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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": "code",
"execution_count": 438,
"metadata": {},
"outputs": [],
"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"
]
},
{
"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": 439,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"fea_arrays = np.load('./fea_arrays.npz')\n",
"K=fea_arrays['K']\n",
"\n",
"l=300 # mm\n",
"nodes = np.array([[1,0,0],[2,0.5,3**0.5/2],[3,1,0],[4,1.5,3**0.5/2],[5,2,0],[6,2.5,3**0.5/2],[7,3,0]])\n",
"nodes[:,1:3]*=l\n",
"elems = np.array([[1,1,2],[2,2,3],[3,1,3],[4,2,4],[5,3,4],[6,3,5],[7,4,5],[8,4,6],[9,5,6],[10,5,7],[11,6,7]])"
]
},
{
"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": "markdown",
"metadata": {},
"source": [
"Problem 1 Part A"
]
},
{
"cell_type": "code",
"execution_count": 440,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The condition of the K matrix is 1.4578e+17\n",
"Machine epsilon for floating point number storage in python is 2.220446049250313e-16\n"
]
}
],
"source": [
"cond_K = np.linalg.cond(K)\n",
"print('The condition of the K matrix is {:.4e}'.format(cond_K))\n",
"print('Machine epsilon for floating point number storage in python is', np.finfo(float).eps)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Considering the above information, __we would expect to have an error of 10^(17-16)__ (where error = 10 ^ (c-t) with c being the magnitude of the condition and t being the measurement error)).\n",
"\n",
"__Or more succinctly: 10.__"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Problem 1 Part B"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The condition of K is so large due to how small he variations are in each of the values. Since we are dealing with te deformation of strong materials (which for this application is very small) the matrix K ends up containing very small values. As such, the intersection of the hyperplanes representing the solution to the system may seemingly consist of many solutions and thus, we have a high condition for the matrix."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Problem 1 Part C"
]
},
{
"cell_type": "code",
"execution_count": 543,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The condition of the K[2:13,2:13] matrix is 5.2235e+01\n"
]
}
],
"source": [
"cond_K_prime = np.linalg.cond(K[2:13,2:13])\n",
"print('The condition of the K[2:13,2:13] matrix is {:.4e}'.format(cond_K_prime))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Using the same equation and considerations as in part A above, __we obtain an error of:__\n",
" \n",
"__10^(-15)__\n",
"\n",
"For our new K matrix which spans K[2:13,2:13]."
]
},
{
"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": "markdown",
"metadata": {},
"source": [
"Problem 2 Part A"
]
},
{
"cell_type": "code",
"execution_count": 442,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The LU factorization for the K[2:13,2:13] matrix is:\n",
"L: [[\t1.00000e+00 \t0.00000e+00 \t0.00000e+00 \t0.00000e+00 \t0.00000e+00\n",
" \t0.00000e+00 \t0.00000e+00 \t0.00000e+00 \t0.00000e+00 \t0.00000e+00\n",
" \t0.00000e+00]\n",
" [\t0.00000e+00 \t1.00000e+00 \t0.00000e+00 \t0.00000e+00 \t0.00000e+00\n",
" \t0.00000e+00 \t0.00000e+00 \t0.00000e+00 \t0.00000e+00 \t0.00000e+00\n",
" \t0.00000e+00]\n",
" [\t-1.66667e-01 \t2.88675e-01 \t1.00000e+00 \t0.00000e+00 \t0.00000e+00\n",
" \t0.00000e+00 \t0.00000e+00 \t0.00000e+00 \t0.00000e+00 \t0.00000e+00\n",
" \t0.00000e+00]\n",
" [\t2.88675e-01 \t-5.00000e-01 \t1.23718e-01 \t1.00000e+00 \t0.00000e+00\n",
" \t0.00000e+00 \t0.00000e+00 \t0.00000e+00 \t0.00000e+00 \t0.00000e+00\n",
" \t0.00000e+00]\n",
" [\t-6.66667e-01 \t0.00000e+00 \t-1.78571e-01 \t-9.62250e-02 \t1.00000e+00\n",
" \t0.00000e+00 \t0.00000e+00 \t0.00000e+00 \t0.00000e+00 \t0.00000e+00\n",
" \t0.00000e+00]\n",
" [\t0.00000e+00 \t0.00000e+00 \t-1.85577e-01 \t-7.22222e-01 \t-8.24786e-02\n",
" \t1.00000e+00 \t0.00000e+00 \t0.00000e+00 \t0.00000e+00 \t0.00000e+00\n",
" \t0.00000e+00]\n",
" [\t0.00000e+00 \t0.00000e+00 \t-4.28571e-01 \t1.28300e-01 \t-2.38095e-01\n",
