Skip to content
Permalink
master
Switch branches/tags

Name already in use

A tag already exists with the provided branch name. Many Git commands accept both tag and branch names, so creating this branch may cause unexpected behavior. Are you sure you want to create this branch?
Go to file
 
 
Cannot retrieve contributors at this time
executable file 1261 lines (1261 sloc) 392 KB
{
"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": 82,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"from pretty_print import array_print as AP \n",
"import matplotlib.pyplot as plt\n",
"import pandas as pd\n",
"import random \n",
"from matplotlib import rcParams\n",
"\n",
"#Set font style and size \n",
"rcParams['font.family'] = 'sans'\n",
"rcParams['font.size'] = 16\n",
"rcParams['lines.linewidth'] = 3\n",
"\n",
"fea_arrays = np.load('./fea_arrays.npz')\n",
"K=fea_arrays['K']*1000 #array is 1000x(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": 83,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The condition of K is : 6.640986594413607e+16\n",
"The condition of K[2:13],[1:13] is: 52.23542514351013\n"
]
}
],
"source": [
"condition_k = np.linalg.cond(K)\n",
"condition_k2 = np.linalg.cond(K[2:13,2:13])\n",
"\n",
"print(\"The condition of K is :\", condition_k)\n",
"print(\"The condition of K[2:13],[1:13] is:\", condition_k2)"
]
},
{
"cell_type": "code",
"execution_count": 84,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1a) The error of u in K*u=F is: 6.641\n"
]
}
],
"source": [
"#Part A\n",
"error_k = condition_k*1e-16\n",
"\n",
"print(\"1a)\", \"The error of u in K*u=F is:\", np.round(error_k, 4))"
]
},
{
"cell_type": "code",
"execution_count": 85,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1b) The conditon of K is so large because it is ill-conditioned. This means thatfor small changes one can get different values. Ill-conditioned matrices are dangerousbecause we still get a result, but we don't know the answer unitl you compare it with the sensitivity of the results.\n"
]
}
],
"source": [
"#Part B\n",
"print(\"1b)\", \"The conditon of K is so large because it is ill-conditioned. This means that\\\n",
"for small changes one can get different values. Ill-conditioned matrices are dangerous\\\n",
"because we still get a result, but we don't know the answer unitl you compare it with the sensitivity \\\n",
"of the results.\")"
]
},
{
"cell_type": "code",
"execution_count": 86,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1c) The expected error of u in K*u=F is: 0.0\n"
]
}
],
"source": [
"#Part C\n",
"error_k2 = condition_k2*1e-16\n",
"\n",
"print(\"1c)\", \"The expected error of u in K*u=F is:\", np.round(error_k2, 4))"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"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": 87,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"2a)\n",
"L:\n",
" [ 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00] \n",
" [ 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00] \n",
" [ -0.17 0.29 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00] \n",
" [ 0.29 -0.50 0.12 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00] \n",
" [ -0.67 0.00 -0.18 -0.10 1.00 0.00 0.00 0.00 0.00 0.00 0.00] \n",
" [ 0.00 0.00 -0.19 -0.72 -0.08 1.00 0.00 0.00 0.00 0.00 0.00]\n",
" [ 0.00 0.00 -0.43 0.13 -0.24 0.33 1.00 0.00 0.00 0.00 0.00] \n",
" [ 0.00 0.00 0.00 0.00 0.25 -0.79 0.18 1.00 0.00 0.00 0.00] \n",
