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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": 144, | |
"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": 144, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"import numpy as np\n", | |
"fea_arrays = np.load('./fea_arrays.npz')\n", | |
"K=fea_arrays['K']\n", | |
"K" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"In this project we are solving the problem, $\\mathbf{F}=\\mathbf{Ku}$, where $\\mathbf{F}$ is measured in Newtons, $\\mathbf{K}$ `=E*A*K` is the stiffness in N/mm, `E` is Young's modulus measured in MPa (N/mm^2), and `A` is the cross-sectional area of the beam measured in mm^2. \n", | |
"\n", | |
"There are three constraints on the motion of the joints:\n", | |
"\n", | |
"i. node 1 displacement in the x-direction is 0 = `u[0]`\n", | |
"\n", | |
"ii. node 1 displacement in the y-direction is 0 = `u[1]`\n", | |
"\n", | |
"iii. node 7 displacement in the y-direction is 0 = `u[13]`\n", | |
"\n", | |
"We can satisfy these constraints by leaving out the first, second, and last rows and columns from our linear algebra description. " | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"### 1. Calculate the condition of `K` and the condition of `K[2:13,2:13]`. \n", | |
"\n", | |
"a. What error would you expect when you solve for `u` in `K*u = F`? \n", | |
"\n", | |
"b. Why is the condition of `K` so large?\n", | |
"\n", | |
"c. What error would you expect when you solve for `u[2:13]` in `K[2:13,2:13]*u=F[2:13]`" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 145, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"The condition of K is 1.4577532625238035e+17\n", | |
"The norm of K is 0.02614064523559687\n", | |
"The condition of K[2:13,2:13] is 52.23542514351006\n", | |
"The norm of K[2:13,2:13] is 0.024166666666666666\n" | |
] | |
} | |
], | |
"source": [ | |
"import matplotlib.pyplot as plt\n", | |
"print('The condition of K is',np.linalg.cond(K))\n", | |
"print('The norm of K is',np.linalg.norm(K))\n", | |
"k = K[2:13,2:13]\n", | |
"print('The condition of K[2:13,2:13] is', np.linalg.cond(k))\n", | |
"print('The norm of K[2:13,2:13] is', np.linalg.norm(k))" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"a) We would get an error since K in its nature is ill-conditioned. Many of the equations seem to be almost dependent which would lead to many solutions.\n", | |
" \n", | |
"b)\n", | |
" The condition of K is so large because the equations seems to almost be dependent.\n", | |
"\n", | |
"c)\n", | |
" There would be no error, but there is still dependency present in the equations, which could create uncertainty in results." | |
] | |
}, | |
{ | |
"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": 146, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"def LUNaive(A):\n", | |
" [m,n] = np.shape(A)\n", | |
" if m!=n: error('Matrix A must be square')\n", | |
" nb = n+1\n", | |
" # 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", | |
"def solveLU(L,U,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": 252, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"The coefficients of the displacements in mm of us are...\n", | |
"[ 1.94855716 -2.125 0.4330127 -4. 1.08253175 -5.375\n", | |
" 1.73205081 -4. 0.21650635 -2.125 2.16506351]\n", | |
"The coefficients of the displacements in mm of ua are...\n", | |
"[ 5.56730617 -6.07142857 1.23717915 -11.42857143 3.09294787\n", | |
" -15.35714286 4.94871659 -11.42857143 0.61858957 -6.07142857\n", | |
" 6.18589574]\n", | |
"The corresponding reaction forces in N for steel and aluminum respectively are...\n", | |
"[ 0.00000000e+00 -5.42101086e-19 0.00000000e+00 -1.08420217e-18\n", | |
" 8.67361738e-19 -5.00000000e-03 -2.60208521e-18 8.67361738e-19\n", | |
" 3.25260652e-19 0.00000000e+00 0.00000000e+00]\n", | |
"and\n", | |
"[-3.46944695e-18 -4.33680869e-19 0.00000000e+00 -2.60208521e-18\n", | |
" -2.16840434e-18 -1.42857143e-02 0.00000000e+00 -6.93889390e-18\n", | |
" 2.16840434e-18 3.46944695e-18 -3.46944695e-18]\n" | |
] | |
} | |
], | |
"source": [ | |
"E_s = 200000 #MPa\n", | |
"E_a = 70000 #MPa\n", | |
"cs = 0.1 #mm^2\n", | |
"F = np.array([0,0,0,0,0,-100,0,0,0,0,0])\n", | |
"L,U = LUNaive(k)\n", | |
"F_EAs = F/(E_s*cs)\n", | |
"F_EAa = F/(E_a*cs)\n", | |