" \t3.34255e-01 \t1.00000e+00 \t0.00000e+00 \t0.00000e+00 \t0.00000e+00\n",
" \t0.00000e+00]\n",
" [\t0.00000e+00 \t0.00000e+00 \t0.00000e+00 \t0.00000e+00 \t2.47436e-01\n",
" \t-7.89474e-01 \t1.84261e-01 \t1.00000e+00 \t0.00000e+00 \t0.00000e+00\n",
" \t0.00000e+00]\n",
" [\t0.00000e+00 \t0.00000e+00 \t0.00000e+00 \t0.00000e+00 \t-5.71429e-01\n",
" \t-9.11606e-02 \t-2.48227e-01 \t-2.16506e-01 \t1.00000e+00 \t0.00000e+00\n",
" \t0.00000e+00]\n",
" [\t0.00000e+00 \t0.00000e+00 \t0.00000e+00 \t0.00000e+00 \t0.00000e+00\n",
" \t0.00000e+00 \t-2.33397e-01 \t-8.75000e-01 \t-3.27685e-01 \t1.00000e+00\n",
" \t0.00000e+00]\n",
" [\t0.00000e+00 \t0.00000e+00 \t0.00000e+00 \t0.00000e+00 \t0.00000e+00\n",
" \t0.00000e+00 \t-5.39007e-01 \t2.40563e-01 \t-5.94595e-01 \t2.88675e-01\n",
" \t1.00000e+00]]\n",
"U: [[\t5.00000e-03 \t0.00000e+00 \t-8.33333e-04 \t1.44338e-03 \t-3.33333e-03\n",
" \t0.00000e+00 \t0.00000e+00 \t0.00000e+00 \t0.00000e+00 \t0.00000e+00\n",
" \t0.00000e+00]\n",
" [\t0.00000e+00 \t5.00000e-03 \t1.44338e-03 \t-2.50000e-03 \t0.00000e+00\n",
" \t0.00000e+00 \t0.00000e+00 \t0.00000e+00 \t0.00000e+00 \t0.00000e+00\n",
" \t0.00000e+00]\n",
" [\t0.00000e+00 \t0.00000e+00 \t7.77778e-03 \t9.62250e-04 \t-1.38889e-03\n",
" \t-1.44338e-03 \t-3.33333e-03 \t0.00000e+00 \t0.00000e+00 \t0.00000e+00\n",
" \t0.00000e+00]\n",
" [\t-2.16840e-19 \t0.00000e+00 \t0.00000e+00 \t3.21429e-03 \t-3.09295e-04\n",
" \t-2.32143e-03 \t4.12393e-04 \t0.00000e+00 \t0.00000e+00 \t0.00000e+00\n",
" \t0.00000e+00]\n",
" [\t-2.08655e-20 \t0.00000e+00 \t0.00000e+00 \t0.00000e+00 \t5.83333e-03\n",
" \t-4.81125e-04 \t-1.38889e-03 \t1.44338e-03 \t-3.33333e-03 \t0.00000e+00\n",
" \t0.00000e+00]\n",
" [\t-1.58328e-19 \t0.00000e+00 \t0.00000e+00 \t0.00000e+00 \t0.00000e+00\n",
" \t3.01587e-03 \t1.00807e-03 \t-2.38095e-03 \t-2.74929e-04 \t0.00000e+00\n",
" \t0.00000e+00]\n",
" [\t7.57746e-20 \t0.00000e+00 \t0.00000e+00 \t0.00000e+00 \t0.00000e+00\n",
" \t0.00000e+00 \t6.18421e-03 \t1.13951e-03 \t-1.53509e-03 \t-1.44338e-03\n",
" \t-3.33333e-03]\n",
" [\t-1.33795e-19 \t0.00000e+00 \t0.00000e+00 \t0.00000e+00 \t0.00000e+00\n",
" \t0.00000e+00 \t0.00000e+00 \t2.55319e-03 \t-5.52782e-04 \t-2.23404e-03\n",
" \t6.14202e-04]\n",
" [\t-3.65146e-20 \t0.00000e+00 \t0.00000e+00 \t0.00000e+00 \t0.00000e+00\n",
" \t0.00000e+00 \t0.00000e+00 \t0.00000e+00 \t2.56944e-03 \t-8.41969e-04\n",
" \t-1.52778e-03]\n",
" [\t-1.11350e-19 \t0.00000e+00 \t0.00000e+00 \t0.00000e+00 \t0.00000e+00\n",
" \t0.00000e+00 \t0.00000e+00 \t0.00000e+00 \t0.00000e+00 \t2.43243e-03\n",
" \t7.02183e-04]\n",
" [\t8.34619e-20 \t0.00000e+00 \t0.00000e+00 \t0.00000e+00 \t0.00000e+00\n",
" \t0.00000e+00 \t-4.33681e-19 \t0.00000e+00 \t0.00000e+00 \t-1.08420e-19\n",
" \t1.11111e-03]]\n"
]
}
],
"source": [
"#First importing a function to decompose the K matrix into an LU factorization\n",
"np.set_printoptions(formatter={'float': \"\\t{:.5e}\".format})\n",
"def LUNaive(A):\n",
" '''LUNaive: naive LU decomposition\n",
" L,U = LUNaive(A): LU decomposition without pivoting.\n",
" solution method requires floating point numbers, \n",
" as such the dtype is changed to float\n",
" \n",
" Arguments:\n",
" ----------\n",
" A = coefficient matrix\n",
" returns:\n",
" ---------\n",
" L = Lower triangular matrix\n",
" U = Upper triangular matrix\n",
" '''\n",
" [m,n] = np.shape(A)\n",
" if m!=n: error('Matrix A must be square')\n",
" nb = n+1\n",
" # Gauss Elimination\n",
" U = A.astype(float)\n",
" L = np.eye(n)\n",
"\n",
" for k in range(0,n-1):\n",
" for i in range(k+1,n):\n",
" if U[k,k] != 0.0:\n",
" factor = U[i,k]/U[k,k]\n",
" L[i,k]=factor\n",
" U[i,:] = U[i,:] - factor*U[k,:]\n",
" return L,U\n",
"\n",
"L_Kprime, U_Kprime = LUNaive(K[2:13,2:13])\n",
"print('The LU factorization for the K[2:13,2:13] matrix is:')\n",
"print('L: {}\\nU: {}'.format(L_Kprime, U_Kprime))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Problem 2 Part B"
]
},
{
"cell_type": "code",
"execution_count": 443,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The solution matrix u for steel is:\n",
"[\t1.94856e+00 \t-2.12500e+00 \t4.33013e-01 \t-4.00000e+00 \t1.08253e+00\n",