" [ 0.00 0.00 0.00 0.00 -0.57 -0.09 -0.25 -0.22 1.00 0.00 0.00] \n",
" [ 0.00 0.00 0.00 0.00 0.00 0.00 -0.23 -0.88 -0.33 1.00 0.00] \n",
" [ 0.00 0.00 0.00 0.00 0.00 0.00 -0.54 0.24 -0.59 0.29 1.00] \n",
"\n",
"U:\n",
" [ 5.00 0.00 -0.83 1.44 -3.33 0.00 0.00 0.00 0.00 0.00 0.00] \n",
" [ 0.00 5.00 1.44 -2.50 0.00 0.00 0.00 0.00 0.00 0.00 0.00] \n",
" [ 0.00 0.00 7.78 0.96 -1.39 -1.44 -3.33 0.00 0.00 0.00 0.00] \n",
" [ 0.00 0.00 0.00 3.21 -0.31 -2.32 0.41 0.00 0.00 0.00 0.00] \n",
" [ 0.00 0.00 0.00 0.00 5.83 -0.48 -1.39 1.44 -3.33 0.00 0.00] \n",
" [ 0.00 0.00 0.00 0.00 0.00 3.02 1.01 -2.38 -0.27 0.00 0.00]\n",
" [ 0.00 0.00 0.00 0.00 0.00 0.00 6.18 1.14 -1.54 -1.44 -3.33] \n",
" [ 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2.55 -0.55 -2.23 0.61] \n",
" [ 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2.57 -0.84 -1.53] \n",
" [ 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2.43 0.70] \n",
" [ 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.11] \n",
"\n"
]
}
],
"source": [
"#Part A\n",
"\n",
"#lu is a built-in partial-pivoting LU decomposition function\n",
"from scipy.linalg import lu\n",
"\n",
"P,L,U = lu(K[2:13,2:13]) \n",
"\n",
"print(\"2a)\")\n",
"print('L:')\n",
"AP([L], ['[L]'])\n",
"print('U:')\n",
"AP([U], ['[U]'])"
]
},
{
"cell_type": "code",
"execution_count": 88,
"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": 89,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"2b)\n",
"Displacements [mm] Steel:\n",
"----------------\n",
"u_1x: 0.00 mm\n",
"u_1y: 0.00 mm\n",
"u_2x: 1.95 mm\n",
"u_2y: -2.12 mm\n",
"u_3x: 0.43 mm\n",
"u_3y: -4.00 mm\n",
"u_4x: 1.08 mm\n",
"u_4y: -5.37 mm\n",
"u_5x: 1.73 mm\n",
"u_5y: -4.00 mm\n",
"u_6x: 0.22 mm\n",
"u_6y: -2.12 mm\n",
"u_7x: 2.17 mm\n",
"u_7y: 0.00 mm\n",
"\n",
"Displacements [mm] Aluminum:\n",
"----------------\n",
"u_1x: 0.00 mm\n",
"u_1y: 0.00 mm\n",
"u_2x: 5.57 mm\n",
"u_2y: -6.07 mm\n",
"u_3x: 1.24 mm\n",
"u_3y: -11.43 mm\n",
"u_4x: 3.09 mm\n",
"u_4y: -15.36 mm\n",
"u_5x: 4.95 mm\n",
"u_5y: -11.43 mm\n",
"u_6x: 0.62 mm\n",
"u_6y: -6.07 mm\n",
"u_7x: 6.19 mm\n",
"u_7y: 0.00 mm\n"
]
}
],
"source": [
"#Part B\n",
"\n",
"#Given Variables \n",
"A = 1e-7 #m^2\n",
"E_steel = 200e9 #Pa\n",
"E_aluminum = 70e9 #Pa\n",
"F = np.zeros(11)\n",
"F[5] = -100 #N\n",
"\n",
"print(\"2b)\")\n",
"\n",
"#Steel\n",
"u_st = solveLU(L, U, F/E_steel/A)\n",
"u_steel = np.zeros(14)\n",
"u_steel[2:13] = u_st*1000 #multiply by 1000 to to convert back to mm\n",
"#print('u [mm], Steel:')\n",
"#AP([u_steel], ['[u_steel]'])\n",
"\n",
"#Aluminum\n",
"u_al = solveLU(L, U, F/E_aluminum/A)\n",
"u_aluminum = np.zeros(14)\n",
"u_aluminum[2:13] = u_al*1000 #multiply by 1000 to to convert back to mm\n",
"#print('u [mm], Aluminum:')\n",
"#AP([u_aluminum], ['[u_aluminum]'])\n",
"\n",
"#print\n",
"xy={0:'x',1:'y'}\n",
"print('Displacements [mm] Steel:\\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('\\nDisplacements [mm] Aluminum:\\n----------------')\n",
"for i in range(len(u_aluminum)):\n",
" print('u_{}{}: {:.2f} mm'.format(int(i/2)+1,xy[i%2],u_aluminum[i]))"
]
},
{
"cell_type": "code",
"execution_count": 90,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"2c)\n",
"Forces [N] Steel:\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",
"Forces [N] Aluminum:\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"
]
}
],
"source": [
"#Part C\n",
"\n",
"print(\"2c)\")\n",
"\n",
"#Steel\n",
