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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": 396, | |
"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": 396, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"import numpy as np\n", | |
"import matplotlib.pyplot as plt\n", | |
"from matplotlib import rcParams\n", | |
"rcParams['font.family'] = 'sans'\n", | |
"rcParams['font.size'] = 16\n", | |
"rcParams['lines.linewidth'] = 3\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": 397, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"Condition of K = 1.4577532625238035e+17\n" | |
] | |
} | |
], | |
"source": [ | |
"t = 16 #based on size of delta for constants\n", | |
"cond_K = np.linalg.cond(K)\n", | |
"print('Condition of K =', cond_K)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 398, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"Error in F: 10 N\n" | |
] | |
} | |
], | |
"source": [ | |
"c2 = 17 #order of magnitude of condition\n", | |
"error_F = 10**(c-t)\n", | |
"print('Error in F:',error_F,'N')" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"__Problem 1:A__ \n", | |
"\n", | |
"As calculated in the above lines of code, the error for each calculated force value will be plus or minus one hundred Newtons. This is dependent on both the condition of the matrix K and the error or numbers stored digitally.\n", | |
"\n", | |
"__Problem 1:B__\n", | |
"\n", | |
"The matrix K has a large condition because it is a large matrix with many values that have small variations." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 399, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"Condition of K[2:13] = 52.23542514351006\n", | |
"Error in F[2:13]: 10\n" | |
] | |
} | |
], | |
"source": [ | |
"cond_K_2_13 = np.linalg.cond(K[2:13,2:13])\n", | |
"print('Condition of K[2:13] =',cond_K_2_13)\n", | |
"error_F2 = 10**(c-t)\n", | |
"print('Error in F[2:13]:',error_F)\n" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 400, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"Error in F[2:13]: 1e-15 N\n" | |
] | |
} | |
], | |
"source": [ | |
"c2= 1 #order of magnitude of condition of K[2:13]\n", | |
"t=16\n", | |
"error_F2 = 10**(c2-t)\n", | |
"print('Error in F[2:13]:',error_F2,'N')" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"__Problem 1:C__\n", | |
"\n", | |
"So for the new matrix calculations of K[2:13] the error of the values obtained is to the magnitude of 10^-15 Newtons. This is a significant drop from the error for the full matrix solution of K." | |
] | |
}, | |
{ | |
"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": 401, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"P matrix\n", | |
"[[1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n", | |
" [0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n", | |
" [0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0.]\n", | |
" [0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0.]\n", | |
" [0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0.]\n", | |
" [0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0.]\n", | |
" [0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0.]\n", | |
" [0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0.]\n", | |
" [0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0.]\n", | |