" \t-5.37500e+00 \t1.73205e+00 \t-4.00000e+00 \t2.16506e-01 \t-2.12500e+00\n",
" \t2.16506e+00]\n",
"The solution matrix u for aluminum is:\n",
"[\t5.56731e+00 \t-6.07143e+00 \t1.23718e+00 \t-1.14286e+01 \t3.09295e+00\n",
" \t-1.53571e+01 \t4.94872e+00 \t-1.14286e+01 \t6.18590e-01 \t-6.07143e+00\n",
" \t6.18590e+00]\n"
]
}
],
"source": [
"#Setting Constants\n",
"A_x = 0.1 #mm^2\n",
"E_steel = 200000 #MPa\n",
"E_alum = 70000 #MPa\n",
"#Creating Force Matrix\n",
"F = np.zeros(11)\n",
"F[5] = -100 #N\n",
"F_div_ea_steel = F*(1/(E_steel*A_x))\n",
"F_div_ea_alum = F*(1/(E_alum*A_x))\n",
"#Importing an LU solver that we predefined from notebook 2:\n",
"def solveLU(L,U,b):\n",
" '''solveLU: solve for x when LUx = b\n",
" x = solveLU(L,U,b): solves for x given the lower and upper \n",
" triangular matrix storage\n",
" uses forward substitution for \n",
" 1. Ly = b\n",
" then backward substitution for\n",
" 2. Ux = y\n",
" \n",
" Arguments:\n",
" ----------\n",
" L = Lower triangular matrix\n",
" U = Upper triangular matrix\n",
" b = output vector\n",
" \n",
" returns:\n",
" ---------\n",
" x = solution of LUx=b '''\n",
" n=len(b)\n",
" x=np.zeros(n)\n",
" y=np.zeros(n)\n",
" \n",
" # forward substitution\n",
" for k in range(0,n):\n",
" y[k] = b[k] - L[k,0:k]@y[0:k]\n",
" # backward substitution\n",
" for k in range(n-1,-1,-1):\n",
" x[k] = (y[k] - U[k,k+1:n]@x[k+1:n])/U[k,k]\n",
" return x\n",
"u_p2steel = solveLU(L_Kprime, U_Kprime, F_div_ea_steel)\n",
"u_p2alum = solveLU(L_Kprime, U_Kprime, F_div_ea_alum)\n",
"#printing resulting u matrices\n",
"print('The solution matrix u for steel is:')\n",
"print(u_p2steel)\n",
"print('The solution matrix u for aluminum is:')\n",
"print(u_p2alum)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Problem 2 Part C"
]
},
{
"cell_type": "code",
"execution_count": 444,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Plugging into the full equation, we get the following resultant forces for the Steel configuration:\n",
"\n",
"STEEL:\n",
"F_1x:-0.00 N\n",
"\n",
"F_1y:50.00 N\n",
"\n",
"F_2x:0.00 N\n",
"\n",
"F_2y:-0.00 N\n",
"\n",
"F_3x:-0.00 N\n",
"\n",
"F_3y:0.00 N\n",
"\n",
"F_4x:0.00 N\n",
"\n",
"F_4y:-100.00 N\n",
"\n",
"F_5x:-0.00 N\n",
"\n",
"F_5y:0.00 N\n",
"\n",
"F_6x:0.00 N\n",
"\n",
"F_6y:0.00 N\n",
"\n",
"F_7x:0.00 N\n",
"\n",
"F_7y:50.00 N\n",
"\n",
"Plugging into the full equation, we get the following resultant forces for the Aluminum configuration:\n",
"\n",
"ALUMINUM:\n",
"F_1x:-0.00 N\n",
"\n",
"F_1y:50.00 N\n",
"\n",
"F_2x:-0.00 N\n",
"\n",
"F_2y:-0.00 N\n",
"\n",
"F_3x:-0.00 N\n",
"\n",
"F_3y:0.00 N\n",
"\n",
"F_4x:0.00 N\n",
"\n",
"F_4y:-100.00 N\n",
"\n",
"F_5x:-0.00 N\n",
"\n",
"F_5y:0.00 N\n",
"\n",
"F_6x:0.00 N\n",
"\n",
"F_6y:-0.00 N\n",
"\n",
"F_7x:0.00 N\n",
"\n",
"F_7y:50.00 N\n",
"\n"
]
}
],
"source": [
"#First we must substitute in the unrestrained isplacements in for u_steel and u_aluminum respectively by observing\n",
"#that theconstraints cause the displacements to be zero\n",
"u_steel_full = np.zeros(14)\n",
"u_alum_full = np.zeros(14)\n",
"u_steel_full[2:13] = u_p2steel\n",
"u_alum_full[2:13] = u_p2alum\n",
"\n",
"F_steel = E_steel*A_x*K@u_steel_full\n",
"F_alum = E_alum*A_x*K@u_alum_full\n",
"\n",
"xy={0:'x',1:'y'}\n",
"print('Plugging into the full equation, we get the following resultant forces for the Steel configuration:')\n",
"print()\n",
"print('STEEL:')\n",
"for i in range(len(F_steel)):\n",
" print('F_{}{}:{:.2f} N\\n'.format(int(i/2)+1,xy[i%2],F_steel[i]))\n",
"print('Plugging into the full equation, we get the following resultant forces for the Aluminum configuration:')\n",
"print()\n",
"print('ALUMINUM:')\n",
"for i in range(len(F_alum)):\n",
" print('F_{}{}:{:.2f} N\\n'.format(int(i/2)+1,xy[i%2],F_alum[i]))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"From the above output we can recognize that, as expected, the reaction forces for both materials are the same."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Problem 2 Part D"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In order to construct this plot from the data that I have obtained above, I will import and use much of the plotting format from the given reference source. "