"F_steel = K*E_steel*A@u_steel/1000 #divide by 1000 to convert to back to mm\n",
"#print('Force [N], Steel:')\n",
"#AP([F_steel], ['[F_steel]'])\n",
"\n",
"#Aluminum\n",
"F_aluminum = K*E_aluminum*A@u_aluminum/1000 #divide by 1000 to convert to back to mm\n",
"#print('Force [N], Aluminum:')\n",
"#AP([F_aluminum], ['[F_aluminum]'])\n",
"\n",
"xy={0:'x',1:'y'}\n",
"print('Forces [N] Steel:\\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]))\n",
"print('\\nForces [N] Aluminum:\\n----------------')\n",
"for i in range(len(F_aluminum)):\n",
" print('F_{}{}: {:.2f} N'.format(int(i/2)+1,xy[i%2],F_aluminum[i]))"
]
},
{
"cell_type": "code",
"execution_count": 91,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"d) Steel\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": [
"#Part D\n",
"\n",
"print(\"d) Steel\")\n",
"\n",
"#Code from extra-FEA_material\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",
"\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",
"\n",
"#Plot Undeformed\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",
"#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",
"s = 5\n",
"\n",
"#Plot Deformed\n",
"plt.plot(r[ix]+u_steel[ix]*s, r[iy]+u_steel[iy]*s, '-',color=(1,0,0,1))\n",
"plt.quiver(r[ix], r[iy], F_steel[ix], F_steel[iy], color=(1,0,0,1), label='Applied Forces')\n",
"plt.quiver(r[ix], r[iy], u_steel[ix], u_steel[iy], color=(0,0,1,1), label='Displacements')\n",
"\n",
"#Labels\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)\n",
"plt.axis(l*np.array([-0.5,3.5,-1,1.5]));"
]
},
{
"cell_type": "code",
"execution_count": 92,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"d) Aluminum\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": [
"#Part D\n",
"\n",
"print(\"d) Aluminum\")\n",
"\n",
"#Code from extra-FEA_material\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",
"\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",
"\n",
"#Plot Undeformed\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",
"#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",
"s = 5\n",
"\n",
"#Plot Deformed\n",
"plt.plot(r[ix]+u_aluminum[ix]*s, r[iy]+u_aluminum[iy]*s, '-',color=(1,0,0,1))\n",
"plt.quiver(r[ix], r[iy], F_aluminum[ix], F_aluminum[iy], color=(1,0,0,1), label='Applied Forces')\n",
"plt.quiver(r[ix], r[iy], u_aluminum[ix], u_aluminum[iy], color=(0,0,1,1), label='Displacements')\n",
"\n",
"#Labels\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)\n",
"plt.axis(l*np.array([-0.5,3.5,-1,1.5]));"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"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": 93,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"3a) The Min Cross-Sectional Area to keep y-deflection < 0.2mm for Aluminum is: 7.68 mm^2\n",
"\n",
"Displacements [mm] Aluminum:\n",
"----------------\n",
"u_1y: 0.00000 mm\n",
"u_2y: -0.07906 mm\n",
"u_3y: -0.14881 mm\n",
"u_4y: -0.19996 mm\n",
"u_5y: -0.14881 mm\n",
"u_6y: -0.07906 mm\n",
"u_7y: 0.00000 mm\n"
]
}
],
"source": [
"#Part A\n",
"\n",
"#Used trial and error method - Aluminum\n",
"A_min = 7.68e-6 #m^2\n",
"E_aluminum = 70e9 #Pa\n",
"F = np.zeros(11)\n",
"F[5] = -100 #N\n",
"\n",
"#Aluminum\n",
"u_al = solveLU(L, U, F/E_aluminum/A_min)\n",
"u_aluminum = np.zeros(14)\n",
"u_aluminum[2:13] = u_al*1000 #multiply by 1000 to to convert back to mm\n",
"\n",
"print(\"3a) The Min Cross-Sectional Area to keep y-deflection < 0.2mm for Aluminum is:\", A_min/1e-6, \"mm^2\")\n",
"print()\n",
