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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": 199,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import pandas as pd\n",
"from pretty_print import array_print as AP\n",
"from matplotlib import rcParams\n",
"import random"
]
},
{
"cell_type": "code",
"execution_count": 200,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"#Set font style and size \n",
"rcParams['font.family'] = 'sans'\n",
"rcParams['font.size'] = 16\n",
"rcParams['lines.linewidth'] = 3"
]
},
{
"cell_type": "code",
"execution_count": 7,
"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": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"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": 13,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"accuracy of K= 2.220446049250313e-16 \n",
"condition of K= 1.4577532625238035e+17\n"
]
}
],
"source": [
"#1A\n",
"#Rounding Error = 10^(c-t), where condition = 10^c and accuracy = 10^-t\n",
"acc_K = np.finfo(float).eps\n",
"cond_K = np.linalg.cond(K)\n",
"print('accuracy of K=', acc_K, '\\ncondition of K=', cond_K)"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1-A) Rounding error of K = 10 mm\n"
]
}
],
"source": [
"#1A continued\n",
"#Rounding Error = 10^(17-16) = 10^1\n",
"print('1-A) Rounding error of K = 10 mm')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"1-B) The condition of K is so large because it is ill-conditioned which is caused by the lack of boundary conditions."
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"condition of K[2:13,2:13] = 52.23542514351006\n",
"1-C) Rounding error of K = 10^-15 mm\n"
]
}
],
"source": [
"#1C\n",
"cond_K2 = np.linalg.cond(K[2:13,2:13])\n",
"print('condition of K[2:13,2:13] =', cond_K2)\n",
"#Rounding Error = 10^(1-16) = 10^15\n",
"print('1-C) Rounding error of K = 10^-15 mm')"
]
},
{
"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": 99,
"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\n",
"\n",
"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": 100,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"L=\n",
" [[ 1. 0. 0. 0. 0. 0. 0. 0. 0.\n",
" 0. 0. ]\n",
" [ 0. 1. 0. 0. 0. 0. 0. 0. 0.\n",
" 0. 0. ]\n",
" [-0.1667 0.2887 1. 0. 0. 0. 0. 0. 0.\n",
" 0. 0. ]\n",
" [ 0.2887 -0.5 0.1237 1. 0. 0. 0. 0. 0.\n",
" 0. 0. ]\n",
" [-0.6667 0. -0.1786 -0.0962 1. 0. 0. 0. 0.\n",
" 0. 0. ]\n",
" [ 0. 0. -0.1856 -0.7222 -0.0825 1. 0. 0. 0.\n",
" 0. 0. ]\n",
" [ 0. 0. -0.4286 0.1283 -0.2381 0.3343 1. 0. 0.\n",
" 0. 0. ]\n",
" [ 0. 0. 0. 0. 0.2474 -0.7895 0.1843 1. 0.\n",
" 0. 0. ]\n",
" [ 0. 0. 0. 0. -0.5714 -0.0912 -0.2482 -0.2165 1.\n",
" 0. 0. ]\n",
" [ 0. 0. 0. 0. 0. 0. -0.2334 -0.875 -0.3277\n",
" 1. 0. ]\n",
" [ 0. 0. 0. 0. 0. 0. -0.539 0.2406 -0.5946\n",
" 0.2887 1. ]]\n",
"U=\n",
" [[ 0.005 0. -0.0008 0.0014 -0.0033 0. 0. 0. 0.\n",
" 0. 0. ]\n",
" [ 0. 0.005 0.0014 -0.0025 0. 0. 0. 0. 0.\n",
" 0. 0. ]\n",
" [ 0. 0. 0.0078 0.001 -0.0014 -0.0014 -0.0033 0. 0.\n",