" [0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0.]\n", | |
" [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]] \n", | |
"\n", | |
"L matrix\n", | |
"[[ 1. 0. 0. 0. 0. 0.\n", | |
" 0. 0. 0. 0. 0. ]\n", | |
" [ 0. 1. 0. 0. 0. 0.\n", | |
" 0. 0. 0. 0. 0. ]\n", | |
" [-0.16666667 0.28867513 1. 0. 0. 0.\n", | |
" 0. 0. 0. 0. 0. ]\n", | |
" [ 0.28867513 -0.5 0.12371791 1. 0. 0.\n", | |
" 0. 0. 0. 0. 0. ]\n", | |
" [-0.66666667 0. -0.17857143 -0.09622504 1. 0.\n", | |
" 0. 0. 0. 0. 0. ]\n", | |
" [ 0. 0. -0.18557687 -0.72222222 -0.08247861 1.\n", | |
" 0. 0. 0. 0. 0. ]\n", | |
" [ 0. 0. -0.42857143 0.12830006 -0.23809524 0.33425542\n", | |
" 1. 0. 0. 0. 0. ]\n", | |
" [ 0. 0. 0. 0. 0.24743583 -0.78947368\n", | |
" 0.18426072 1. 0. 0. 0. ]\n", | |
" [ 0. 0. 0. 0. -0.57142857 -0.09116057\n", | |
" -0.24822695 -0.21650635 1. 0. 0. ]\n", | |
" [ 0. 0. 0. 0. 0. 0.\n", | |
" -0.23339692 -0.875 -0.32768529 1. 0. ]\n", | |
" [ 0. 0. 0. 0. 0. 0.\n", | |
" -0.53900709 0.24056261 -0.59459459 0.28867513 1. ]] \n", | |
"\n", | |
"U matrix\n", | |
"[[ 0.005 0. -0.00083333 0.00144338 -0.00333333 0.\n", | |
" 0. 0. 0. 0. 0. ]\n", | |
" [ 0. 0.005 0.00144338 -0.0025 0. 0.\n", | |
" 0. 0. 0. 0. 0. ]\n", | |
" [ 0. 0. 0.00777778 0.00096225 -0.00138889 -0.00144338\n", | |
" -0.00333333 0. 0. 0. 0. ]\n", | |
" [ 0. 0. 0. 0.00321429 -0.00030929 -0.00232143\n", | |
" 0.00041239 0. 0. 0. 0. ]\n", | |
" [ 0. 0. 0. 0. 0.00583333 -0.00048113\n", | |
" -0.00138889 0.00144338 -0.00333333 0. 0. ]\n", | |
" [ 0. 0. 0. 0. 0. 0.00301587\n", | |
" 0.00100807 -0.00238095 -0.00027493 0. 0. ]\n", | |
" [ 0. 0. 0. 0. 0. 0.\n", | |
" 0.00618421 0.00113951 -0.00153509 -0.00144338 -0.00333333]\n", | |
" [ 0. 0. 0. 0. 0. 0.\n", | |
" 0. 0.00255319 -0.00055278 -0.00223404 0.0006142 ]\n", | |
" [ 0. 0. 0. 0. 0. 0.\n", | |
" 0. 0. 0.00256944 -0.00084197 -0.00152778]\n", | |
" [ 0. 0. 0. 0. 0. 0.\n", | |
" 0. 0. 0. 0.00243243 0.00070218]\n", | |
" [ 0. 0. 0. 0. 0. 0.\n", | |
" 0. 0. 0. 0. 0.00111111]] \n", | |
"\n" | |
] | |
} | |
], | |
"source": [ | |
"from scipy.linalg import lu\n", | |
"#Part A:\n", | |
"K_new = K[2:13,2:13]\n", | |
"P_K, L_K,U_K = lu(K_new)\n", | |
"print('P matrix')\n", | |
"print(P_K, '\\n')\n", | |
"print('L matrix')\n", | |
"print(L_K, '\\n')\n", | |
"print('U matrix')\n", | |
"print(U_K, '\\n')" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"So from the PLU decomposition printed above, we can see that no partial pivoting was needed since the matrix P is the identity matrix." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 402, | |
"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", | |
" 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": 403, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"Steel\n", | |
"displacements:\n", | |
" u_1x:0.00 mm\n", | |
" u_1y:0.00 mm\n", | |
" u_2x:1.95 mm\n", | |
" u_2y:-2.13 mm\n", | |
" u_3x:0.43 mm\n", | |
" u_3y:-4.00 mm\n", | |
" u_4x:1.08 mm\n", | |
" u_4y:-5.38 mm\n", | |
" u_5x:1.73 mm\n", | |
" u_5y:-4.00 mm\n", | |
" u_6x:0.22 mm\n", | |
" u_6y:-2.13 mm\n", | |
" u_7x:2.17 mm\n", | |
" u_7y:0.00 mm\n", | |
"forces:\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", | |
"Aluminum\n", | |
"displacements:\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", | |