"#print('u [mm], Aluminum:')\n",
"#AP([u_aluminum], ['[u_aluminum]'])\n",
"\n",
"xy={0:'x',1:'y'}\n",
"print('Displacements [mm] Aluminum:\\n----------------')\n",
"for i in range(len(u_aluminum)):\n",
" if (i % 2) != 0:\n",
" print('u_{}{}: {:.5f} mm'.format(int(i/2)+1,xy[i%2],u_aluminum[i]))"
]
},
{
"cell_type": "code",
"execution_count": 94,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"3b) The Min Cross-Sectional Area to keep y-deflection < 0.2mm for Steel is: 2.69 mm^2\n",
"\n",
"Displacements [mm] Steel:\n",
"----------------\n",
"u_1y: 0.00000 mm\n",
"u_2y: -0.07900 mm\n",
"u_3y: -0.14870 mm\n",
"u_4y: -0.19981 mm\n",
"u_5y: -0.14870 mm\n",
"u_6y: -0.07900 mm\n",
"u_7y: 0.00000 mm\n"
]
}
],
"source": [
"#Part B\n",
"\n",
"#Used trial and error method - Steel\n",
"A_min2 = 2.69e-6 #m^2\n",
"E_steel = 200e9 #Pa\n",
"F = np.zeros(11)\n",
"F[5] = -100 #N\n",
"\n",
"#Steel\n",
"u_st = solveLU(L, U, F/E_steel/A_min2)\n",
"u_steel = np.zeros(14)\n",
"u_steel[2:13] = u_st*1000 #multiply by 1000 to to convert back to mm\n",
"\n",
"print(\"3b) The Min Cross-Sectional Area to keep y-deflection < 0.2mm for Steel is:\", np.round(A_min2/1e-6,2), \"mm^2\")\n",
"print()\n",
"#print('u [mm], Steel:')\n",
"#AP([u_steel], ['[u_steel]'])\n",
"\n",
"xy={0:'x',1:'y'}\n",
"print('Displacements [mm] Steel:\\n----------------')\n",
"for i in range(len(u_steel)):\n",
" if (i % 2) != 0:\n",
" print('u_{}{}: {:.5f} mm'.format(int(i/2)+1,xy[i%2],u_steel[i]))"
]
},
{
"cell_type": "code",
"execution_count": 95,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"3c) Mass of Aluminum: 0.06125 N\n",
" Mass of Steel: 0.06096 N\n"
]
}
],
"source": [
"#Part C\n",
"\n",
"l = .3 #m -- length of truss\n",
"g = 9.81 #m/s^2\n",
"\n",
"#Aluminum\n",
"density_aluminum = 2710 #kg/m^3\n",
"mass_aluminum = l*A_min*density_aluminum\n",
"weight_aluminum = mass_aluminum*g\n",
"\n",
"#Steel\n",
"density_steel = 7700 #kg/m^3\n",
"mass_steel = l*A_min2*density_steel\n",
"weight_steel = mass_steel*g\n",
"\n",
"print(\"3c) Mass of Aluminum:\", np.round(weight_aluminum, 5), \"N\")\n",
"print(\" Mass of Steel:\", np.round(weight_steel, 5), \"N\")"
]
},
{
"cell_type": "code",
"execution_count": 96,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"3d) Cost of Aluminum: $ 0.0096 per beam\n",
" Cost of Steel: $ 0.00296 per beam\n",
" Steel is cheaper.\n"
]
}
],
"source": [
"#Part D\n",
"\n",
"#Aluminum\n",
"price_aluminum = 1545/1000 #$/kg\n",
"cost_aluminum = mass_aluminum*price_aluminum\n",
"\n",
"#Steel\n",
"price_steel = 476/1000 #$/kg\n",
"cost_steel = mass_steel*price_steel\n",
"\n",
"print(\"3d) Cost of Aluminum: $\", np.round(cost_aluminum, 4), \"per beam\")\n",
"print(\" Cost of Steel: $\", np.round(cost_steel, 5), \"per beam\")\n",
"print(\" Steel is cheaper.\")"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"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": 97,
"metadata": {},
"outputs": [],
"source": [
"#Import Data \n",
"aluminum = pd.read_csv('../data/al_price.csv')\n",
"x_al = aluminum[\"Year\"]\n",
"y_al = aluminum[\"dollars/MT\"]\n",
"\n",
"steel = pd.read_csv('../data/steel_price.csv')\n",
"x_st = steel[\"Year\"]\n",
"y_st = steel[\"dollars/MT\"]"
]
},
{
"cell_type": "code",
"execution_count": 98,
"metadata": {},
"outputs": [],
"source": [
"#Part A\n",
"np.random.seed(100)\n",
"al_rand = random.sample(range(0, len(x_al)), len(x_al))\n",
"st_rand = random.sample(range(0, len(x_st)), len(x_st))\n",