" 0. 0. ]\n",
" [-0. 0. 0. 0.0032 -0.0003 -0.0023 0.0004 0. 0.\n",
" 0. 0. ]\n",
" [-0. 0. 0. 0. 0.0058 -0.0005 -0.0014 0.0014 -0.0033\n",
" 0. 0. ]\n",
" [-0. 0. 0. 0. 0. 0.003 0.001 -0.0024 -0.0003\n",
" 0. 0. ]\n",
" [ 0. 0. 0. 0. 0. 0. 0.0062 0.0011 -0.0015\n",
" -0.0014 -0.0033]\n",
" [-0. 0. 0. 0. 0. 0. 0. 0.0026 -0.0006\n",
" -0.0022 0.0006]\n",
" [-0. 0. 0. 0. 0. 0. 0. 0. 0.0026\n",
" -0.0008 -0.0015]\n",
" [-0. 0. 0. 0. 0. 0. 0. 0. 0.\n",
" 0.0024 0.0007]\n",
" [ 0. 0. 0. 0. 0. 0. -0. 0. 0.\n",
" -0. 0.0011]]\n"
]
}
],
"source": [
"#2A\n",
"L,U = LUNaive(K[2:13,2:13])\n",
"print('L=\\n',L.round(4))\n",
"print('U=\\n',U.round(4))"
]
},
{
"cell_type": "code",
"execution_count": 177,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Aluminum Displacements:\n",
"----------------\n",
"u_1x:5.57 mm\n",
"u_1y:-6.07 mm\n",
"u_2x:1.24 mm\n",
"u_2y:-11.43 mm\n",
"u_3x:3.09 mm\n",
"u_3y:-15.36 mm\n",
"u_4x:4.95 mm\n",
"u_4y:-11.43 mm\n",
"u_5x:0.62 mm\n",
"u_5y:-6.07 mm\n",
"u_6x:6.19 mm\n",
"\n",
"Aluminum Forces:\n",
"----------------\n",
"F_1x:-0.00 N\n",
"F_1y:-0.00 N\n",
"F_2x:0.00 N\n",
"F_2y:0.00 N\n",
"F_3x:0.00 N\n",
"F_3y:-100.00 N\n",
"F_4x:0.00 N\n",
"F_4y:-0.00 N\n",
"F_5x:0.00 N\n",
"F_5y:0.00 N\n",
"F_6x:0.00 N\n",
"\n",
"\n",
"Steel Displacements:\n",
"----------------\n",
"u_1x:1.95 mm\n",
"u_1y:-2.12 mm\n",
"u_2x:0.43 mm\n",
"u_2y:-4.00 mm\n",
"u_3x:1.08 mm\n",
"u_3y:-5.38 mm\n",
"u_4x:1.73 mm\n",
"u_4y:-4.00 mm\n",
"u_5x:0.22 mm\n",
"u_5y:-2.12 mm\n",
"u_6x:2.17 mm\n",
"\n",
"Steel Forces:\n",
"----------------\n",
"F_1x:0.00 N\n",
"F_1y:-0.00 N\n",
"F_2x:-0.00 N\n",
"F_2y:0.00 N\n",
"F_3x:0.00 N\n",
"F_3y:-100.00 N\n",
"F_4x:-0.00 N\n",
"F_4y:0.00 N\n",
"F_5x:-0.00 N\n",
"F_5y:0.00 N\n",
"F_6x:0.00 N\n"
]
}
],
"source": [
"#2B&C\n",
"#Constants:\n",
"E_alum = 70e3 #MPa\n",
"E_steel = 200e3 #MPa\n",
"A = 0.1 #mm^2\n",
"F = np.zeros([11])\n",
"F[5] = -100 #N\n",
"\n",
"b_alum = F/(E_alum*A)\n",
"b_steel = F/(E_steel*A)\n",
"\n",
"u_alum = solveLU(L,U,b_alum)\n",
"u_steel = solveLU(L,U,b_steel)\n",
"\n",
"F_alum = E_alum*A*K[2:13,2:13]@u_alum\n",
"F_steel = E_steel*A*K[2:13,2:13]@u_steel\n",
"\n",
"\n",
"xy={0:'x',1:'y'}\n",
"print('Aluminum Displacements:\\n----------------')\n",
"for i in range(len(u_alum)):\n",
" print('u_{}{}:{:.2f} mm'.format(int(i/2)+1,xy[i%2],u_alum[i]))\n",
"print('\\nAluminum Forces:\\n----------------')\n",
"for i in range(len(F_alum)):\n",
" print('F_{}{}:{:.2f} N'.format(int(i/2)+1,xy[i%2],F_alum[i]))\n",
"\n",
"xy={0:'x',1:'y'}\n",
"print('\\n\\nSteel Displacements:\\n----------------')\n",
"for i in range(len(u_steel)):\n",
" print('u_{}{}:{:.2f} mm'.format(int(i/2)+1,xy[i%2],u_steel[i]))\n",
"print('\\nSteel Forces:\\n----------------')\n",
"for i in range(len(F_steel)):\n",
" print('F_{}{}:{:.2f} N'.format(int(i/2)+1,xy[i%2],F_steel[i])) "
]
},
{
"cell_type": "code",
"execution_count": 180,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"#2-D\n",
