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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": 1,
"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": 2,
"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": 3,
"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": 4,
"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": 5,
"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": 6,
"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": 7,
"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": 10,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"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",
"f_alum(5)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"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": [
"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",
"f_steel(5)"
]
},
{
"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": 12,
"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": 13,
"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": 14,
"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": 15,
"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": 16,
"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": 17,
"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": 18,
"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": 19,
"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": 20,
"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": 21,
"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": 22,
"metadata": {},
"outputs": [
{
"data": {
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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": 23,
"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": 24,
"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": 25,
"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": 26,
"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": 27,
"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": 28,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The equation for steel by this plot has the following form:\n",
"\n",
"\tSteel Price(tn) = 236.5158 + 109.5874*tn + -145.8878*(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": 29,
"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": 30,
"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": 31,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The equation for aluminum by this plot has the following form:\n",
"\n",
"\tAluminum Price(tn) = 651.4685 + 8350.0460*tn + -17021.1051*(tn-0.55)*H(0.55) + 12570.5332*(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": 32,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Price of steel: 242.04475046319334\n",
"Price of aluminum 7132.1242168652425\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__ = $7132.12 USD/tonne\n",
"\n",
"__Steel in 2025__ = $242.04 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 7000 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
}