"#u = np.array([n2x,n2y,n3x,n3y,n4x,n4y,n5x,n5y,n6x,n6y,n7x])\n", | |
"us = solveLU(L,U,F_EAs)\n", | |
"ua = solveLU(L,U,F_EAa)\n", | |
"print('The coefficients of the displacements in mm of us are...')\n", | |
"print(us)\n", | |
"print('The coefficients of the displacements in mm of ua are...')\n", | |
"print(ua)\n", | |
"F_s = k@us\n", | |
"F_a = k@ua\n", | |
"print('The corresponding reaction forces in N for steel and aluminum respectively are...')\n", | |
"print(F_s)\n", | |
"print('and')\n", | |
"print(F_a)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 230, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"def f(s,F,u):\n", | |
" plt.plot(r[ix],r[iy],'-',color=(0,0,0,1))\n", | |
" plt.plot(r[ix]+u[ix]*s,r[iy]+u[iy]*s,'-',color=(1,0,0,1))\n", | |
" #plt.quiver(r[ix],r[iy],u[ix],u[iy],color=(0,0,1,1),label='displacements')\n", | |
" plt.quiver(r[ix],r[iy],F[ix],F[iy],color=(1,0,0,1),label='applied forces')\n", | |
" plt.quiver(r[ix],r[iy],u[ix],u[iy],color=(0,0,1,1),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('Deformation scale = {:.1f}x'.format(s))\n", | |
" plt.legend(bbox_to_anchor=(1,0.5))" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 231, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stderr", | |
"output_type": "stream", | |
"text": [ | |
"No handles with labels found to put in legend.\n" | |
] | |
}, | |
{ | |
"data": { | |
"image/png": 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\n", 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"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
}, | |
{ | |
"data": { | |
"application/vnd.jupyter.widget-view+json": { | |
"model_id": "6e5a07bb8a544351a5f20d7c248ebd77", | |
"version_major": 2, | |
"version_minor": 0 | |
}, | |
"text/plain": [ | |
"interactive(children=(IntSlider(value=5, description='s', max=10), Output()), _dom_classes=('widget-interact',…" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
}, | |
{ | |
"data": { | |
"text/plain": [ | |
"<function __main__.<lambda>(s)>" | |
] | |
}, | |
"execution_count": 231, | |
"metadata": {}, | |
"output_type": "execute_result" | |
}, | |
{ | |
"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": [ | |
"from __future__ import print_function\n", | |
"from ipywidgets import interact, interactive, fixed, interact_manual\n", | |
"import ipywidgets as widgets\\\n", | |
"\n", | |
"length = 300 #mm\n", | |
"node = 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", | |
"node[:,1:3]*=length\n", | |
"r = np.block([n[1:3] for n in node])\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", | |
"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=30)\n", | |
"plt.plot(r[0],r[1],'>',color='k',markersize=30)\n", | |
"plt.plot(r[-2],r[-1],'^',color='r',markersize=30)\n", | |
"for n in node:\n", | |
" if n[2]>0.8*length: offset=0.1\n", | |
" else: offset=-length/5\n", | |
" plt.text(n[1]-length/3,n[2]+offset,'n {}'.format(int(n[0])),color='b') \n", | |
"s = 5\n", | |
"plt.legend(bbox_to_anchor=(1,0.5))\n", | |
"plt.title('Steel deformation Scale of = {:.1f}x'.format(s), size=20)\n", | |
"plt.xlabel('x (mm)', size=15)\n", | |
"plt.ylabel('y (mm)', size=15)\n", | |
"interact(lambda s: f(s,F_s,us),s=(0,10,1))" | |
] | |
}, | |
{ | |
"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": 196, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"-15357142.857142858\n", | |
"-2.000754527162978\n", | |
"0.7675675675675676\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": [ | |
"E_s = 200000 #MPa\n", | |
"E_a = 70000 #MPa\n", | |
"N = 1000\n", | |
"cs = np.linspace(0.1, 1,N) #mm^2\n", | |
"F = np.array([0,0,0,0,0,-100,0,0,0,0,0])\n", | |
"\n", | |
"L,U = LUNaive(k)\n", | |
"#F_EAa = F/(E_a*cs)\n", | |
"O = []\n", | |
"def delta_n41(state):\n", | |
" F_EAa = F/(E_a*state)\n", | |
" ua = solveLU(L,U,F_EAa)\n", | |
" return ua[5]\n", | |
"def delta_n4a(state):\n", | |
" for x in np.nditer(state):\n", | |
" Q = delta_n41(x)\n", | |
" O.append(Q)\n", | |
" P = np.array(O)\n", | |
" return P\n", | |
"A = delta_n4a(cs)\n", | |
"S = delta_n4s(cs)\n", | |
"print(delta_n41(cs1))\n", | |
"#u = np.array([n2x,n2y,n3x,n3y,n4x,n4y,n5x,n5y,n6x,n6y,n7x])\n", | |
"plt.plot(cs,A)\n", | |
"D = np.linspace(-1.9999999999,-2.0000000001,1000)\n", | |
"plt.plot(cs,D)\n", | |