"\n",
"#70 training\n",
"train_per = 0.7\n",
"al_x_train =np.sort(x_al[al_rand[:int(len(x_al)*train_per)]])\n",
"al_y_train =np.sort(y_al[al_rand[:int(len(y_al)*train_per)]])\n",
"st_x_train =np.sort(x_st[st_rand[:int(len(x_st)*train_per)]])\n",
"st_y_train =np.sort(y_st[st_rand[:int(len(y_st)*train_per)]])\n",
"\n",
"#30 testing\n",
"al_x_test=np.sort(x_al[al_rand[int(len(x_al)*train_per):]])\n",
"al_y_test=np.sort(y_al[al_rand[int(len(y_al)*train_per):]])\n",
"st_x_test=np.sort(x_st[st_rand[int(len(x_st)*train_per):]])\n",
"st_y_test=np.sort(y_st[st_rand[int(len(y_st)*train_per):]])"
]
},
{
"cell_type": "code",
"execution_count": 99,
"metadata": {},
"outputs": [],
"source": [
"#Part B"
]
},
{
"cell_type": "code",
"execution_count": 100,
"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": [
"#Aluminum\n",
"max_N = 47 #trial and error \n",
"\n",
"Z_al_train = np.block([[al_x_train**0]]).T\n",
"for i in range(1,max_N):\n",
" Z_al_train = np.hstack((Z_al_train, al_x_train.reshape(-1,1)**i))\n",
"a_al_train = np.linalg.solve(Z_al_train.T@Z_al_train, Z_al_train.T@al_y_train)\n",
"\n",
"#Plot\n",
"plt.plot(al_x_train, al_y_train,'o', label='Aluminum Data')\n",
"plt.plot(al_x_train, Z_al_train@a_al_train, label='Polynomial of Order {}'.format(max_N), linewidth=3)\n",
"plt.title('Aluminum -- Price vs. Time')\n",
"plt.xlabel('Time\\n(Years)')\n",
"plt.ylabel('Price\\n($)')\n",
"plt.legend(loc='center left', bbox_to_anchor=(1, 0.5));"
]
},
{
"cell_type": "code",
"execution_count": 101,
"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": [
"#Steel\n",
"max_N = 47 #trial and error \n",
"\n",
"Z_st_train = np.block([[st_x_train**0]]).T\n",
"for i in range(1, max_N):\n",
" Z_st_train = np.hstack((Z_st_train, st_x_train.reshape(-1,1)**i))\n",
"a_st_train = np.linalg.solve(Z_st_train.T@Z_st_train, Z_st_train.T@st_y_train)\n",
"\n",
"#Plot\n",
"plt.plot(st_x_train, st_y_train,'o', label='Steel Data')\n",
"plt.plot(st_x_train, Z_st_train@a_st_train, label='Polynomial of Order {}'.format(max_N), linewidth=3)\n",
"plt.title('Steel -- Price vs. Time')\n",
"plt.xlabel('Time\\n(Years)')\n",
"plt.ylabel('Price\\n($)')\n",
"plt.legend(loc='center left', bbox_to_anchor=(1, 0.5));"
]
},
{
"cell_type": "code",
"execution_count": 109,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"---- n=1 -------\n",
"the coefficient of determination for this fit is 0.638\n",
"the correlation coefficient this fit is 0.799\n",
"---- n=2 -------\n",
"the coefficient of determination for this fit is 0.748\n",
"the correlation coefficient this fit is 0.865\n",
"---- n=3 -------\n",
"the coefficient of determination for this fit is 0.748\n",
"the correlation coefficient this fit is 0.865\n",
"---- n=4 -------\n",
"the coefficient of determination for this fit is 0.748\n",
"the correlation coefficient this fit is 0.865\n",
"---- n=5 -------\n",
"the coefficient of determination for this fit is 0.748\n",
"the correlation coefficient this fit is 0.865\n",
"---- n=6 -------\n",
"the coefficient of determination for this fit is 0.748\n",
"the correlation coefficient this fit is 0.865\n",
"---- n=7 -------\n",
"the coefficient of determination for this fit is 0.747\n",
"the correlation coefficient this fit is 0.864\n",
"---- n=8 -------\n",
"the coefficient of determination for this fit is 0.747\n",
"the correlation coefficient this fit is 0.864\n",
"---- n=9 -------\n",
"the coefficient of determination for this fit is 0.753\n",