"forces:\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 B: (Steel)\n", | |
"A = .1 #mm^2\n", | |
"E_s = 200*10**3 #MPa, steel\n", | |
"F_s_free = np.zeros(11)\n", | |
"F_s_free[5] = -100\n", | |
"u_free = solveLU(L_K,U_K,F_s_free/A/E_s)\n", | |
"u_all_s = np.zeros(14)\n", | |
"u_all_s[2:13] = u_free\n", | |
"\n", | |
"F_all_s = K*A*E_s@u_all_s\n", | |
"print('Steel')\n", | |
"xy={0:'x',1:'y'}\n", | |
"print('displacements:')\n", | |
"for i in range(len(u_all_s)):\n", | |
" print(' u_{}{}:{:.2f} mm'.format(int(i/2)+1,xy[i%2],u_all_s[i]))\n", | |
"print('forces:')\n", | |
"for i in range(len(F_all_s)):\n", | |
" print(' F_{}{}:{:.2f} N'.format(int(i/2)+1,xy[i%2],F_all_s[i]))\n", | |
" \n", | |
"\n", | |
"print()\n", | |
"#Aluminum\n", | |
"E_a = 70*10**3 #MPa, aluminum\n", | |
"F_a_free = np.zeros(11)\n", | |
"F_a_free[5] = -100\n", | |
"u_free = solveLU(L_K,U_K,F_a_free/A/E_a)\n", | |
"u_all_a = np.zeros(14)\n", | |
"u_all_a[2:13] = u_free\n", | |
"\n", | |
"\n", | |
"F_all_a = K*A*E_a@u_all_a\n", | |
"print('Aluminum')\n", | |
"xy={0:'x',1:'y'}\n", | |
"print('displacements:')\n", | |
"for i in range(len(u_all_a)):\n", | |
" print(' u_{}{}:{:.2f} mm'.format(int(i/2)+1,xy[i%2],u_all_a[i]))\n", | |
"print('forces:')\n", | |
"for i in range(len(F_all_a)):\n", | |
" print(' F_{}{}:{:.2f} N'.format(int(i/2)+1,xy[i%2],F_all_a[i]))" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 404, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
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\n", | |
"text/plain": [ | |
"<Figure size 1152x576 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
}, | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 1152x576 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"#Part D:\n", | |
"# code adapted from extra-FEA_material notebook\n", | |
"\n", | |
"#Alumnium truss plot\n", | |
"plt.figure(figsize=(16,8))\n", | |
"scale = 10\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", | |
"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", | |
"r0 = np.block([1000*n[1:3] for n in nodes])\n", | |
"plt.plot(r0[ix],r0[iy],'-',color='k');\n", | |
"r_a = r0 + u_all_a*scale\n", | |
"plt.plot(r_a[ix],r_a[iy],'-',color='g');\n", | |
"plt.quiver(r0[ix],r0[iy],F_all_a[ix],F_all_a[iy],color=(1,0,0,1),label='Applied Forces (N)');\n", | |
"plt.quiver(r0[ix],r0[iy],u_all_a[ix],u_all_a[iy],color=(0,0,1,1),label='Displacements (10x Scale)');\n", | |
"plt.title('Aluminum Truss (Unloaded vs Loaded)\\n')\n", | |
"plt.xlabel('Millimeters')\n", | |
"plt.ylabel('Millimeters')\n", | |
"plt.legend(bbox_to_anchor=(1.01, 1))\n", | |
"plt.text(3300,500,'Note: Forces are 100 N \\n central load and two\\n 50 N reaction forces\\n at truss ends.');\n", | |
"plt.show()\n", | |
"\n", | |
"#Steel truss plot\n", | |
"plt.figure(figsize=(16,8))\n", | |
"plt.plot(r0[ix],r0[iy],'-',color='k');\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", | |
"r_s = r0 + u_all_s*scale\n", | |
"plt.plot(r_s[ix],r_s[iy],'-',color='g');\n", | |
"plt.quiver(r0[ix],r0[iy],F_all_s[ix],F_all_s[iy],color=(1,0,0,1),label='Applied Forces (N)');\n", | |
"plt.quiver(r0[ix],r0[iy],u_all_s[ix],u_all_s[iy],color=(0,0,1,1),label='Displacements (10x Scale)');\n", | |
"plt.title('Steel Truss (Unloaded vs Loaded)\\n')\n", | |