"print(A[741])\n", | |
"print(cs[741])\n", | |
"plt.xlabel('Cross-Sectional Area (mm^2)')\n", | |
"plt.ylabel('Displacement (mm)')\n", | |
"plt.title('Area vs Node 4 y-Displacement');" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 197, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"-2.0020973154362407\n", | |
"0.2684684684684685\n" | |
] | |
}, | |
{ | |
"data": { | |
"image/png": 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6f9aayCGqrGvinbU7eGvtDt5as4NV22sBSE9NYdrw/nz2pNHMLClk5qhCBuZmxDlakUMXswTg7mfGatsiPaG6vpl31u2r8D/YVgNAdno/ZpUO4OKjR3Ds6EKmDu9PRqqGIZbE0+ebgER6yp6WVt7fvJO5K8qZu7KcRVuqcQ/Gop9VWshXz57A8WMHMm1EAWn91CtHEl+8uoFeBPwPUAw8a2YL3f2ceMQiiW1bdQOvrwwq/DdWlbOrYQ8pBkeVFHLD6eM5YexAZpQU6AhfklK8egE9CTwZj31LYmttdd7bVMWLy8qYu6J8b7PO4PwMPjp1CKdMGMRJ44ron62xcUTUBCSHvYbmFt5cU8GLS8uYs3w7FbWNpKYYx44ewDfPncQpE4uZODhPXTJF9qMEIIel6t3NvPJBGS8uLWPuynLqm1rIzUjl1InFnD1lCKdOLCZfI2CKdEkJQA4bdY17mLO8jGfe/5DXV1bQ1NLKoLwMLjpqOGdPGcLsMQPUli9yAJQApE9raG7h1Q+288yiD3nlg+00NLcytH8mVx4/in+ZNpTpIwpI0Q1YIgdFCUD6nNZW5511lTw+fzPPL9lKXVMLRbnpfHLWSM6bPoyZJYWq9EV6gBKA9BmbKut5YsFmnliwmU2Vu8nLSOX/TBvG+TOGcdzoAaSqb75Ij1ICkLja3dTCc4u38vj8zby1dgdmcOLYIm45ayLnTBlCVrra9EViRQlA4mJdRR2/f3sDf5y/merdzYwamM0tZ03g4pkjGF6QFe/wRJKCEoD0mj0trbz8wXYefnsDb6yqIDXFOGfqEK44bhSzxwxQP32RXqYEIDFXvbuZP7y7kd++uZ4PqxsY2j+Tm8+awKeOGcmg/Mx4hyeStJQAJGY2V9Xzm7+v59F3N1LX1MIJYwfy3fOncMakQbqgK9IHKAFIj1uypZr7X1/Ls4u3AnDetKF8/uQxTB3eP86RiUgkJQDpMQs2VnHPnFXMXVlObkYqnz2xlGtOHM0wXdQV6ZOUAOSQzd9Qyd1zVvHGqgoKs9P493Mm8pnjR2ksHpE+TglADtr8DZX8+KWV/H31DgbmpPONcyfxmdmjyMnQn5XI4UD/qXLAVm+v4YfPr+ClZWUU5aZz68cmc/nsErLT9eckcjjRf6xErWxXA3fPWclj/9hEdnoqt5w1gc+dPFoVv8hhSv+50q36pj3c99oafvXGWlpanSuPL+XLp49jYG5GvEMTkUOgBCCdcneeXbyV/3x2OVurGzhv+jD+/eyJlAzMjndoItIDlACkQyvLavjun5fy1todTB6az08vO4pjSgfEOywR6UFKANJOfdMefvLSSh74+3pyM1L5/gVT+PRxo+in8fdFEo4SgOz1t1UVfPPJRWyq3M1lx47k38+ZxICc9HiHJSIxogQg7Kxv4vZnl/P4/M2MKcrhsetmc9yYgfEOS0RiTAkgyc1ZVsY3/rSYqvom/vXUsdxwxngy0/QQFpFkoASQpOqb9nD7s8t55J2NTB6az0OfPYYpwzRYm0gyUQJIQu9v2slNjy1k/Y46vnDKGG4+awIZqTrqF0k2UScAM8sBGty9JYbxSAy1tjr3vraan8xZxeC8DB75/GyOH6u2fpFk1WkCMLMU4FPA5cAxQCOQYWblwHPA/e6+qleilENWWdfETY8t5PWV5Zw3fRi3XziV/lkarVMkmXV1BvAqMAf4JrDE3VsBzGwAcBpwh5k96e4Pxz5MORTvbazi336/gIraJv7roiO57NiRev6uiHSZAM509+b9Z7p7JfAE8ISZ6RCyD3N3fvvWBm5/dhmD8zN54osncOQIXegVkUCnCSCy8jezQmBk5PruvqCjBCF9Q9OeVv7vU0t4bN4mzpg0iB9/cgb9s5WvRWSfbi8Cm9n3gauBNYCHsx04PXZhyaGorGvi+ofn8+66Sr58+ji+cuYEUjSUg4jsJ5peQJ8Exrp7U0/t1MzuBM4DmggSyzXuvrOntp/MVpXV8LmH5rFtVwP3fGoGF8wYHu+QRKSPSolinSVAQQ/v9yVgqrtPA1YSXGiWQ/T22h1cfO+b1De18Nh1s1X5i0iXojkD+AHwnpktIegKCoC7n3+wO3X3FyMm3wYuOdhtReWv34Bti2O6i3irrGvEymt5OLUfkwbnkfGybuwSSShDjoRz7+jRTUaTAB4CfggsBlp7dO+BzwKPdbbQzK4DrgMoKSmJwe4Pf2U1DayrqCM3I5VJQ/JITYnmxE5Ekp25e9crmM1191MOeMNmc4AhHSy61d3/HK5zKzALuNi7CwSYNWuWz5s370BDSVjuzs9fXc1dL67ktInF3Hv5TLLSdeQvIu2Z2Xx3n7X//GjOAOab2Q+Ap2nfBLSgqw+5+5ndBHQV8H+AM6Kp/KU9d+dHL67kZ6+u5uKjhvPDS6aR1k9H/iISvWgSwFHhz9kR8w6pG6iZfRT4OnCKu9cf7HaSlbtz5wsruPe1NVx27Ej+88Ij1c1TRA5YtwnA3U+LwX5/BmQAL4VDErzt7tfHYD8Jx9354fMr+MXcNXz6uBJuv2CqKn8ROSjR3AhWAFwJlNL+TuAbDnan7j7uYD+b7P77haDyv2J2Cd87X5W/iBy8aJqAniPoqhmrXkASpV/MXcN9r63h8uNK+P4FUzWgm4gckmgSQKa73xzzSKRLj767kTv++gHnTx+myl9EekQ03UZ+Z2bXmtlQMxvQ9op5ZLLX80u28q0nF3PKhGLu+sR0NfuISI+I5gygCbgTuJX2g8GNiVVQss9ba3Zwwx8WclRJIfddcTTpqerqKSI9I5oEcDMwzt0rYh2MtLe2vJbrH55PycBsHrjqGLLT9QhnEek50RxOLgXUV7+XVdU18dkH/0G/FOOBq47RWP4i0uOiOaRsARaa2au0vxP4oLuBStea9rRy/cPz+XBnA49cexwlA7PjHZKIJKBoEsBT4Ut6yXf+vIR31lVy96UzmFWq6+0iEhvR3An8UG8EIoFH393Io//YxL+dNpYLj9J4/iISO51eAzCzZ8zsvI4e/G5mY8zse2b22diGl1wWb67mO08v5eTxRdx81sR4hyMiCa6rM4BrCXoA3W1mlUA5kAmMBlYDP2sb1lkOXVX4HN/i3Azu+dRR9FNffxGJsU4TgLtvA74GfM3MSoGhwG5gpUbw7Fmtrc5Njy2kvKaRP15/PANy0uMdkogkgag6lrv7emB9TCNJYr/+21rmrizn9gunMn1kTz9+WUSkY7qtNM6WbKnmzhdWcM6UwVx+nB55KSK9RwkgjnY3tXDjo+8xICedOy6epgHeRKRXdZsAzOzGaObJgfv+s8tYW1HHjz85g0K1+4tIL4vmDOCqDuZd3cNxJJ3XVmznkXc2cu3JYzhxXFG8wxGRJNTpRWAzuwz4NDDazJ6OWJQH7Ih1YImspqGZb/1pMeMG5XLL2RPiHY6IJKmuegG9CWwFioAfRcyvARbFMqhEd8dfP2Drrgae+OIJZKT2i3c4IpKkuroPYAOwATi+98JJfG+t2cHv39nI508azdElhfEOR0SSWDQXgS82s1VmVm1mu8ysxsx29UZwiWZ3Uwvf+NMiRg3M5pazNdSDiMRXNDeC/Tdwnrsvj3Uwie7e11azYUc9f7h2NlnpavoRkfiKphdQmSr/Q7e+oo5fzl3LhTOGcfzYgfEOR0QkqjOAeWb2GMEzASIfCPOnmEWVYNyd255ZSnpqCt/62OR4hyMiAkSXAPIJHgl5dsQ8B5QAovTSsjJeW1HOt/9lMoPyM+MdjogIEN0DYa7pjUASVUNzC9/7yzImDM7lqhNK4x2OiMhe0fQCmmBmL5vZknB6mpl9O/ahJYYH/r6OzVW7+Y/zp5LWT