"l=300 # mm\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",
"s = 5\n",
"\n",
"u = np.zeros(2*len(nodes))\n",
"u[2:13] = u_alum\n",
"u[2:13] = u_steel\n",
"F = np.zeros(2*len(nodes))\n",
"F[2:13] = F_steel\n",
"F[2:13] = F_alum\n",
"\n",
"plt.figure(figsize=(10,8))\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",
" \n",
"plt.plot(r[ix],r[iy],'-',color='k')\n",
"plt.plot(r[ix]+u[ix]*s,r[iy]+u[iy]*s,'-',color='m')\n",
"plt.quiver(r[ix],r[iy],F[ix],F[iy],color='r',label='Applied Forces')\n",
"plt.quiver(r[ix],r[iy],u[ix],u[iy],color='b',label='Displacements')\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('Aluminum Truss Deformation\\nScale = 5x')\n",
"plt.legend();"
]
},
{
"cell_type": "code",
"execution_count": 181,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(10,8))\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",
"# label the nodes\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",
" \n",
"plt.plot(r[ix],r[iy],'-',color='k')\n",
"plt.plot(r[ix]+u[ix]*s,r[iy]+u[iy]*s,'-',color='g')\n",
"plt.quiver(r[ix],r[iy],F[ix],F[iy],color='r',label='Applied Forces')\n",
"plt.quiver(r[ix],r[iy],u[ix],u[iy],color='b',label='Displacement')\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 Truss Deformation\\nScale = 5x')\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": 187,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Minimum Aluminum Cross Sectional Area: 7.6786 mm^2.\n",
"Minimum Steel Cross Sectional Area: 2.6875 mm^2.\n"
]
}
],
"source": [
"#3A-B:\n",
"A = 0.1 #mm^2\n",
"y_alum = np.min(u_alum[iy[0]])\n",
"y_steel = np.min(u_steel[iy[0]])\n",
"A_alum = A*(abs((y_alum))/0.2)\n",
"A_steel = A*(abs((y_steel))/0.2)\n",
"print('Minimum Aluminum Cross Sectional Area:', A_alum.round(4), 'mm^2.')\n",
"print('Minimum Steel Cross Sectional Area:', A_steel.round(4), 'mm^2.')"
]
},
{
"cell_type": "code",
"execution_count": 194,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Weight of Aluminum Truss: 0.6736 N\n",
"Weight of Steel Truss: 0.7004 N\n"
]
}
],
"source": [
"#3C\n",
"den_alum = 2710e-9 #g/mm^3\n",
"den_steel = 8050e-9 #g/mm^3\n",
"N = 11\n",
"vol_alum = A_alum*l*N\n",
"vol_steel = A_steel*l*N\n",
"\n",
"weight_alum = den_alum*vol_alum*9.81\n",
"weight_steel = den_steel*vol_steel*9.81\n",
"print('Weight of Aluminum Truss:', weight_alum.round(4),'N')\n",
"print('Weight of Steel Truss:', weight_steel.round(4), 'N')\n"
]
},
{
"cell_type": "code",
"execution_count": 196,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Cost of Aluminum Truss: $ 10206617.18\n",
"Cost of Steel Truss: $ 3269301.16\n"
]
}
],
"source": [
"price_alum = 1545*9806.65 # $/N\n",
"price_steel = 476*9806.65 # $/N\n",
"\n",
"cost_alum = price_alum*weight_alum\n",
"cost_steel = price_steel*weight_steel\n",
"print('Cost of Aluminum Truss: $', cost_alum.round(2))\n",
"print('Cost of Steel Truss: $', cost_steel.round(2))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"3D) The Steel Truss is cheaper to build."