]
},
{
"cell_type": "code",
"execution_count": 445,
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "930a4741c4d144ada9f7ce2f2a324286",
"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"
}
],
"source": [
"from __future__ import print_function\n",
"from ipywidgets import interact, interactive, fixed, interact_manual\n",
"import ipywidgets as widgets\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",
"\n",
"def f_alum(s):\n",
" '''This function allows for user interaction to alter the scaling factor on the aluminum deformation such that it is\n",
" more/less visible as compared to the rest of the data exhibited on the graph.\n",
" Arguments: s - scaling factor for dsplacement\n",
" Output: plot with the corresponding scaling factor'''\n",
" \n",
" plt.plot(r[ix],r[iy],'-',color=(0,0,0,1))\n",
" plt.plot(r[ix]+u_alum_full[ix]*s,r[iy]+u_alum_full[iy]*s,'-',color=(1,0,0,1))\n",
" plt.quiver(r[ix],r[iy],F_alum[ix],F_alum[iy],color=(1,0,0,1),label='applied forces')\n",
" plt.quiver(r[ix],r[iy],u_alum_full[ix],u_alum_full[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('Aluminum Configuration\\nDeformation scale = {:.1f}x'.format(s))\n",
" plt.legend(bbox_to_anchor=(1,0.5))\n",
" \n",
"interact(f_alum,s=(0,10,1));"
]
},
{
"cell_type": "code",
"execution_count": 446,
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "5c351130d4dc498aa8ac0d9e598c860d",
"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"
}
],
"source": [
"def f_steel(s):\n",
" '''This function allows for user interaction to alter the scaling factor on the steel deformation such that it is\n",
" more/less visible as compared to the rest of the data exhibited on the graph.\n",
" Arguments: s - scaling factor for dsplacement\n",
" Output: plot with the corresponding scaling factor'''\n",
" \n",
" plt.plot(r[ix],r[iy],'-',color=(0,0,0,1))\n",
" plt.plot(r[ix]+u_steel_full[ix]*s,r[iy]+u_steel_full[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_full[ix],u_steel_full[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('Steel Configuration\\nDeformation scale = {:.1f}x'.format(s))\n",
" plt.legend(bbox_to_anchor=(1,0.5))\n",
" \n",
"interact(f_steel,s=(0,10,1));"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"From the results above, we see that with the same magnitude force applied in the same location to both structures, the aluminum configuration has much more deformation than the steel configuration. Intuitively, this makes sense since we know steel to be a stronger, less flexible material which is why it is used in many rugged applications such as in the building of bridges and buildings. "
]
},
{
"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": "markdown",
"metadata": {},
"source": [
"Problem 3 Part A"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We will approach this problem recursively in order to minimize the cross section required. To limit the number of times that we iterate over, we will solve for the minimum cross section up to 0.001mm."
]
},
{
"cell_type": "code",
"execution_count": 447,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The minimum area to keep total deflections in aluminum under this 0.2mm limit is 7.6790 mm.\n"
]
}
],
"source": [
"max_y = 100 #initial condition well satisfied for loop. \n",
"new_area = 0.1;\n",
"while (max_y>0.2):\n",
" new_area = new_area + 0.001\n",
" F_new_aluminum = F*(1/(E_alum*new_area))\n",
" u_int_alum = solveLU(L_Kprime, U_Kprime, F_new_aluminum)\n",
" #Since the rest of the deflections are zero due to the initial conditions, we need only check these indices\n",
" max_y = max(abs(u_int_alum))\n",
"alum_min = new_area \n",
"print('The minimum area to keep total deflections in aluminum under this 0.2mm limit is {:.4f} mm.'.format(alum_min)) "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Problem 3 Part B"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The same approach as before will be taken for steel. We expect the required minimum cross sectional area to be much smaller for steel than aluminum since its value for the modulus of elasticity is so much greater."