0MviUjfEU2N9Cvgm0AzgLsvAj4Vy6ASxY7aRu57dQ1nTh6sC78i0udEkwCy3f3d/ebtiUUwieZ/XllNXdMevnGu+vyLSN8TTQKoMLOxBBd+MbNLCIaIkC6sr6jj4bc3cOkxJYwblBfvcERE/kk0vYD+DbgfmGRmW4B1wBUxjSoB3PnCCtJTU/jKmePjHYqISIei6QW0FjjTzHKAFHeviX1Yh7elH1bz7OKt3HD6OHX7FJE+q9sEYGYFwJVAKZDa9tQqd7/hYHdqZt8HLgBage3A1e7+4cFur6+5Z84q8jJT+dzJY+IdiohIp6K5BvAcQeW/GJgf8ToUd7r7NHefAfwF+M4hbq/PWLKlmheXlfG5k0bTPyst3uGIiHQqmmsAme5+c0/u1N0jRxPNIbzAnAjueXkV+ZmpXHPi6HiHIiLSpWgSwO/M7FqCI/XIsYAqD2XHZvafBE1L1cBpXax3HXAdQElJyaHsMuaWbKnmpWVlfOXMCTr6F5E+L5omoCbgTuAt9jX/zOvuQ2Y2x8yWdPC6AMDdb3X3kcDvgS91th13v9/dZ7n7rOLi4mi+U9z8tO3o/6TSeIciItKtaM4AbgbGuXvFgWzY3c+MctVHgGeB7x7I9vuaNeW1vLS8jC+fNo78TB39i0jfF80ZwFKC0UB7jJlFdo4/H/igJ7cfD79+Yy3p/VK4UgO+ichhIpozgBZgoZm9SvtrAAfdDRS4w8wmEnQD3QBcfwjbirvtNQ08sWALl8wcQVFuRrzDERGJSjQJ4Knw1WPc/eM9ub14e+jN9TS3tHKt+v2LyGEkmjuBHzKzLKDE3Vf0QkyHlbrGPTz89kbOOWIIo4ty4h2OiEjUonkewHnAQuD5cHqGmT0d68AOF3+ct4nq3c1cd4qO/kXk8BLNReDbgGOBnQDuvhDQXU4Ez/r97dsbmD6ygKNLCuMdjojIAYkmAexx9+r95iXMnbuH4s01O1hbXseVs0fFOxQRkQMWzUXgJWb2aaBf2H3zBuDN2IZ1ePjdWxsozE7jX6YNjXcoIiIHLJozgC8DUwi6gD5CMHTDTbEM6nCwtXo3Ly0v45PHjCQzrV+8wxEROWDR9AKqB24NXxL6wzsbaXXniuPU/CMih6doegG9FD4ToG260MxeiG1YfVvTnlYeeXcTp08cxMgB2fEOR0TkoETTBFTk7jvbJty9ChgUu5D6vlc+KKOitpErdPFXRA5j0SSAVjPbOw6zmY0iyXsB/XHeZgbnZ/CRCX17dFIRka5E0wvoVuBvZjY3nP4I4fj8yWh7TQOvrSznuo+MoV+KxTscEZGDFs1F4OfN7GhgNmDAVw50aOhE8uSCLbS0OpfMHBHvUEREDkk0ZwAQjAi6HcgEjjAz3P312IXVN7k7f5y/maNLChhbnBvvcEREDkm3CcDMPg/cCIwgGBNoNsHTwU6PbWh9z8JNO1m9vZYfXHxkvEMRETlk0VwEvhE4Btjg7qcBRwHlMY2qj3piwWYy01J056+IJIRoEkCDuzcAmFmGu38ATIxtWH1Pc0srzy3expmTB+uRjyKSEKK5BrA5vBHsKeAlM6sCPoxtWH3Pm2t2UFnXxHnTh8U7FBGRHhFNL6CLwre3hY+F7E/4bIBk8sz7H5KXmcqpE9X3X0QSQ6cJwMwGdDB7cfgzF6iMSUR9UOOeFl5Yso1zpg4hI1UDv4lIYujqDGA+wR2/Hd3t5EDSPAJr7opyahr3qPlHRBJKpwnA3fXUr9Azi7YyICedE8YOjHcoIiI9JqobwczsYuAkgiP/N9z9qZhG1YfsbmphzrIyLj56OGn9ouk0JSJyeIhmOOh7gesJ2v+XANeb2c9jHVhf8caqcnY3t3DuVPX9F5HEEs0ZwCnAVHd3ADN7iH0XgxPei8vKyM9M5bgxHV0TFxE5fEXTprECKImYHgksik04fcuellZeXl7GGZMHq/lHRBJONGcAA4HlZvZuOH0M8JaZPQ3g7ufHKrh4m7ehiqr6Zs46YnC8QxER6XHRJIDvxDyKPuqlZWWkp6bowS8ikpCiSQDzgN3u3mpmE4BJwF/dvTm2ocWXu/Pism2cNK6I3IxoR80WETl8RNOw/TqQaWbDgZeBa4AHYxlUX/DBtho2Ve7mbDX/iEiCiiYBmLvXAxcD/xOODTQltmHF35xlZZjBGZOVAEQkMUWVAMzseOBy4NlwXsIPiDN3ZTnThvenOC8j3qGIiMRENAngJuCbwJPuvtTMxgCvxjas+Kqub2bBxipO0cVfEUlg0QwHPReYGzG9FtCgGA8AAA9VSURBVLihJ3ZuZl8F7gSK+9KD5v++poJWh1M09LOIJLCuhoO+291vMrNnCMYAaudQ+/+b2UjgLGDjoWwnFuauKCc/M5XpIwriHYqISMx0dQbwu/DnXTHa90+ArwF/jtH2D4q7M3dlOSePLyZVd/+KSALrajjo+eHPuWZWHL7vkYfBm9n5wBZ3f9+so8cNtFv3OuA6gJKSki7X7Qkry2rZtqtB7f8ikvC6agIy4LvAlwgeCpNiZnsIuoJ+r7sNm9kcYEgHi24FvgWcHU2A7n4/cD/ArFmz/qkpqqfNXbkdQHf/ikjC66oJ6CbgROAYd18HEPYAus/MvuLuP+lqw+5+ZkfzzexIYDTQdvQ/AlhgZse6+7aD+A49au7KciYNyWNI/8x4hyIiElNdNXJfCVzWVvnD3h5AV4TLDoq7L3b3Qe5e6u6lwGbg6L5Q+Tc0t/CPdVWcPL4o3qGIiMRcVwkgraOumeF1gLTYhRQ/8zdU0dTSygljlQBEJPF11QTUdJDLDkh4FtAnvLVmB/1SjFmlhfEORUQk5rpKANPNbFcH8w1IyAbyt9buYOrw/uRlJuQJjohIO111A0348X4i1TXu4f1NO/n8yWPiHYqISK/QnU6h+Ruq2NPqHD92YLxDERHpFUoAobfW7iA1xZg1Su3/IpIclABCb63ZwfSRBeTo6V8ikiSUAIDaxj0s3lLN7DED4h2KiEivUQIAFm7cSUurc0ypEoCIJA8lAIILwGZwtNr/RSSJKAEA8zZUMnFwHvnq/y8iSSTpE0BLq/Pexp3M1NG/iCSZpE8AK7bVUNu4RwlARJJO0ieA+RurAJg1SheARSS5KAGsr6Q4L4ORA7LiHYqISK9K+gQwb0MVM0sK6e7RlCIiiSapE8D2XQ1srtqt4Z9FJCkldQJ4b9NOAI4qKYhzJCIivS+pE8CizTvpl2IcMbR/vEMREel1SZ4AqpkwOI+s9KR69IGICJDECcDdWbylmukjdPQvIskpaRPAxsp6dtY3M22E2v9FJDklbQJ4f3M1ANN0BiAiSSppE8DizTvJSE1h4pC8eIciIhIXSZsA3t9czRHD8knrl7RFICJJLilrv5ZWZ8mWaqYNV/OPiCSvpEwAa8trqW9q0QVgEUlqSZkAFm/RBWARkaRMAMs+3EVGagqji3LiHYqISNwkZQJYvm0XE4fkkaoLwCKSxJKuBnR3lm+tYfKQ/HiHIiISV0mXALbXNFJZ18QRw5QARCS5JV0CWLZ1FwCThyoBiEhyi0sCMLPbzGyLmS0MXx/rrX0v+zBIAJOG6g5gEUluqXHc90/c/a7e3unyrbsYUZhFfmZab+9aRKRPSbomoOVbd6n5R0SE+CaAL5nZIjN7wMx65aG8u5taWFdRpwQgIkIME4CZzTGzJR28LgDuA8YCM4CtwI+62M51ZjbPzOaVl5cfUkwrympodThCCUBEJHbXANz9zGjWM7NfAX/pYjv3A/cDzJo1yw8lpuVhDyAlABGR+PUCGhoxeRGwpDf2u7Kshuz0fowozOqN3YmI9Gnx6gX032Y2A3BgPfCF3tjp6u21jBuUS0qK9cbuRET6tLgkAHf/TDz2u3p7LcePGRiPXYuI9DlJ0w20pqGZrdUNjBucG+9QRET6hKRJAKu31wIwfpDuABYRgSRKAKv2JgCdAYiIQBIlgNXba0lPTWHkgOx4hyIi0ickTQJYVVbD2OJc+qkHkIgIkEwJYHutmn9ERCIkRQKob9rD5qrdjFMCEBHZKykSwNryOkAXgEVEIiVFAli1vQaA8boHQERkr+RIAGW1pKYYowbmxDsUEZE+IykSwKiB2Vx89HDS+iXF1xURiUo8HwnZay49poRLjymJdxgiIn2KDolFRJKUEoCISJJSAhARSVJKACIiSUoJQEQkSSkBiIgkKSUAEZEkpQQgIpKkzN3jHUPUzKwc2BDvOA5REVAR7yD6EJXHPiqL9lQe7R1KeYxy9+L9Zx5WCSARmNk8d58V7zj6CpXHPiqL9lQe7cWiPNQEJCKSpJQARESSlBJA77s/3gH0MSqPfVQW7ak82uvx8tA1ABGRJKUzABGRJKUEICKSpJQAYsTMPmpmK8xstZl9o4Pll5vZovD1pplNj0ecvaG7sohY7xgzazGzS3ozvt4WTXmY2almttDMlprZ3N6OsTdF8b/S38yeMbP3w/K4Jh5x9gYze8DMtpvZkk6Wm5n9NCyrRWZ29CHt0N316uEX0A9YA4wB0oH3gSP2W+cEoDB8fy7wTrzjjldZRKz3CvAccEm8447z30YBsAwoCacHxTvuOJfHt4Afhu+LgUogPd6xx6g8PgIcDSzpZPnHgL8CBsw+1HpDZwCxcSyw2t3XunsT8ChwQeQK7v6mu1eFk28DI3o5xt7SbVmEvgw8AWzvzeDiIJry+DTwJ3ffCODuiVwm0ZSHA3lmZkAuQQLY07th9g53f53g+3XmAuC3HngbKDCzoQe7PyWA2BgObIqY3hzO68znCLJ6Iuq2LMxsOHAR8ItejCteovnbmAAUmtlrZjbfzK7steh6XzTl8TNgMvAhsBi40d1beye8PudA65YuJcVD4ePAOpjXYX9bMzuNIAGcFNOI4ieasrgb+Lq7twQHeQktmvJIBWYCZwBZwFtm9ra7r4x1cHEQTXmcAywETgfGAi+Z2RvuvivWwfVBUdct0VACiI3NwMiI6REERy/tmNk04NfAue6+o5di623RlMUs4NGw8i8CPmZme9z9qd4JsVdFUx6bgQp3rwPqzOx1YDqQiAkgmvK4BrjDg0bw1Wa2DpgEvNs7IfYpUdUt0VITUGz8AxhvZqPNLB34FPB05ApmVgL8CfhMgh7Ztem2LNx9tLuXunsp8Djwrwla+UMU5QH8GTjZzFLNLBs4Dljey3H2lmjKYyPB2RBmNhiYCKzt1Sj7jqeBK8PeQLOBanfferAb0xlADLj7HjP7EvACQS+HB9x9qZldHy7/BfAdYCBwb3jku8cTcOTDKMsiaURTHu6+3MyeBxYBrcCv3b3DboGHuyj/Pr4PPGhmiwmaQL7u7gk5TLSZ/QE4FSgys83Ad4E02FsWzxH0BFoN1BOcHR38/sKuRSIikmTUBCQikqSUAEREkpQSgIhIklICEBFJUkoAIiJJSglAumVmQ8zsUTNbY2bLzOw5M5vQS/v+rJktDkc+XGJmHY0j1N02CszsXyOmh5nZ4z0bKYRDN3TYldfMis2s2cy+0NP73W8/F5rZd2K4/aHhSJQLzCwvYn62mT1rZh+EI3beEbHsS4k8gufhTAlAuhQOwPUk8Jq7j3X3IwhGZxy833r9YrDvEcCtwEnuPo1g9MNFB7GpAmBvAnD3D929t4ec/gTBoH+XdbZCD5Xh14B7e2A7/ySs8J8Cvg48BDxuZmkRq9zl7pOAo4ATzezccP4DwA2xiEkOjRKAdOc0oDnyhi13X+jub4Rj1r9qZo8QDNKFmd0cHqkvMbObwnk54dHh++H8S8P5d4RnFIvM7K4O9j0IqAFqw/3Wuvu68LNjzez5cLC0N8xsUjh/sJk9Ge7rfTM7AbgDGGvB+Pp3mlmpheOtm1mmmf0mPMt4LxybCTO72sz+FO5jlZn9d1tQZnafmc0Lj3T/I8pyvAy4BRhhweB3bduqNbPvmdk7wPFmNtPM5obf6wULR3o0s2vN7B/hd3oivEO4nfCsrLHtJikzezCM9VUzW2tmp1gw3vxyM3twvxh+GO5zjpkdG57NrDWz88N10oA/EAzL/IS730NwV+qvwt9Nvbu/Gr5vAhYQjnDr7vXAejM7Nsqykt4S7/Gv9erbL4Ijt590suxUoA4YHU7PJEgEOQTD9i4lOBr8OPCriM/1BwYAK9h3M2JBB9vvR3CH6EbgN8B5EcteBsaH748DXgnfPwbcFPH5/kApEeOrR04TVMq/Cd9PCveVCVxNMNxA/3B6AzAyXG9AxPZfA6aF068Bszr4HiOBVeH7/wJujljmwCfD92nAm0BxOH0pwZ2xAAMjPnM78OUO9nMN8KOI6QcJhlc2gmGEdwFHEhz4zQdmRMRwbvj+SeDFMJbpwMKD+JspCMtuTMS8W4Fb4v33rFf7l84A5FC96+FROcGIpk+6e5271xKMdXQyQVI4MzzKPNndqwkqowbg12Z2McFt7e24ewvwUeASgoHQfmJmt5lZLsEDdf5oZguBXwJtY6KfDtzX9vlwX105CfhduP4HBBV92/WNl9292t0bCB7QMiqc/0kzWwC8B0wBjuhmH58C/jd8/yjtm4FaCJ6DAMEYN1MJRrtcCHybfc+JmBqe6SwGLg/3u7+hQPl+857xoAZeDJS5+2IPhlJeSpAIAZqA58P3i4G57t4cvi/lAJhZKsGZwk/dPXK8nu3AsAPZlsSexgKS7iwlqIA7UxfxvsOxnN19pZnNJBjD5Adm9qK7fy9sEjiDoIL8kpmdRXBkCvC0u38nrLzeBd41s5cIzgR+DOx09xmH9M26iDnUGPG+BUg1s9HAV4Fj3L0qbErJ7GYflwGDzezycHqYmY1391VAQ5jo2mJZ6u7Hd7CNB4EL3f19M7ua4Oxrf7sJzlg6+g6t+32fVvb9/zeH5dxuPXdvDSv0A3E/wdnO3fvNzwzjkz5EZwDSnVeADDO7tm2GBc/uPaWDdV8HLgx7hOQQPOTlDTMbBtS7+8PAXcDR4VF8f3d/DriJoDmixd1nhK/vWNBbJ/KZpzOADR6MA7/OzD4RxmO275nKLwNfDOf3M7N8gusIeXTsdYIj6rY29BKCpqnO5BMkvWoLRqY8t4t1MbOJQI67D/d9I57+gCDp7W8FUGxmx4efTTOztiP9PGBr2BZ/eQefhWDE0HFdxRNLZnY7QQK6qYPFE4CEHNDucKYEIF0KjwwvAs6yoBvoUuA2OhiD3N0XEBypvgu8QzCK5XsE7c7vhs0atxK0YecBfzGzRcBc4Csd7D4NuMuCroULCdrEbwyXXQ58zszeJzhLaeseeiNwWthUMh+Y4sGzFv4eXoC+c7993Av0C9d/DLja3RvphLu/T9D0s5Sgd8vfO1s3dBlBu3qkJ+igN5AHF08vAX4Yfq+FBE1dAP+XoExfAj7oZF+vA0eZ9f5TdWxfj60jgAXhBffPR6xyIjCnt+OSrmk0UJEEYmb3ELT795nK1syOIrjw/Zl4xyLt6QxAJLH8F/BPXUTjrIjgDEb6GJ0BiIgkKZ0BiIgkKSUAEZEkpQQgIpKklABERJKUEoCISJL6/xgmFQ1kukTFAAAAAElFTkSuQmCC\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"cs = np.linspace(0.1,1,N)\n", | |
"O = []\n", | |
"def delta_n42(state):\n", | |
" F_EAs = F/(E_s*state)\n", | |
" ua = solveLU(L,U,F_EAs)\n", | |
" return ua[5]\n", | |
"def delta_n4s(state):\n", | |
" for x in np.nditer(state):\n", | |
" Q = delta_n42(x)\n", | |
" O.append(Q)\n", | |
" P = np.array(O)\n", | |
" return P\n", | |
"S = delta_n4s(cs)\n", | |
"plt.plot(cs,S)\n", | |
"plt.plot(cs,D)\n", | |
"print(S[187])\n", | |
"print(cs[187])\n", | |
"plt.xlabel('Cross-Sectional Area (mm^2)')\n", | |
"plt.ylabel('Displacement (mm)')\n", | |
"plt.title('Area vs Node 4 y-Displacement');" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 237, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"The price of making the bridge out of steel and aluminum respectively are 0.0033381070800000004 and 0.01056674322 dollars\n", | |
"Therefore steel will be the cheaper option, being cheaper than aluminum by 68.40931012990016 %\n" | |
] | |
} | |
], | |
"source": [ | |