"the correlation coefficient this fit is 0.868\n",
"---- n=10 -------\n",
"the coefficient of determination for this fit is 0.752\n",
"the correlation coefficient this fit is 0.867\n",
"---- n=11 -------\n",
"the coefficient of determination for this fit is 0.735\n",
"the correlation coefficient this fit is 0.857\n",
"---- n=12 -------\n",
"the coefficient of determination for this fit is 0.784\n",
"the correlation coefficient this fit is 0.885\n",
"---- n=13 -------\n",
"the coefficient of determination for this fit is 0.252\n",
"the correlation coefficient this fit is 0.502\n",
"---- n=14 -------\n",
"the coefficient of determination for this fit is 0.584\n",
"the correlation coefficient this fit is 0.764\n",
"---- n=15 -------\n",
"the coefficient of determination for this fit is 0.471\n",
"the correlation coefficient this fit is 0.687\n",
"---- n=16 -------\n",
"the coefficient of determination for this fit is 0.819\n",
"the correlation coefficient this fit is 0.905\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": [
"#Part C\n",
"#Steel\n",
"Z_st = np.block([[st_x_train**0]]).T\n",
"Z_st_test = np.block([[st_x_test**0]]).T\n",
"Z_st_train = np.block([[st_x_train**0]]).T\n",
"\n",
"max_N = 17\n",
"SSE_st_train=np.zeros(max_N)\n",
"SSE_st_test=np.zeros(max_N)\n",
"for i in range(1,max_N):\n",
" Z_st = np.hstack((Z_st,st_x_train.reshape(-1,1)**i))\n",
" Z_st_test=np.hstack((Z_st_test,st_x_test.reshape(-1,1)**i))\n",
" A_st = np.linalg.solve(Z_st.T@Z_st,Z_st.T@st_y_train)\n",
" St_st = np.std(st_y_train)\n",
" Sr_st = np.std(st_y_train-Z_st@A_st)\n",
" r2_st = 1-Sr_st/St_st\n",
" print('---- n={:d} -------'.format(i))\n",
" print('the coefficient of determination for this fit is {:.3f}'.format(r2_st))\n",
" print('the correlation coefficient this fit is {:.3f}'.format(r2_st**0.5))\n",
" plt.plot(st_x_train,st_y_train-Z_st@A_st,'-',label='order {:d}'.format(i))\n",
" SSE_st_train[i]=np.sum((st_y_train-Z_st@A_st)**2)/len(st_y_train)\n",
" SSE_st_test[i]=np.sum((st_y_test-Z_st_test@A_st)**2)/len(st_y_test)\n",
"\n",
"plt.legend(loc='center left', bbox_to_anchor=(1, 0.5));\n",
"plt.title('Error in Predicted vs Measured Values',size=20)\n",
"plt.xlabel('Years')\n",
"plt.ylabel('Y Error');"
]
},
{
"cell_type": "code",
"execution_count": 110,
"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.semilogy(np.arange(2,max_N), SSE_st_train[2:], label='Training error')\n",
"plt.semilogy(np.arange(2,max_N), SSE_st_test[2:], label='Testing error')\n",
"plt.title('Reduction in Error with Higher Order Fits')\n",
"plt.legend()\n",
"plt.xlabel('Polynomial Order')\n",
"plt.ylabel('Total Sum of Square Error');"
]
},
{
"cell_type": "code",
"execution_count": 111,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"---- n=1 -------\n",
"the coefficient of determination for this fit is 0.820\n",
"the correlation coefficient this fit is 0.906\n",
"---- n=2 -------\n",
"the coefficient of determination for this fit is 0.836\n",
"the correlation coefficient this fit is 0.914\n",
"---- n=3 -------\n",
"the coefficient of determination for this fit is 0.836\n",
"the correlation coefficient this fit is 0.914\n",
"---- n=4 -------\n",
"the coefficient of determination for this fit is 0.836\n",
"the correlation coefficient this fit is 0.914\n",
"---- n=5 -------\n",
"the coefficient of determination for this fit is 0.836\n",
"the correlation coefficient this fit is 0.914\n",