]
},
{
"cell_type": "code",
"execution_count": 448,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The minimum area to keep total deflections in steel under this 0.2mm limit is 2.6880 mm.\n"
]
}
],
"source": [
"max_y1 = 100 #initial condition well satisfied for loop. \n",
"new_area1 = 0.1;\n",
"while (max_y1>0.2):\n",
" new_area1 = new_area1 + 0.001\n",
" F_new_steel = F*(1/(E_steel*new_area1))\n",
" u_int_steel = solveLU(L_Kprime, U_Kprime, F_new_steel)\n",
" #Since the rest of the deflections are zero due to the initial conditions, we need only check these indices\n",
" max_y1 = max(abs(u_int_steel))\n",
"steel_min = new_area1 \n",
"print('The minimum area to keep total deflections in steel under this 0.2mm limit is {:.4f} mm.'.format(steel_min)) "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Problem 3 Part C"
]
},
{
"cell_type": "code",
"execution_count": 449,
"metadata": {},
"outputs": [],
"source": [
"number_of_rods = 11\n",
"rod_length = 300 #mm\n",
"Total_rod_length = (number_of_rods*rod_length)/1000 #in m\n",
"steel_x_section = steel_min/1000 #in m^2\n",
"alum_x_section = alum_min/1000 #in m^2 \n",
"density_alum = 2700 #kg/m^3\n",
"density_steel = 8000 #kg/m^3\n",
"weight_aluminum = density_alum*alum_x_section*Total_rod_length\n",
"weight_steel = density_steel*steel_x_section*Total_rod_length"
]
},
{
"cell_type": "code",
"execution_count": 450,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The weight of steel required for the solved cross sectional area is 70.96320 kg.\n",
"\n",
"The weight of aluminum required for the solved cross sectional area is 68.41989 kg\n"
]
}
],
"source": [
"print('The weight of steel required for the solved cross sectional area is {:.5f} kg.'.format(weight_steel))\n",
"print()\n",
"print('The weight of aluminum required for the solved cross sectional area is {:.5f} kg'.format(weight_aluminum))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Problem 3 Part D"
]
},
{
"cell_type": "code",
"execution_count": 451,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The cost to build the aluminum truss is about 105.71 US dollars.\n",
"\n",
"The cost to build the steel truss is about 33.78 US dollars.\n"
]
}
],
"source": [
"price_alum = 1545 # USD/tonne\n",
"price_steel = 476 # USD/tonne\n",
"\n",
"cost_alum_truss = price_alum*weight_aluminum*(1/1000) #in USD\n",
"cost_steel_truss = price_steel*weight_steel*(1/1000) #in USD\n",
"\n",
"print('The cost to build the aluminum truss is about {:.2f} US dollars.'.format(cost_alum_truss))\n",
"print()\n",
"print('The cost to build the steel truss is about {:.2f} US dollars.'.format(cost_steel_truss))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As we can see from the output above, it is __much cheaper to build the steel truss__ as compared to the aluminum one. "
]
},
{
"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": 452,
"metadata": {},
"outputs": [],
"source": [
"#importing and organizing the available data\n",
"steel=np.loadtxt('../data/steel_price.csv',skiprows=1,delimiter=',')\n",
"al = np.loadtxt('../data/al_price.csv',skiprows=1,delimiter=',')\n",
"steel_year = steel[:,0]\n",
"steel_price = steel[:,1]\n",
"aluminum_year = al[:,0]\n",
"aluminum_price = al[:,1]\n",
"#normalizing years such that we do not have such large error for higher order fits\n",
"steel_year_normalized = (steel_year-steel_year.min())/(steel_year.max()-steel_year.min())\n",
"aluminum_year_normalized = (aluminum_year-aluminum_year.min())/(aluminum_year.max()-aluminum_year.min())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Problem 4 Part A"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Separating for steel:"
]
},
{
"cell_type": "code",
"execution_count": 463,
"metadata": {},
"outputs": [],
"source": [
"# randomizing testing/training indices\n",
"import random\n",
"i_rand= random.sample(range(0,len(steel_year)),len(steel_year))\n",
"# choosing the first portion of data as training\n",
"train_per=0.7\n",
"steel_time_train= steel_year_normalized[i_rand[:int(len(steel_year)*train_per)]]\n",
"steel_price_train= steel_price[i_rand[:int(len(steel_year)*train_per)]]\n",
"\n",
"steel_tr_un_normalized = steel_time_train*(steel_year.max()-steel_year.min())+steel_year.min()\n",
"\n",
"# choosing the second portion of data as testing\n",
"steel_time_test=steel_year_normalized[i_rand[int(len(steel_year)*train_per):]]\n",
"steel_price_test=steel_price[i_rand[int(len(steel_year)*train_per):]]\n",
"\n",
