s))\n",
" print('The correlation coefficient this fit is: {:.3f}\\n'.format(r2s**0.5))\n",
" plt.plot(tstrain,Pstrain-Zs@As,'-',label='order {:d}'.format(i))\n",
" SSEstrain[i]=np.sum((Pstrain-Zs@As)**2)/len(Pstrain)\n",
" SSEstest[i]=np.sum((Pstest-Zstest@As)**2)/len(Pstest)\n",
" \n",
"plt.legend(loc='center left', bbox_to_anchor=(1.3, .5));\n",
"plt.title('Error in Predicted vs Measured Values',size=20)\n",
"plt.xlabel('X values')\n",
"plt.ylabel('Y Error ');"
]
},
{
"cell_type": "code",
"execution_count": 58,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"error aluminum\n",
"---- n = 1 ----\n",
"the coefficient of determination for this fit is 0.845\n",
"the correlation coefficient this fit is 0.919\n",
"\n",
"---- n = 2 ----\n",
"the coefficient of determination for this fit is 0.860\n",
"the correlation coefficient this fit is 0.927\n",
"\n",
"---- n = 3 ----\n",
"the coefficient of determination for this fit is 0.860\n",
"the correlation coefficient this fit is 0.927\n",
"\n",
"---- n = 4 ----\n",
"the coefficient of determination for this fit is 0.860\n",
"the correlation coefficient this fit is 0.927\n",
"\n",
"---- n = 5 ----\n",
"the coefficient of determination for this fit is 0.860\n",
"the correlation coefficient this fit is 0.927\n",
"\n",
"---- n = 6 ----\n",
"the coefficient of determination for this fit is 0.860\n",
"the correlation coefficient this fit is 0.927\n",
"\n",
"---- n = 7 ----\n",
"the coefficient of determination for this fit is 0.860\n",
"the correlation coefficient this fit is 0.927\n",
"\n",
"---- n = 8 ----\n",
"the coefficient of determination for this fit is 0.860\n",
"the correlation coefficient this fit is 0.927\n",
"\n",
"---- n = 9 ----\n",
"the coefficient of determination for this fit is 0.860\n",
"the correlation coefficient this fit is 0.927\n",
"\n",
"---- n = 10 ----\n",
"the coefficient of determination for this fit is 0.860\n",
"the correlation coefficient this fit is 0.927\n",
"\n",
"---- n = 11 ----\n",
"the coefficient of determination for this fit is 0.860\n",
"the correlation coefficient this fit is 0.927\n",
"\n",
"---- n = 12 ----\n",
"the coefficient of determination for this fit is 0.860\n",
"the correlation coefficient this fit is 0.927\n",
"\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"Za = np.block([[tatrain**0]]).T\n",
"Zatest = np.block([[tatest**0]]).T\n",
"Zatrain = np.block([[tatrain**0]]).T\n",
"\n",
"maxn= 13\n",
"SSEatrain=np.zeros(maxn)\n",
"SSEatest=np.zeros(maxn)\n",
"print('error aluminum')\n",
"for i in range(1,maxn):\n",
" Za = np.hstack((Za,tatrain.reshape(-1,1)**i))\n",
" Zatest=np.hstack((Zatest,tatest.reshape(-1,1)**i))\n",
" Aa = np.linalg.solve(Za.T@Za,Za.T@Patrain)\n",
" Sta = np.std(Patrain)\n",
" Sra = np.std(Patrain-Za@Aa)\n",
" r2a = 1-Sra/Sta\n",
" print('---- n = {:d} ----'.format(i))\n",
" print('the coefficient of determination for this fit is {:.3f}'.format(r2a))\n",
" print('the correlation coefficient this fit is {:.3f}\\n'.format(r2a**0.5))\n",
" plt.plot(tatrain,Patrain-Za@Aa,'-',label='order {:d}'.format(i))\n",
" SSEatrain[i]=np.sum((Patrain-Za@Aa)**2)/len(Patrain)\n",
" SSEatest[i]=np.sum((Patest-Zatest@Aa)**2)/len(Patest)\n",
"\n",
"plt.legend(loc='center left', bbox_to_anchor=(1.3, 0.5));\n",
"plt.title('Error in predicted vs measured values',size=20)\n",
"plt.xlabel('X values')\n",
"plt.ylabel('Y Error');"
]
},
{
"cell_type": "code",
"execution_count": 59,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The Cost of Steel in 2025: $ -1741442.68\n",
"The Cost of Aluminum in 2025: $ 799501885.61\n"
]
}
],
"source": [
"for i in range(0,47):\n",
" prices=astrain[i]*2025**i\n",
"print('The Cost of Steel in 2025: $',round(prices,2))\n",
"for i in range(0,47):\n",
" pricea = aatrain[i]*2025**i\n",
"print('The Cost of Aluminum in 2025: $',round(pricea,2))"
]
},
{
"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>"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"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": "3.7.3"
}
},
"nbformat": 4,
"nbformat_minor": 4
}