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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": 10,
"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": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import numpy as np\n",
"fea_arrays = np.load('./fea_arrays.npz')\n",
"K=fea_arrays['K']\n",
"K\n"
]
},
{
"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",
"\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": 11,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"a.\n",
"condition of k = 1.4577532625238035e+17\n",
"2.220446049250313e-16\n",
"would expect to have an error of 10 \n",
"b.\n",
"the condition of K is so large because the matrix can have many different solutions and is ill-conditioned\n",
"c.\n",
"52.23542514351006\n",
"would expect the error to be 1^-14\n"
]
}
],
"source": [
"print('a.')\n",
"cond_K = np.linalg.cond(K)\n",
"print('condition of k = ', cond_K)\n",
"print(np.finfo(float).eps)\n",
"print(\"would expect to have an error of 10 \")\n",
"\n",
"print('b.')\n",
"print('the condition of K is so large because the matrix can have many different solutions and is ill-conditioned')\n",
"\n",
"print('c.')\n",
"print(np.linalg.cond(K[2:13,2:13]))\n",
"print('would expect the error to be 1^-14') "
]
},
{
"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": 12,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[[ 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. ]] [[ 5.00000000e-03 0.00000000e+00 -8.33333333e-04 1.44337567e-03\n",
" -3.33333333e-03 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
" 0.00000000e+00 0.00000000e+00 0.00000000e+00]\n",
" [ 0.00000000e+00 5.00000000e-03 1.44337567e-03 -2.50000000e-03\n",
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
" 0.00000000e+00 0.00000000e+00 0.00000000e+00]\n",
" [ 0.00000000e+00 0.00000000e+00 7.77777778e-03 9.62250449e-04\n",
" -1.38888889e-03 -1.44337567e-03 -3.33333333e-03 0.00000000e+00\n",
" 0.00000000e+00 0.00000000e+00 0.00000000e+00]\n",
" [-2.16840434e-19 0.00000000e+00 0.00000000e+00 3.21428571e-03\n",
" -3.09294787e-04 -2.32142857e-03 4.12393049e-04 0.00000000e+00\n",
" 0.00000000e+00 0.00000000e+00 0.00000000e+00]\n",
" [-2.08654805e-20 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
" 5.83333333e-03 -4.81125224e-04 -1.38888889e-03 1.44337567e-03\n",
" -3.33333333e-03 0.00000000e+00 0.00000000e+00]\n",
" [-1.58327936e-19 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
" 0.00000000e+00 3.01587302e-03 1.00807190e-03 -2.38095238e-03\n",
" -2.74928700e-04 0.00000000e+00 0.00000000e+00]\n",
" [ 7.57746398e-20 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
" 0.00000000e+00 0.00000000e+00 6.18421053e-03 1.13950711e-03\n",
" -1.53508772e-03 -1.44337567e-03 -3.33333333e-03]\n",
" [-1.33795162e-19 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 2.55319149e-03\n",
" -5.52782173e-04 -2.23404255e-03 6.14202414e-04]\n",
" [-3.65145909e-20 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
" 2.56944444e-03 -8.41969143e-04 -1.52777778e-03]\n",
" [-1.11350493e-19 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
" 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
" 0.00000000e+00 2.43243243e-03 7.02182760e-04]\n",