"plt.xlabel('Millimeters')\n", | |
"plt.ylabel('Millimeters')\n", | |
"plt.legend(bbox_to_anchor=(1.01, 1))\n", | |
"plt.text(3300,500,'Note: Forces are 100 N \\n central load and two\\n 50 N reaction forces\\n at truss ends.');" | |
] | |
}, | |
{ | |
"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": 405, | |
"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": [ | |
"#Part A:\n", | |
"j=100\n", | |
"max_deflect = np.zeros(j)\n", | |
"areas = np.linspace(.5,4,j)\n", | |
"for i in range(j):\n", | |
" A = areas[i] #mm^2\n", | |
" E_s = 200*10**3 #MPa, steel\n", | |
" F_s_free = np.zeros(11)\n", | |
" F_s_free[5] = -100\n", | |
" u_free = solveLU(L_K,U_K,F_s_free/A/E_s)\n", | |
" u_all_s = np.zeros(14)\n", | |
" u_all_s[2:13] = u_free\n", | |
" max_deflect[i] = max(abs(u_all_s))\n", | |
"\n", | |
" \n", | |
"plt.plot(areas,max_deflect);\n", | |
"plt.xlabel('Cross Sectional Area mm^2');\n", | |
"plt.ylabel('Max Deflection mm');\n", | |
"plt.title('Aluminum Truss Area vs Deflection');" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"From the above plot, we can see that truss deflection and cross sectional area are not linearly related. We can use a root finding function from previous lessons to find the minimum area for deflections less than 0.2 millimeters. This process is completed below." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 406, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"def mod_secant(func,dx,x0,es=0.0001,maxit=50):\n", | |
" '''mod_secant: Modified secant root location zeroes\n", | |
" root,[fx,ea,iter]=mod_secant(func,dfunc,xr,es,maxit,p1,p2,...):\n", | |
" uses modified secant method to find the root of func\n", | |
" arguments:\n", | |
" ----------\n", | |
" func = name of function\n", | |
" dx = perturbation fraction\n", | |
" xr = initial guess\n", | |
" es = desired relative error (default = 0.0001 )\n", | |
" maxit = maximum allowable iterations (default = 50)\n", | |
" p1,p2,... = additional parameters used by function\n", | |
" returns:\n", | |
" --------\n", | |
" root = real root\n", | |
" fx = func evaluated at root\n", | |
" ea = approximate relative error ( )\n", | |
" iter = number of iterations'''\n", | |
"\n", | |
" iter = 0;\n", | |
" xr=x0\n", | |
" for iter in range(0,maxit):\n", | |
" xrold = xr;\n", | |
" dfunc=(func(xr+dx)-func(xr))/dx;\n", | |
" xr = xr - func(xr)/dfunc;\n", | |
" if xr != 0:\n", | |
" ea = abs((xr - xrold)/xr) * 100;\n", | |
" else:\n", | |
" ea = abs((xr - xrold)/1) * 100;\n", | |
" if ea <= es:\n", | |
" break\n", | |
" return xr,[func(xr),ea,iter]" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 407, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"Minimum Area (aluminum) = 7.6785714 mm^2\n", | |
"Minimum Area (steel) = 2.6875014 mm^2\n" | |
] | |
} | |
], | |
"source": [ | |
"def max_deflect_alum(A):\n", | |
" deflection = 0.2\n", | |
" E_a = 70*10**3 #MPa\n", | |
" F_a_free = np.zeros(11)\n", | |
" F_a_free[5] = -100\n", | |
" u_free = solveLU(L_K,U_K,F_a_free/A/E_a)\n", | |
" u_all_a = np.zeros(14)\n", | |
" u_all_a[2:13] = u_free\n", | |
" max_deflect = max(abs(u_all_a))\n", | |
" return max_deflect - deflection\n", | |
"area_a, other_a = mod_secant(max_deflect_alum,.05,3,es=.01)\n", | |