"steel_te_un_normalized = steel_time_test*(steel_year.max()-steel_year.min())+steel_year.min()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Separating for aluminum:"
]
},
{
"cell_type": "code",
"execution_count": 464,
"metadata": {},
"outputs": [],
"source": [
"# randomizing testing/training indices\n",
"import random\n",
"i_rand= random.sample(range(0,len(aluminum_year)),len(aluminum_year))\n",
"# choosing the first portion of data as training\n",
"train_per=0.7\n",
"aluminum_time_train=aluminum_year_normalized[i_rand[:int(len(aluminum_year)*train_per)]]\n",
"aluminum_price_train=aluminum_price[i_rand[:int(len(aluminum_year)*train_per)]]\n",
"\n",
"aluminum_tr_un_normalized = aluminum_time_train*(aluminum_year.max()-aluminum_year.min())+aluminum_year.min()\n",
"# choosing the second portion of data as testing\n",
"aluminum_time_test=aluminum_year_normalized[i_rand[int(len(aluminum_year)*train_per):]]\n",
"aluminum_price_test=aluminum_price[i_rand[int(len(aluminum_year)*train_per):]]\n",
"\n",
"aluminum_te_un_normalized = aluminum_time_test*(aluminum_year.max()-aluminum_year.min())+aluminum_year.min()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Problem 4 Part B"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To be rigorous, I will choose a polynimial order of 16 to be the largest polynomial fit, n. Despite this, I do not expect to use such a high order because this will most likely result in a solution that overfits the data set. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First completing the fits for steel:"
]
},
{
"cell_type": "code",
"execution_count": 465,
"metadata": {},
"outputs": [],
"source": [
"Z_steel_train=np.block([[steel_time_train**0]]).T\n",
"Z_steel_test=np.block([[steel_time_test**0]]).T\n",
"#np.append(Z,np.array([t**i]),axis=0)\n",
"max_N=17\n",
"SSE_steel_train=np.zeros(max_N)\n",
"SSE_steel_test=np.zeros(max_N)\n",
"for i in range(1,max_N):\n",
" Z_steel_train=np.hstack((Z_steel_train,steel_time_train.reshape(-1,1)**i))\n",
" Z_steel_test=np.hstack((Z_steel_test,steel_time_test.reshape(-1,1)**i))\n",
" ans = np.linalg.solve(Z_steel_train.T@Z_steel_train,Z_steel_train.T@steel_price_train)\n",
" SSE_steel_train[i]=np.sum((steel_price_train-Z_steel_train@ans)**2)/len(steel_price_train)\n",
" SSE_steel_test[i]=np.sum((steel_price_test-Z_steel_test@ans)**2)/len(steel_price_test)\n",
" \n",
"#For ease of analysis later on I have also calculated the sum of squares error for each polynomial fit for the test and train\n",
"#data sets."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now for aluminum:"
]
},
{
"cell_type": "code",
"execution_count": 466,
"metadata": {},
"outputs": [],
"source": [
"Z_aluminum_train=np.block([[aluminum_time_train**0]]).T\n",
"Z_aluminum_test=np.block([[aluminum_time_test**0]]).T\n",
"#np.append(Z,np.array([t**i]),axis=0)\n",
"max_N=17\n",
"SSE_aluminum_train=np.zeros(max_N)\n",
"SSE_aluminum_test=np.zeros(max_N)\n",
"for i in range(1,max_N):\n",
" Z_aluminum_train=np.hstack((Z_aluminum_train,aluminum_time_train.reshape(-1,1)**i))\n",
" Z_aluminum_test=np.hstack((Z_aluminum_test,aluminum_time_test.reshape(-1,1)**i))\n",
" ans2 = np.linalg.solve(Z_aluminum_train.T@Z_aluminum_train,Z_aluminum_train.T@aluminum_price_train)\n",
" SSE_aluminum_train[i]=np.sum((aluminum_price_train-Z_aluminum_train@ans2)**2)/len(aluminum_price_train)\n",
" SSE_aluminum_test[i]=np.sum((aluminum_price_test-Z_aluminum_test@ans2)**2)/len(aluminum_price_test)\n",
" \n",
"#For ease of analysis later on I have also calculated the sum of squares error for each polynomial fit for the test and train\n",
"#data sets."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Problem 4 Part C"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Steel:"
]
},
{
"cell_type": "code",
"execution_count": 467,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize = ((10,6)))\n",
"plt.semilogy(np.arange(1,max_N),SSE_steel_train[1:],label='Training Error')\n",
"plt.semilogy(np.arange(1,max_N),SSE_steel_test[1:],label='Testing Error')\n",
"plt.xlabel('Order')\n",
"plt.ylabel('Sum-of-Squares Error')\n",
"plt.legend();\n",
"plt.title('Error for Each Steel grouping as a Function of Order');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Aluminum:"
]
},
{
"cell_type": "code",
"execution_count": 468,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize = ((10,6)))\n",
"plt.semilogy(np.arange(1,max_N),SSE_aluminum_train[1:],label='Training Error')\n",
"plt.semilogy(np.arange(1,max_N),SSE_aluminum_test[1:],label='Testing Error')\n",
"plt.xlabel('Order')\n",