" [ 8.34619222e-20 0.00000000e+00 0.00000000e+00 0.00000000e+00\n",
" 0.00000000e+00 0.00000000e+00 -4.33680869e-19 0.00000000e+00\n",
" 0.00000000e+00 -1.08420217e-19 1.11111111e-03]]\n"
]
}
],
"source": [
"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, U = LUNaive(K[2:13,2:13])\n",
"print(L, U)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[ 1.94855716 -2.125 0.4330127 -4. 1.08253175 -5.375\n",
" 1.73205081 -4. 0.21650635 -2.125 2.16506351]\n",
"[ 5.56730617 -6.07142857 1.23717915 -11.42857143 3.09294787\n",
" -15.35714286 4.94871659 -11.42857143 0.61858957 -6.07142857\n",
" 6.18589574]\n"
]
}
],
"source": [
"A = 0.1\n",
"E_st = 200000\n",
"E_al = 70000\n",
"F = np.zeros(11)\n",
"F[5] = -100\n",
"\n",
"F_st= F/(E_st*A)\n",
"\n",
"\n",
"F_al= F/(E_al*A)\n",
"\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",
"\n",
"u_st= solveLU(L, U, F_st)\n",
"u_al= solveLU(L, U, F_al)\n",
"print(u_st)\n",
"print(u_al)"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[ 1.94855716 -2.125 0.4330127 -4. 1.08253175 -5.375\n",
" 1.73205081 -4. 0.21650635 -2.125 2.16506351]\n",
"[ 5.56730617 -6.07142857 1.23717915 -11.42857143 3.09294787\n",
" -15.35714286 4.94871659 -11.42857143 0.61858957 -6.07142857\n",
" 6.18589574]\n"
]
}
],
"source": [
"u_ste = np.zeros(14)\n",
"u_alu = np.zeros(14)\n",
"A = 0.1\n",
"E_st = 200000\n",
"E_al = 70000\n",
"F = np.zeros(11)\n",
"F[5] = -100\n",
"\n",
"F_st= F/(E_st*A)\n",
"u_st= solveLU(L, U, F_st)\n",
"\n",
"F_al= F/(E_al*A)\n",
"u_al= solveLU(L, U, F_al)\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",
"\n",
"u_st= solveLU(L, U, F_st)\n",
"u_al= solveLU(L, U, F_al)\n",
"print(u_st)\n",
"print(u_al)"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[ 1.94855716 -2.125 0.4330127 -4. 1.08253175 -5.375\n",
" 1.73205081 -4. 0.21650635 -2.125 2.16506351]\n",
"[ 5.56730617 -6.07142857 1.23717915 -11.42857143 3.09294787\n",
" -15.35714286 4.94871659 -11.42857143 0.61858957 -6.07142857\n",
" 6.18589574]\n"
]
}
],
"source": [
"A = 0.1\n",
"E_st = 200000\n",
"E_al = 70000\n",
"F = np.zeros(11)\n",
"F[5] = -100\n",
"\n",
"F_st= F/(E_st*A)\n",
"u_st= solveLU(L, U, F_st)\n",
"\n",
"F_al= F/(E_al*A)\n",
"u_al= solveLU(L, U, F_al)\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",
"\n",
"u_st= solveLU(L, U, F_st)\n",
"u_al= solveLU(L, U, F_al)\n",
"print(u_st)\n",
"print(u_al)"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Steel displacements:\n",
"u_1x= 0.0 mm.\n",
"u_1y= 0.0 mm.\n",
"u_2x= 1.949 mm.\n",
"u_2y= -2.125 mm.\n",
"u_3x= 0.433 mm.\n",
"u_3y= -4.0 mm.\n",
"u_4x= 1.083 mm.\n",
"u_4y= -5.375 mm.\n",
"u_5x= 1.732 mm.\n",
"u_5y= -4.0 mm.\n",
"u_6x= 0.2165 mm.\n",
"u_6y= -2.125 mm.\n",
"u_7x= 2.165 mm.\n",
"u_7y= 0.0 mm.\n",
"\n",
"Steel 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",
"Aluminium Displacements:\n",
"u_1x= 0.0 mm.\n",
"u_1y= 0.0 mm.\n",
"u_2x= 5.567 mm.\n",
"u_2y= -6.071 mm.\n",
"u_3x= 1.237 mm.\n",
"u_3y= -11.43 mm.\n",
"u_4x= 3.093 mm.\n",
"u_4y= -15.36 mm.\n",
"u_5x= 4.949 mm.\n",
"u_5y= -11.43 mm.\n",
"u_6x= 0.6186 mm.\n",
"u_6y= -6.071 mm.\n",
"u_7x= 6.186 mm.\n",
"u_7y= 0.0 mm.\n",
"\n",
"Aluminium 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": [
"u_ste = np.zeros(14)\n",
"u_alu = np.zeros(14)\n",
"u_ste[2:13] = u_st\n",