]
},
{
"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": 325,
"metadata": {},
"outputs": [],
"source": [
"#4A\n",
"data_alum = pd.read_csv('../data/al_price.csv')\n",
"data_steel = pd.read_csv('../data/steel_price.csv')\n",
"\n",
"al_year = data_alum['Year'].values\n",
"al_year_n = (al_year-al_year.min())/(al_year.max()-al_year.min())\n",
"st_year = data_steel['Year'].values\n",
"st_year_n = (st_year-st_year.min())/(st_year.max()-st_year.min())\n",
"al_price = data_alum['dollars/MT'].values\n",
"st_price = data_steel['dollars/MT'].values\n",
"\n",
"rand_al = random.sample(range(0,len(al_year_n)),len(al_year_n))\n",
"rand_st = random.sample(range(0,len(st_year_n)),len(st_year_n))\n",
"\n",
"train_al = rand_al[:int(0.7*len(al_year_n))]\n",
"test_al = rand_al[int(0.7*len(al_year_n)):]\n",
"train_st = rand_st[:int(0.7*len(st_year_n))]\n",
"test_st = rand_st[int(0.7*len(st_year_n)):]\n",
"\n",
"al_year_train = al_year_n[np.sort(train_al)]\n",
"al_year_test = al_year_n[np.sort(test_al)]\n",
"al_price_train = al_price[np.sort(train_al)]\n",
"al_price_test = al_price[np.sort(test_al)]\n",
"\n",
"st_year_train = st_year_n[np.sort(train_st)]\n",
"st_year_test = st_year_n[np.sort(test_st)]\n",
"st_price_train = st_price[np.sort(train_st)]\n",
"st_price_test = st_price[np.sort(test_st)]\n",
"\n",
"Z_train_al = np.block([[al_year_train**0]]).T\n",
"Z_test_al = np.block([[al_year_test**0]]).T\n",
"Z_train_st = np.block([[st_year_train**0]]).T\n",
"Z_test_st = np.block([[st_year_test**0]]).T"
]
},
{
"cell_type": "code",
"execution_count": 326,
"metadata": {},
"outputs": [],
"source": [
"max_N = 11\n",
"SSE_train_al = np.zeros(max_N)\n",
"SSE_test_al = np.zeros(max_N)\n",
"\n",
"for i in range(1,max_N):\n",
" Z_train_al=np.hstack((Z_train_al,al_year_train.reshape(-1,1)**i))\n",
" Z_test_al=np.hstack((Z_test_al,al_year_test.reshape(-1,1)**i))\n",
" A_al = np.linalg.solve(Z_train_al.T@Z_train_al,Z_train_al.T@al_train)\n",
" SSE_train_al[i]=np.sum((al_train-Z_train_al@A_al)**2)/len(al_train)\n",
" SSE_test_al[i]=np.sum((al_test-Z_test_al@A_al)**2)/len(al_test)"
]
},
{
"cell_type": "code",
"execution_count": 327,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(6,4))\n",
"plt.plot(al_year_train,al_price_train,'o', label = 'price data')\n",
"plt.plot(al_year_train,Z_train_al@A_al, 'y',label = 'best fit')\n",
"plt.title('Price of Aluminum with Best Fit Curve')\n",
"plt.xlabel('Time (years)')\n",
"plt.ylabel('Price (dollars/ MT)')\n",
"plt.legend();"
]
},
{
"cell_type": "code",
"execution_count": 328,
"metadata": {},
"outputs": [
{
"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": [
"plt.plot(np.arange(1,max_N),SSE_train_al[1:],label='Training Error')\n",
"plt.plot(np.arange(1,max_N),SSE_test_al[1:],label='Testing Error')\n",
"plt.title('Aluminum Price Model Error')\n",
"plt.ylabel('Sum of error')\n",
"plt.xlabel('Polynomial Order')\n",
"plt.legend();"
]
},
{
"cell_type": "code",
"execution_count": 317,
"metadata": {},
"outputs": [],
"source": [
"SSE_train_st = np.zeros(max_N)\n",