"print('Minimum Area (aluminum) =',round(area_a,7),'mm^2')\n", | |
"\n", | |
"\n", | |
"#Part B\n", | |
"# We can repeat this root finding process for the steel truss\n", | |
"def max_deflect_steel(A):\n", | |
" deflection = 0.2\n", | |
" E_s = 200*10**3 #MPa\n", | |
" F_s_free = np.zeros(11)\n", | |
" F_s_free[5] = -100\n", | |
" u_free = solveLU(L_K,U_K,F_s_free/A/E_s)\n", | |
" u_all_s = np.zeros(14)\n", | |
" u_all_s[2:13] = u_free\n", | |
" max_deflect = max(abs(u_all_s))\n", | |
" return max_deflect - deflection\n", | |
"area_s, other_s = mod_secant(max_deflect_steel,.05,.1,es=.01)\n", | |
"print('Minimum Area (steel) =',round(area_s,7),'mm^2')" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 408, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"Part C:\n", | |
" The aluminum truss requires 0.2281 kg of aluminum\n", | |
"\n", | |
" The steel truss requires 0.23376 kg of mild steel\n", | |
"\n", | |
"Part D:\n", | |
" The aluminum truss requires 352.41 dollars\n", | |
"\n", | |
" The steel truss requires 111.27 dollars\n" | |
] | |
} | |
], | |
"source": [ | |
"#Part C calculations:\n", | |
"area_min_a = 7.68/1000/1000 #from above, in m^2\n", | |
"area_min_s = 2.69/1000/1000 #from above, in m^2\n", | |
"L = 1 #meter\n", | |
"density_a = 2700 #kg/m^3\n", | |
"density_s = 7900 #kg/m^3\n", | |
"V_a =11*L*area_min_a #m^3\n", | |
"V_s =11*L*area_min_s #m^3\n", | |
"mass_a = V_a*density_a #kg\n", | |
"mass_s = V_s*density_s #kg\n", | |
"print('Part C:')\n", | |
"print(' The aluminum truss requires',round(mass_a,5),'kg of aluminum\\n')\n", | |
"print(' The steel truss requires',round(mass_s,5),'kg of mild steel\\n')\n", | |
"\n", | |
"#Part D Calculations:\n", | |
"price_a = 1545 #$/1000 kg\n", | |
"price_s = 476 #$/1000 kg\n", | |
"total_cost_a = price_a*mass_a\n", | |
"total_cost_s = price_s*mass_s\n", | |
"print('Part D:')\n", | |
"print(' The aluminum truss requires',round(total_cost_a,2),'dollars\\n')\n", | |
"print(' The steel truss requires',round(total_cost_s,2),'dollars')" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"So it is significantly cheaper to create the truss out of steel." | |
] | |
}, | |
{ | |
"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": 409, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
}, | |
{ | |
"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": [ | |
"import pandas as pd\n", | |
"al_price = pd.read_csv('../data/al_price.csv')\n", | |
"st_price = pd.read_csv('../data/steel_price.csv')\n", | |
"al_price\n", | |
"st_price\n", | |
"al_prices = al_price['dollars/MT'].values\n", | |
"al_years = al_price['Year'].values\n", | |
"st_prices = st_price['dollars/MT'].values\n", | |
"st_years = st_price['Year'].values\n", | |
"plt.plot(al_price['Year'],al_price['dollars/MT'],linewidth=0,marker='o');\n", | |
"plt.title('Alumninum Price');\n", | |
"plt.show()\n", | |
"plt.plot(st_price['Year'],st_price['dollars/MT'],linewidth=0,marker='o');\n", | |
"plt.title('Steel Price');" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 410, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"#Part A:\n", | |
"import random\n", | |
"i_rand=random.sample(range(0,len(al_prices)),len(al_prices))\n", | |
"train_per=0.7\n", | |
"al_years_train=al_years[i_rand[:int(len(al_years)*train_per)]]\n", | |