"plt.ylabel('Sum-of-Squares Error')\n",
"plt.legend();\n",
"plt.title('Error for Each Aluminum grouping as a Function of Order');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Problem 4 Part D"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As we have previously mentioned, we do not want to overfit the data. Thus, even though we observe progressively smaller sum-of-squares error for the larger polynomial fits, we may not necessarily want to use them. Observing the plots in part C of this problem, we may be tempted to use as high as a fourth-degree polynomial for our fits. If this is done, we get the following results: "
]
},
{
"cell_type": "code",
"execution_count": 387,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"def fit_help_st(n):\n",
" array =np.block([[steel_time_train**0]]).T\n",
" for i in range(1,n+1):\n",
" array = np.hstack((array,steel_time_train.reshape(-1,1)**i))\n",
" \n",
" return array\n",
"Fit_steel = fit_help_st(4)\n",
"a_steel = np.linalg.solve(Fit_steel.T@Fit_steel, Fit_steel.T@steel_price_train)\n",
"plt.figure(figsize = (10,6))\n",
"plt.title('Showing Valididty of Fourth Degree Fit for Steel')\n",
"plt.ylabel('Price (in USD/tonne)')\n",
"plt.xlabel('Time(in years)')\n",
"plt.plot(steel_tr_un_normalized, steel_price_train, 's', label = 'Actual Price - Training')\n",
"plt.plot(steel_tr_un_normalized, Fit_steel@a_steel,'x', label = 'Fourth-Degree Polynomial Fit')\n",
"plt.plot(steel_te_un_normalized, steel_price_test, 'o', label = 'Actual Price - Testing')\n",
"plt.legend(fontsize = 14);"
]
},
{
"cell_type": "code",
"execution_count": 388,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"def fit_help_al(n):\n",
" '''Function returns proper z array for degree fit of n'''\n",
" array =np.block([[aluminum_time_train**0]]).T\n",
" for i in range(1,n+1):\n",
" array = np.hstack((array,aluminum_time_train.reshape(-1,1)**i))\n",
" \n",
" return array\n",
"Fit_aluminum = fit_help_al(4)\n",
"a_aluminum = np.linalg.solve(Fit_aluminum.T@Fit_aluminum, Fit_aluminum.T@aluminum_price_train)\n",
"plt.figure(figsize = (10,6))\n",
"plt.title('Showing Valididty of Fourth Degree Fit for Aluminum')\n",
"plt.ylabel('Price (in USD/tonne)')\n",
"plt.xlabel('Time(in years)')\n",
"plt.plot(aluminum_tr_un_normalized, aluminum_price_train, 's', label = 'Actual Price - Training')\n",
"plt.plot(aluminum_tr_un_normalized, Fit_aluminum@a_aluminum,'x', label = 'Fourth-Degree Polynomial Fit')\n",
"plt.plot(aluminum_te_un_normalized, aluminum_price_test, 'o', label = 'Actual Price - Testing')\n",
"plt.legend(fontsize = 14);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As we see represented in the plots above and supported by the training/testing error curves in the previous problem, the fourth degree polynomial provides a reasonable representation of the given data within the testing bounds, but has these flares at the extrema which will prove to skew the data immensely when extrapolating later on. In order to avoid this, we will instead utilize a piecewise linear function, as discussed in the project discussion session."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First Steel:"
]
},
{
"cell_type": "code",
"execution_count": 515,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"Z_picwise_steel = np.block([[steel_time_train**0], [steel_time_train**1], [(steel_time_train - 0.5)*(steel_time_train>=0.5)]]).T\n",
"fit_picwise_steel = np.linalg.solve(Z_picwise_steel.T@Z_picwise_steel, Z_picwise_steel.T@steel_price_train)\n",
"plt.figure(figsize = (10,6))\n",
"plt.title('Showing Improvement on Extrema Behaviour with Piecewise Function\\nSteel', fontsize = 18);\n",
"plt.ylabel('Price in USD/tonne');\n",
"plt.xlabel('Year');\n",
"plt.plot(steel_tr_un_normalized, Z_picwise_steel@fit_picwise_steel, 'x', label = 'Piecewise Linear Fit');\n",
"plt.plot(steel_tr_un_normalized, steel_price_train, 'o', label = 'Actual Price Variation - Training');\n",
"plt.plot(steel_te_un_normalized, steel_price_test, 's', label = 'Actual Price Variation - Testing');\n",
"plt.legend();"
]
},
{
"cell_type": "code",
"execution_count": 516,
"metadata": {},
"outputs": [],
"source": [
"s_0 = fit_picwise_steel[0]\n",
"s_1 = fit_picwise_steel[1]\n",
"s_2 = fit_picwise_steel[2]"
]
},
{
"cell_type": "code",
"execution_count": 519,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The equation for steel by this plot has the following form:\n",
"\n",
"\tSteel Price(tn) = 236.4574 + 109.1334*tn + -145.6456*(tn-0.5)*H(0.5)\n",
"\n",