"SSE_test_st = np.zeros(max_N)\n",
"for i in range(1,max_N):\n",
" Z_train_st=np.hstack((Z_train_st,st_year_train.reshape(-1,1)**i))\n",
" Z_test_st=np.hstack((Z_test_st,st_year_test.reshape(-1,1)**i))\n",
" A_st= np.linalg.solve(Z_train_st.T@Z_train_st,Z_train_st.T@st_train) \n",
" SSE_train_st[i]=np.sum((st_train-Z_train_st@A_st)**2)/len(st_train)\n",
" SSE_test_st[i]=np.sum((st_test-Z_test_st@A_st)**2)/len(st_test)"
]
},
{
"cell_type": "code",
"execution_count": 318,
"metadata": {},
"outputs": [
{
"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": [
"plt.figure(figsize=(6,4))\n",
"plt.plot(st_year_train,st_price_train,'o', label = 'price data')\n",
"plt.plot(st_year_train,Z_train_st@A_st, color = 'orange',label = 'best fit')\n",
"plt.title('Price of Steel with Best Fit Curve')\n",
"plt.xlabel('Time (years)')\n",
"plt.ylabel('Price (dollars/ MT)')\n",
"plt.legend();"
]
},
{
"cell_type": "code",
"execution_count": 319,
"metadata": {},
"outputs": [
{
"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": [
"plt.plot(np.arange(1,max_N),SSE_train_st[1:],label='Training Error')\n",
"plt.plot(np.arange(1,max_N),SSE_test_st[1:],label='Testing Error')\n",
"plt.title('Steel Price Model Error')\n",
"plt.ylabel('Sum of error')\n",
"plt.xlabel('Polynomial Order')\n",
"plt.legend();"
]
},
{
"cell_type": "code",
"execution_count": 329,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Predicted Price of Aluminum Year 2025: $ 2076.1\n",
"Predicted Price of Steel Year 2025: $ 270.4\n"
]
}
],
"source": [
"ftr_al = np.linspace(2016,2025,len(al_year_n))\n",
"ftr_al_n = (ftr_al - ftr_al.min()) / (ftr_al.max() - ftr_al.min())\n",
"ftr_st = np.linspace(2016,2025,len(st_year_n))\n",
"ftr_st_n = (ftr_st - ftr_st.min()) / (ftr_st.max() - ftr_st.min())\n",
"\n",
"pred_rand_al =random.sample(range(0,len(ftr_al)),len(ftr_al))\n",
"pred_train_al = pred_rand_al[:int(0.7*len(ftr_al))]\n",
"pred_rand_st =random.sample(range(0,len(ftr_st)),len(ftr_st))\n",
"pred_train_st = pred_rand_st[:int(0.7*len(ftr_st))]\n",
"\n",
"y_al = ftr_al_n[np.sort(train_al)]\n",
"Z_train_al = np.block([[y_al**0]]).T\n",
"y_st = ftr_st_n[np.sort(pred_train_st)]\n",
"Z_train_st = np.block([[y_st**0]]).T\n",
"\n",
"max_N = 11\n",
"for i in range(1,max_N):\n",
" Z_train_al = np.hstack((Z_train_al,y_al.reshape(-1,1)**i))\n",
" Z_train_st = np.hstack((Z_train_st,y_st.reshape(-1,1)**i))\n",
" \n",
"print('Predicted Price of Aluminum Year 2025: $', round((Z_train_al@A_al)[-1],1))\n",
"print('Predicted Price of Steel Year 2025: $', round((Z_train_st@A_st)[-1],1))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"4E) Based on the predicted price of aluminum vs steel in 2025, Steel will still be cheaper to build the truss with. Also becuase steel showed a lower deflection while under load, the maintenance costs and risk of an accident will be much less by using steel rather than aluminum."
]
},
{
"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>"
]
}
],
"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
}