"---- n=6 -------\n",
"the coefficient of determination for this fit is 0.836\n",
"the correlation coefficient this fit is 0.914\n",
"---- n=7 -------\n",
"the coefficient of determination for this fit is 0.837\n",
"the correlation coefficient this fit is 0.915\n",
"---- n=8 -------\n",
"the coefficient of determination for this fit is 0.836\n",
"the correlation coefficient this fit is 0.914\n",
"---- n=9 -------\n",
"the coefficient of determination for this fit is 0.836\n",
"the correlation coefficient this fit is 0.915\n",
"---- n=10 -------\n",
"the coefficient of determination for this fit is 0.836\n",
"the correlation coefficient this fit is 0.914\n",
"---- n=11 -------\n",
"the coefficient of determination for this fit is 0.836\n",
"the correlation coefficient this fit is 0.914\n",
"---- n=12 -------\n",
"the coefficient of determination for this fit is 0.836\n",
"the correlation coefficient this fit is 0.914\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": [
"#Aluminum\n",
"Z_al = np.block([[al_x_train**0]]).T\n",
"Z_al_test = np.block([[al_x_test**0]]).T\n",
"Z_al_train = np.block([[al_x_train**0]]).T\n",
"\n",
"max_N = 13\n",
"SSE_al_train=np.zeros(max_N)\n",
"SSE_al_test=np.zeros(max_N)\n",
"for i in range(1,max_N):\n",
" Z_al = np.hstack((Z_al,al_x_train.reshape(-1,1)**i))\n",
" Z_al_test=np.hstack((Z_al_test,al_x_test.reshape(-1,1)**i))\n",
" A_al = np.linalg.solve(Z_al.T@Z_al,Z_al.T@al_y_train)\n",
" St_al = np.std(al_y_train)\n",
" Sr_al = np.std(al_y_train-Z_al@A_al)\n",
" r2_al = 1-Sr_al/St_al\n",
" print('---- n={:d} -------'.format(i))\n",
" print('the coefficient of determination for this fit is {:.3f}'.format(r2_al))\n",
" print('the correlation coefficient this fit is {:.3f}'.format(r2_al**0.5))\n",
" plt.plot(al_x_train,al_y_train-Z_al@A_al,'-',label='order {:d}'.format(i))\n",
" SSE_al_train[i]=np.sum((al_y_train-Z_al@A_al)**2)/len(al_y_train)\n",
" SSE_al_test[i]=np.sum((al_y_test-Z_al_test@A_al)**2)/len(al_y_test)\n",
"\n",
"plt.legend(loc='center left', bbox_to_anchor=(1, 0.5));\n",
"plt.title('Error in Predicted vs Measured Values',size=20)\n",
"plt.xlabel('Years')\n",
"plt.ylabel('Y Error');"
]
},
{
"cell_type": "code",
"execution_count": 112,
"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.semilogy(np.arange(2,max_N), SSE_al_train[2:], label='Training error')\n",
"plt.semilogy(np.arange(2,max_N), SSE_al_test[2:], label='Testing error')\n",
"plt.title('Reduction in Error with Higher Order Fits')\n",
"plt.legend()\n",
"plt.xlabel('Polynomial Order')\n",
"plt.ylabel('Total Sum of Square Error');"
]
},
{
"cell_type": "code",
"execution_count": 113,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"d) The cost of steel in 2025: $ 8335201.91\n",
" The cost of aluminum in 2025: $ -344532244.59\n"
]
}
],
"source": [
"#Part D\n",
"\n",
"#Steel\n",
"for i in range(0,47):\n",
" cost_steel = a_st_train[i]*2025**i\n",
"print('d) The cost of steel in 2025: $',round(cost_steel, 2))\n",
"\n",
"#Aluminum\n",
"for i in range(0,47):\n",
" cost_aluminum = a_al_train[i]*2025**i\n",
"print(' The cost of aluminum in 2025: $', round(cost_aluminum, 2))"
]
},
{
"cell_type": "code",
"execution_count": 114,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Yes, I would change my answer in 3.b\n"
]
}
],
"source": [
"#Part E\n",
"\n",
"print(\"Yes, I would change my answer in 3.b\")"
]
},
{
"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
}