"al_prices_train=al_prices[i_rand[:int(len(al_years)*train_per)]]\n", | |
"al_years_test=al_years[i_rand[int(len(al_years)*train_per):]]\n", | |
"al_prices_test=al_prices[i_rand[int(len(al_years)*train_per):]]\n", | |
"\n", | |
"i_rand2=random.sample(range(0,len(st_prices)),len(st_prices))\n", | |
"st_years_train=st_years[i_rand2[:int(len(st_years)*train_per)]]\n", | |
"st_prices_train=st_prices[i_rand2[:int(len(st_years)*train_per)]]\n", | |
"st_years_test=st_years[i_rand2[int(len(st_years)*train_per):]]\n", | |
"st_prices_test=st_prices[i_rand2[int(len(st_years)*train_per):]]" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 411, | |
"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" | |
}, | |
{ | |
"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 B and C:\n", | |
"Z_al=np.block([[al_years_train**0]]).T\n", | |
"Z_al_test=np.block([[al_years_test**0]]).T\n", | |
"\n", | |
"max_N=21\n", | |
"SSE_train_al =np.zeros(max_N)\n", | |
"SSE_test_al =np.zeros(max_N)\n", | |
"for i in range(1,max_N):\n", | |
" Z_al=np.hstack((Z_al,al_years_train.reshape(-1,1)**i))\n", | |
" Z_al_test=np.hstack((Z_al_test,al_years_test.reshape(-1,1)**i))\n", | |
" A_al = np.linalg.solve(Z_al.T@Z_al,Z_al.T@al_prices_train)\n", | |
" St_al=np.std(al_prices_train)\n", | |
" Sr_al=np.std(al_prices_train-Z_al@A_al)\n", | |
" r2_al=1-Sr_al/St_al\n", | |
"\n", | |
" #plt.plot(al_years_train,abs(al_prices_train-Z_al@A_al),label='Train, order {:d}'.format(i))\n", | |
" #plt.plot(al_years_test,abs(al_prices_test-Z_al_test@A_al),label='Test, order {:d}'.format(i))\n", | |
" SSE_train_al[i]=np.sum((al_prices_train-Z_al@A_al)**2)/len(al_prices_train)\n", | |
" SSE_test_al[i]=np.sum((al_prices_test-Z_al_test@A_al)**2)/len(al_prices_test)\n", | |
" \n", | |
"Z_st=np.block([[st_years_train**0]]).T\n", | |
"Z_st_test=np.block([[st_years_test**0]]).T\n", | |
"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_st=np.hstack((Z_st,st_years_train.reshape(-1,1)**i))\n", | |
" Z_st_test=np.hstack((Z_st_test,st_years_test.reshape(-1,1)**i))\n", | |
" A_st = np.linalg.solve(Z_st.T@Z_st,Z_st.T@st_prices_train)\n", | |
" St_st=np.std(st_prices_train)\n", | |
" Sr_st=np.std(st_prices_train-Z_st@A_st)\n", | |
" r2_st=1-Sr_st/St_st\n", | |
" SSE_train_st[i]=np.sum((st_prices_train-Z_st@A_st)**2)/len(st_prices_train)\n", | |
" SSE_test_st[i]=np.sum((st_prices_test-Z_st_test@A_st)**2)/len(st_prices_test)\n", | |
"plt.semilogy(np.arange(1,max_N),SSE_train_al[1:],label='Aluminum Testing Data',marker='o',linewidth=0)\n", | |
"plt.semilogy(np.arange(1,max_N),SSE_test_al[1:],label='Aluminum Training Data',marker='o',linewidth=0)\n", | |
"plt.xlabel('Fit Function Order')\n", | |
"plt.ylabel('SSE')\n", | |
"plt.legend(bbox_to_anchor=(1, .9));\n", | |
"plt.show()\n", | |
"plt.semilogy(np.arange(1,max_N),SSE_train_st[1:],label='Steel Testing Data',marker='o',linewidth=0)\n", | |
"plt.semilogy(np.arange(1,max_N),SSE_test_st[1:],label='Steel Training Data',marker='o',linewidth=0)\n", | |
"plt.xlabel('Fit Function Order')\n", | |
"plt.ylabel('SSE')\n", | |