"rho_s = 7.9*10**(-9) #Tonne/mm^3\n", | |
"rho_a = 2.7*10**(-9) #tonne/mm^3\n", | |
"cs_s = 0.269 #mm^2\n", | |
"cs_a = 0.7676 #mm^2\n", | |
"N_T = 11 #Number of Trusses\n", | |
"L = 300 #mm each truss\n", | |
"cost_s = 476 #$/tonne\n", | |
"cost_a = 1545 #$/tonne\n", | |
"Price_s = N_T*L*rho_s*cs_s*cost_s\n", | |
"Price_a = N_T*L*rho_a*cs_a*cost_a\n", | |
"print('The price of making the bridge out of steel and aluminum respectively are',Price_s,'and',Price_a,'dollars')\n", | |
"print('Therefore steel will be the cheaper option, being cheaper than aluminum by',((Price_a-Price_s)/Price_a)*100,'%')" | |
] | |
}, | |
{ | |
"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": 247, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"import pandas as pd\n", | |
"data_s = pd.read_csv('../data/steel_price.csv')\n", | |
"data_a = pd.read_csv('../data/al_price.csv')\n", | |
"year_s = data_s['Year']\n", | |
"price_s = data_s['dollars/MT']\n", | |
"year_a = data_a['Year']\n", | |
"price_a = data_a['dollars/MT']\n" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 253, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"The constants are [-1.31541794e+04 6.65479504e+00]\n", | |
"3048519.0273679895 and 134778404.24740294\n" | |
] | |
}, | |
{ | |
"ename": "AttributeError", | |
"evalue": "'Series' object has no attribute 'reshape'", | |
"output_type": "error", | |
"traceback": [ | |
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", | |
"\u001b[0;31mAttributeError\u001b[0m Traceback (most recent call last)", | |
"\u001b[0;32m<ipython-input-253-294d5e8a0cd9>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m 30\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 31\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mmax_N\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 32\u001b[0;31m \u001b[0mZ\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mhstack\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mZ\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0my_train\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreshape\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 33\u001b[0m \u001b[0mZtest\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mhstack\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mZtest\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0my_test\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreshape\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 34\u001b[0m \u001b[0mA\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlinalg\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msolve\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mZ\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mT\u001b[0m\u001b[0;34m@\u001b[0m\u001b[0mZ\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mZ\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mT\u001b[0m\u001b[0;34m@\u001b[0m\u001b[0mp_train\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", | |
"\u001b[0;32m/opt/conda/lib/python3.7/site-packages/pandas/core/generic.py\u001b[0m in \u001b[0;36m__getattr__\u001b[0;34m(self, name)\u001b[0m\n\u001b[1;32m 5177\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_info_axis\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_can_hold_identifiers_and_holds_name\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mname\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5178\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mname\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 5179\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mobject\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__getattribute__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mname\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 5180\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5181\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m__setattr__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mname\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvalue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", | |
"\u001b[0;31mAttributeError\u001b[0m: 'Series' object has no attribute 'reshape'" | |
] | |
} | |
], | |
"source": [ | |
"data_s = pd.read_csv('../data/steel_price.csv')\n", | |
"data_a = pd.read_csv('../data/al_price.csv')\n", | |