"where tn is the normalized year and H(0.5) is the heaviside function activated at tn = 0.5\n"
]
}
],
"source": [
"print('The equation for steel by this plot has the following form:\\n')\n",
"print('\\tSteel Price(tn) = {:.4f} + {:.4f}*tn + {:.4f}*(tn-0.5)*H(0.5)\\n'.format(s_0,s_1,s_2))\n",
"print('where tn is the normalized year and H(0.5) is the heaviside function activated at tn = 0.5')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now Aluminum:"
]
},
{
"cell_type": "code",
"execution_count": 529,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"Z_picwise_aluminum = np.block([[aluminum_time_train**0], [aluminum_time_train**1], [(aluminum_time_train - 0.55)*(aluminum_time_train>=0.55)],[(aluminum_time_train - 0.9)*(aluminum_time_train>=0.9)]]).T\n",
"fit_picwise_aluminum = np.linalg.solve(Z_picwise_aluminum.T@Z_picwise_aluminum, Z_picwise_aluminum.T@aluminum_price_train)\n",
"plt.figure(figsize = (10,6))\n",
"plt.title('Showing Improvement on Extrema Behaviour with Piecewise Function\\nAluminum', fontsize = 18);\n",
"plt.ylabel('Price in USD/tonne');\n",
"plt.xlabel('Year');\n",
"plt.plot(aluminum_tr_un_normalized, Z_picwise_aluminum@fit_picwise_aluminum, 'x', label = 'Piecewise Linear Fit');\n",
"plt.plot(aluminum_tr_un_normalized, aluminum_price_train, 'o', label = 'Actual Price Variation - Training');\n",
"plt.plot(aluminum_te_un_normalized, aluminum_price_test, 's', label = 'Actual Price Variation - Testing');\n",
"plt.legend(fontsize = 13);"
]
},
{
"cell_type": "code",
"execution_count": 530,
"metadata": {},
"outputs": [],
"source": [
"a_0 = fit_picwise_aluminum[0]\n",
"a_1 = fit_picwise_aluminum[1]\n",
"a_2 = fit_picwise_aluminum[2]\n",
"a_3 = fit_picwise_aluminum[3]"
]
},
{
"cell_type": "code",
"execution_count": 540,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The equation for aluminum by this plot has the following form:\n",
"\n",
"\tAluminum Price(tn) = 571.0218 + 8639.0485*tn + -17685.0534*(tn-0.55)*H(0.55) + 11599.8675*(tn-0.9)*H(0.9)\n",
"\n",
"where tn is the normalized year and H(0.55), H(0.9) are heaviside functions activated at tn = 0.55 and tn = 0.9, respectively.\n"
]
}
],
"source": [
"print('The equation for aluminum by this plot has the following form:\\n')\n",
"print('\\tAluminum Price(tn) = {:.4f} + {:.4f}*tn + {:.4f}*(tn-0.55)*H(0.55) + {:.4f}*(tn-0.9)*H(0.9)\\n'.format(a_0,a_1,a_2,a_3))\n",
"print('where tn is the normalized year and H(0.55), H(0.9) are heaviside functions activated at tn = 0.55 and tn = 0.9, respectively.')"
]
},
{
"cell_type": "code",
"execution_count": 541,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Price of steel: 241.47182423235816\n",
"Price of aluminum 5380.592682501736\n"
]
}
],
"source": [
"def steel1(t):\n",
" tn = (t-steel_year.min())/(steel_year.max()-steel_year.min())\n",
" ans = s_0 + s_1*tn + s_2*(tn-0.5)*(tn>=0.5)\n",
" return ans\n",
"\n",
"def alum1(t):\n",
" tn = (t-aluminum_year.min())/(aluminum_year.max()-aluminum_year.min())\n",
" ans = a_0 + a_1*tn + a_2*(tn-0.55)*(tn>=0.55) + a_3*(tn-0.9)*(tn>=0.9)\n",
" return ans\n",
"\n",
"print('Price of steel:', steel1(2025))\n",
"print('Price of aluminum', alum1(2025))\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"__Utilizing these relationships, we get the following for the price of steel and the price of aluminum in the year 2025:__\n",
"\n",
"__Aluminum in 2025__ = $5380.59 USD/tonne\n",
"\n",
"__Steel in 2025__ = $241.47 USD /tonne\n",
"\n",
"**Note: the relationships above use the normalized year, NOT the actual year. The normalized year is found by using the equation: material_year - material.min() / (material.max() - material.min())\n",
"The opposite arithmetic then recovers the actual year and that is what is plotted above for simplicity of observation.** "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Problem 4 Part E"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In part d above, we found that the price of steel is predicted to stagnate around the area of 250 USD/tonne through the year 2025 whereas aluminum increases again to beyond 5000 USD/tonne. Judging by this pattern of aluminum continuing to increase and the price of steel slowly decreasing in this time period, as well as steel being wholly less volatile than the aluminum pricing, __I would not__ change my decision made inproblem 3.d about using steel as the material to build the truss with. Steel still seems to be the superior material conidering the strength and economical implications. "
]
},
{
"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
}