"plt.legend(bbox_to_anchor=(1, .9));" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"__Part D:__ From the above plots, we can see for both aluminum and steel pricing models, the error reduction does not decrease further for regression function orders greater than 2. So for our final model, we will use a second order polynomial function. However, there is also a signicant change in the model in 2018. The price was increasing before that point but began decreasing after that point. To combat his, we will use a piecewise defined function split at this point. " | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 412, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"4th Order 2025 Price: -31959.68\n", | |
"\n", | |
"4th Order Piecewise 2025 Price: 19275.55\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", | |
"#aluminum function definition\n", | |
"Z_al_d=np.block([[al_years_train**4],[al_years_train**3],[al_years_train**2],[al_years_train**1],[al_years_train**0]]).T\n", | |
"Z_al_testd=np.block([[al_years_train**4],[al_years_train**3],[al_years_train**2],[al_years_train**1],[al_years_train**0]]).T\n", | |
"A_al_d1 = np.linalg.solve(Z_al_d.T@Z_al_d,Z_al_d.T@al_prices_train)\n", | |
"fcn_al1 = lambda year: A_al_d1[0]*year**4+A_al_d1[1]*year**3+A_al_d1[2]*year**2+A_al_d1[3]*year**1+A_al_d1[4]*year**0\n", | |
"#print(A_al_d)\n", | |
"\n", | |
"Z_al_d=np.block([[al_years_train**4],[al_years_train**3],[al_years_train**2],[al_years_train**1],[al_years_train**0],\\\n", | |
" [(al_years_train>=2018)*al_years_train**4],[(al_years_train>=2018)*al_years_train**3],[(al_years_train>=2018)*al_years_train**2]\\\n", | |
" ,[(al_years_train>=2018)*al_years_train**1],[(al_years_train>=2018)*al_years_train**0]]).T\n", | |
"Z_al_testd=np.block([[al_years_train**4],[al_years_train**3],[al_years_train**2],[al_years_train**1],[al_years_train**0]]).T\n", | |
"A_al_d2 = np.linalg.solve(Z_al_d.T@Z_al_d,Z_al_d.T@al_prices_train)\n", | |
"fcn_al2 = lambda year: A_al_d2[0]*year**4+A_al_d2[1]*year**3+A_al_d2[2]*year**2+A_al_d2[3]*year**1+A_al_d2[4]*year**0\\\n", | |
" +(year>=2018)*A_al_d2[5]*year**4+(year>=2018)*A_al_d2[6]*year**3+(year>=2018)*A_al_d2[7]*year**2\\\n", | |
" +(year>=2018)*A_al_d2[8]*year**1+(year>=2018)*A_al_d2[9]*year**0\n", | |
"\n", | |
"years_plt = np.linspace(2016,2025,100)\n", | |
"plt.plot(al_price['Year'],al_price['dollars/MT'],linewidth=0,marker='o',label='Aluminum Data');\n", | |
"plt.plot(years_plt,fcn_al1(years_plt),label='4th Order')\n", | |
"plt.plot(years_plt,fcn_al2(years_plt),label='4th Order Piecewise')\n", | |
"plt.title('Alumninum Price');\n", | |
"plt.xlabel('Year');\n", | |
"plt.ylabel('Dollars/metric ton');\n", | |
"plt.legend();\n", | |
"\n", | |
"print('4th Order 2025 Price:',round(fcn_al1(2025),2))\n", | |
"print()\n", | |
"print('4th Order Piecewise 2025 Price:',round(fcn_al2(2025),2))" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"The basic fourth order model is not suffient to match the aluminum data as seen in the above plot, since it predicts a negative value for the year 2025. By using a piecewise function the model predicts a price of 6876 dollars per metric ton. This is not unreasonable, it is not much higher than the value at the peak in 2018." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 413, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"4th Order 2025 Price: 49.36 dollars/metric ton\n", | |
"\n", | |
"4th Order Piecewise 2025 Price: 349.79 dollars/metric ton\n" | |
] | |
}, | |
{ | |
"data": { | |