"year_s = data_s['Year']\n", | |
"price_s = data_s['dollars/MT']\n", | |
"year_a = data_a['Year']\n", | |
"price_a = data_a['dollars/MT']\n", | |
"\n", | |
"import random \n", | |
"np.random.seed(100)\n", | |
"rand = random.sample(range(0,len(year_s)),len(year_s))\n", | |
"train = 0.70\n", | |
"N=30\n", | |
"y_train = year_s[rand[:int(len(year_s)*train)]]\n", | |
"p_train = price_s[rand[:int(len(year_s)*train)]]\n", | |
"y_test = year_s[rand[int(len(year_s)*train):]]\n", | |
"p_test = price_s[rand[int(len(year_s)*train):]]\n", | |
"\n", | |
"Z = np.block([[y_train**0],[y_train]]).T\n", | |
"Ztest = np.block([[p_test**0],[p_test]]).T\n", | |
"a = np.linalg.solve(Z.T@Z,Z.T@p_train)\n", | |
"print('The constants are',a)\n", | |
"s_train = np.sum(((y_train-Z@a)**2)/len(y_train))\n", | |
"s_test = np.sum(((p_test-Ztest@a)**2)/len(p_test))\n", | |
"print(s_train, 'and',s_test)\n", | |
"max_N = 30\n", | |
"s_train = np.zeros(max_N)\n", | |
"s_test = np.zeros(max_N)\n", | |
"Z_s = np.block([[y_train**0]]).T\n", | |
"Ztest = np.block([[y_test**0]]).T\n", | |
"\n", | |
"for i in range(1,max_N):\n", | |
" Z=np.hstack((Z_s,y_train.reshape(-1,1)**i))\n", | |
" Ztest=np.hstack((Ztest,y_test.reshape(-1,1)**i))\n", | |
" A = np.linalg.solve(Z.T@Z,Z.T@p_train)\n", | |
" s_train[i] = np.sum(((p_train-Z@A)**2)/len(p_train))\n", | |
" s_test[i] = np.sum(((p_test-Ztest@A)**2)/len(p_test))\n", | |
" \n", | |
"plt.semilogy(np.arange(1,max_N),s_train[1:],label='Train Error')\n", | |
"plt.semilogy(np.arange(1,max_N),s_test[1:], 'o',label='Test Error')\n", | |
"plt.xlabel('Order')\n", | |
"plt.ylabel('Error')\n", | |
"plt.legend();" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 255, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"The constants are [-6.51475657e+05 3.24391797e+02]\n", | |
"1576135.3451664052 and 284971174646.1287\n" | |
] | |
}, | |
{ | |
"ename": "AttributeError", | |
"evalue": "'Series' object has no attribute 'reshape'", | |
"output_type": "error", | |
"traceback": [ | |
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", | |
"\u001b[0;31mAttributeError\u001b[0m Traceback (most recent call last)", | |
"\u001b[0;32m<ipython-input-255-9e0a579f3545>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m 21\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 22\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mmax_N\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 23\u001b[0;31m \u001b[0mZ\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mhstack\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mZ\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0my_train\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreshape\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 24\u001b[0m \u001b[0mZtest\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mhstack\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mZtest\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0my_test\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreshape\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 25\u001b[0m \u001b[0mA\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlinalg\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msolve\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mZ\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mT\u001b[0m\u001b[0;34m@\u001b[0m\u001b[0mZ\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mZ\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mT\u001b[0m\u001b[0;34m@\u001b[0m\u001b[0mp_train\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", | |
"\u001b[0;32m/opt/conda/lib/python3.7/site-packages/pandas/core/generic.py\u001b[0m in \u001b[0;36m__getattr__\u001b[0;34m(self, name)\u001b[0m\n\u001b[1;32m 5177\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_info_axis\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_can_hold_identifiers_and_holds_name\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mname\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5178\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mname\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 5179\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mobject\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__getattribute__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mname\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 5180\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5181\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m__setattr__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mname\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvalue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", | |
"\u001b[0;31mAttributeError\u001b[0m: 'Series' object has no attribute 'reshape'" | |
] | |
} | |
], | |
"source": [ | |
"rand = random.sample(range(0,len(year_a)),len(year_a))\n", | |
"train = 0.70\n", | |
"N=30\n", | |
"y_train = year_a[rand[:int(len(year_a)*train)]]\n", | |
"p_train = price_a[rand[:int(len(year_a)*train)]]\n", | |
"y_test = year_a[rand[int(len(year_a)*train):]]\n", | |
"p_test = price_a[rand[int(len(year_a)*train):]]\n", | |
"\n", | |
"Z = np.block([[y_train**0],[y_train]]).T\n", | |
"Ztest = np.block([[p_test**0],[p_test]]).T\n", | |
"a = np.linalg.solve(Z.T@Z,Z.T@p_train)\n", | |
"print('The constants are',a)\n", | |
"s_train = np.sum(((y_train-Z@a)**2)/len(y_train))\n", | |
"s_test = np.sum(((p_test-Ztest@a)**2)/len(p_test))\n", | |
"print(s_train, 'and',s_test)\n", | |
"max_N = 30\n", | |
"s_train = np.zeros(max_N)\n", | |
"s_test = np.zeros(max_N)\n", | |
"Z = np.block([[y_train**0]]).T\n", | |
"Ztest = np.block([[y_test**0]]).T\n", | |
"\n", | |
"for i in range(1,max_N):\n", | |
" Z=np.hstack((Z,y_train.reshape(-1,1)**i))\n", | |
" Ztest=np.hstack((Ztest,y_test.reshape(-1,1)**i))\n", | |
" A = np.linalg.solve(Z.T@Z,Z.T@p_train)\n", | |
" s_train[i] = np.sum(((p_train-Z@A)**2)/len(p_train))\n", | |
" s_test[i] = np.sum(((p_test-Ztest@A)**2)/len(p_test))\n", | |
" \n", | |
"plt.semilogy(np.arange(1,max_N),s_train[1:],label='Train Error')\n", | |
"plt.semilogy(np.arange(1,max_N),s_test[1:], 'o',label='Test Error')\n", | |
"plt.xlabel('Order')\n", | |
"plt.ylabel('Error')\n", | |
"plt.legend();" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 276, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"The predicted value of steel per tonne in 2025 is 316.28110235738734 Dollars\n" | |
] | |
}, | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 720x720 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"plt.figure(figsize=(10,10))\n", | |
"plt.plot(year_s,price_s,label='Data')\n", | |
"Z1 = np.block([[year_s],[year_s**0],[(year_s-2014)*(year_s>=2014)]]).T\n", | |
"a1 = np.linalg.solve(Z1.T@Z1,Z1.T@price_s)\n", | |
"st_2025 = np.zeros(11)\n", | |
"for i,x in enumerate(range(2014,2025)):\n", | |
" st_2025[i] = a1[0]*x+a1[1]+a1[2]*(x-2014)*(x>=2014)\n", | |
"print('The predicted value of steel per tonne in 2025 is',st_2025[10],'Dollars')\n", | |
"plt.plot(year_s, Z1@a1,label='Steel Price Regression Line')\n", | |
"plt.title('Year vs Steel Price')\n", | |
"plt.xlabel('Year')\n", | |
"plt.ylabel('Dollars per Tonne')\n", | |
"plt.legend();" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 278, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"The predicted value of aluminum per tonne in 2025 is 5292.5608117608035 Dollars\n" | |
] | |
}, | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 720x720 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"plt.figure(figsize=(10,10))\n", | |
"plt.plot(year_a,price_a,label='Data')\n", | |
"Z1 = np.block([[year_a],[year_a**0],[(year_a-2014)*(year_a>=2014)]]).T\n", | |
"a1 = np.linalg.solve(Z1.T@Z1,Z1.T@price_a)\n", | |
"al_2025 = np.zeros(11)\n", | |
"for i,x in enumerate(range(2014,2025)):\n", | |
" al_2025[i] = a1[0]*x+a1[1]+a1[2]*(x-2014)*(x>=2014)\n", | |
"print('The predicted value of aluminum per tonne in 2025 is',al_2025[10],'Dollars')\n", | |
"plt.plot(year_a, Z1@a1,label='Steel Price Regression Line')\n", | |
"plt.title('Year vs Steel Price')\n", | |
"plt.xlabel('Year')\n", | |
"plt.ylabel('Dollars per Tonne')\n", | |
"plt.legend();" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Based on this data, aluminum will be even more costly to construct a bridge out of, with our estimates for 2025 seeing aluminum predicted to be 16.7 times more expensive per tonne. So it would be less logical to use aluminum instead of steel in this case." | |
] | |
}, | |
{ | |
"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 | |
} |