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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"#steel function definition\n", | |
"Z_st_d=np.block([[st_years_train**4],[st_years_train**3],[st_years_train**2],[st_years_train**1],[st_years_train**0]]).T\n", | |
"Z_st_testd=np.block([[st_years_train**4],[st_years_train**3],[st_years_train**2],[st_years_train**1],[st_years_train**0]]).T\n", | |
"A_st_d1 = np.linalg.solve(Z_st_d.T@Z_st_d,Z_st_d.T@st_prices_train)\n", | |
"fcn_st1 = lambda year: A_st_d1[0]*year**4+A_st_d1[1]*year**3+A_st_d1[2]*year**2+A_st_d1[3]*year**1+A_st_d1[4]*year**0\n", | |
"\n", | |
"\n", | |
"Z_st_d=np.block([[st_years_train**4],[st_years_train**3],[st_years_train**2],[st_years_train**1],[st_years_train**0],\\\n", | |
" [(st_years_train>=2018)*st_years_train**4],[(st_years_train>=2018)*st_years_train**3],\\\n", | |
" [(st_years_train>=2018)*st_years_train**2]\\\n", | |
" ,[(st_years_train>=2018)*st_years_train**1],[(st_years_train>=2018)*st_years_train**0]]).T\n", | |
"#Z_st_testd=np.block([[st_years_train**4],[st_years_train**3],[st_years_train**2],[st_years_train**1],[st_years_train**0]]).T\n", | |
"A_st_d2 = np.linalg.solve(Z_st_d.T@Z_st_d,Z_st_d.T@st_prices_train)\n", | |
"fcn_st2 = lambda year: A_st_d2[0]*year**4+A_st_d2[1]*year**3+A_st_d2[2]*year**2+A_st_d2[3]*year**1+A_st_d2[4]*year**0\\\n", | |
" +(year>=2018)*A_st_d2[5]*year**4+(year>=2018)*A_st_d2[6]*year**3+(year>=2018)*A_st_d2[7]*year**2\\\n", | |
" +(year>=2018)*A_st_d2[8]*year**1+(year>=2018)*A_st_d2[9]*year**0\n", | |
"\n", | |
"\n", | |
"years_plt = np.linspace(2015,2025,100)\n", | |
"plt.plot(st_price['Year'],st_price['dollars/MT'],linewidth=0,marker='o',label='Steel Data');\n", | |
"plt.plot(years_plt,fcn_st1(years_plt),label='4th Order')\n", | |
"plt.plot(years_plt,fcn_st2(years_plt),label='4th Order Piecewise')\n", | |
"plt.title('Steel Price');\n", | |
"plt.xlabel('Year');\n", | |
"plt.ylabel('Dollars/metric ton');\n", | |
"plt.legend();\n", | |
"\n", | |
"print('4th Order 2025 Price:',round(fcn_st1(2025),2),'dollars/metric ton')\n", | |
"print()\n", | |
"print('4th Order Piecewise 2025 Price:',round(fcn_st2(2025),2),'dollars/metric ton')\n" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Two models for the price of steel are shown above. The fourth order model suggests a downward trend in price, with a prediced price in 2025 of 78 dollars per ton. The second model splits the data in 2018, and predicts a price of 350 dollars per ton in 2025. Neither model seems particularly accurate." | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"For a final suggestion, I would recommend continuing with using steel for creation of the truss. While neither the price models for steel nor aluminum are particularly trustworthy, the price of steel seems less violatile in the past 5 years when compared to aluminum. Furthermore the aluminum truss costs significantly more than the steel price with current prices. To make a more informed decision on the future price of steel and aluminum, I would recommend finding datasets that cover a larger period of time to reduce the impact or temporary spikes in prices on the extrapolated value for 2025 price." | |
] | |
}, | |
{ | |
"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 | |
} |