"u_alu[2:13] = u_al\n",
"F_st= E_st*A*K@u_ste\n",
"F_al= E_al*A*K@u_alu\n",
"xy= {0:'x', 1:'y'}\n",
"print('Steel displacements:')\n",
"for i in range(len(u_ste)):\n",
" print('u_{}{}= {:.4} mm.'.format(int(i/2)+1, xy[i%2], u_ste[i])) \n",
"print('\\nSteel forces:')\n",
"for i in range(len(F_st)):\n",
" print('F_{}{}= {:.2f} N.'.format(int(i/2)+1, xy[i%2], F_st[i]))\n",
"print('\\nAluminium Displacements:')\n",
"for i in range(len(u_alu)):\n",
" print('u_{}{}= {:.4} mm.'.format(int(i/2)+1, xy[i%2], u_alu[i]))\n",
"print('\\nAluminium Forces: ')\n",
"for i in range(len(F_al)):\n",
" print('F_{}{}= {:.2f} N.'.format(int(i/2)+1, xy[i%2], F_al[i]))\n"
]
},
{
"cell_type": "code",
"execution_count": 18,
"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": [
"import matplotlib.pyplot as plt\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]])\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",
"plt.plot(r[ix],r[iy],'-',color='k')\n",
"plt.plot(r[ix],r[iy],'o',color='b')\n",
"plt.plot(r[0],r[1],'^',color='r',markersize=20)\n",
"plt.plot(r[0],r[1],'>',color='k',markersize=20)\n",
"plt.plot(r[-2],r[-1],'^',color='r',markersize=20)\n",
"s = 5\n",
"plt.plot(r[ix]+u_ste[ix]*s,r[iy]+u_ste[iy]*s,'-',color=(0,1,0))\n",
"plt.quiver(r[ix],r[iy],F_st[ix],F_st[iy],color=(0,0,1),label='Applied forces')\n",
"plt.quiver(r[ix],r[iy],u_ste[ix],u_ste[iy],color=(1,1,0),label='Displacements')\n",
"plt.title('Steel Forces and Displacements')\n",
"plt.legend(loc='center left', bbox_to_anchor=(1,0.5));\n",
"plt.xlabel('x (mm)')\n",
"plt.ylabel('y (mm)')\n",
"plt.axis(l*np.array([-0.5,3.5,-1,1.5]));"
]
},
{
"cell_type": "code",
"execution_count": 19,
"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": [
"import matplotlib.pyplot as plt\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]])\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",
"plt.plot(r[ix],r[iy],'-',color='k')\n",
"plt.plot(r[ix],r[iy],'o',color='b')\n",
"plt.plot(r[0],r[1],'^',color='r',markersize=20)\n",
"plt.plot(r[0],r[1],'>',color='k',markersize=20)\n",
"plt.plot(r[-2],r[-1],'^',color='r',markersize=20)\n",
"s = 5\n",
"plt.plot(r[ix]+u_alu[ix]*s,r[iy]+u_alu[iy]*s,'-',color=(0,1,0))\n",
"plt.quiver(r[ix],r[iy],F_al[ix],F_al[iy],color=(0,0,1),label='Applied forces')\n",
"plt.quiver(r[ix],r[iy],u_alu[ix],u_alu[iy],color=(1,1,0),label='Displacements')\n",
"plt.title('Aluminium Forces and Displacements')\n",
"plt.legend(loc='center left', bbox_to_anchor=(1,0.5))\n",
"plt.xlabel('x (mm)')\n",
"plt.ylabel('y (mm)')\n",
"plt.axis(l*np.array([-0.5,3.5,-1,1.5]));"
]
},
{
"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": 30,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" the minimum cross-sectional area to keep total y-deflections <0.2 𝑚𝑚 7.679000000000899\n"
]
}
],
"source": [
"max_y = 100\n",
"new_area = 0.1;\n",
"while (max_y>0.2):\n",
" new_area = new_area + 0.001\n",
" F_new_al = F*(1/(E_al*new_area))\n",
" u_int_al = solveLU(L, U, F_new_al)\n",
" max_y = max(abs(u_int_al))\n",
"alum_min = new_area \n",
"print(' the minimum cross-sectional area to keep total y-deflections <0.2 𝑚𝑚', alum_min)"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" the minimum cross-sectional area to keep total y-deflections <0.2 𝑚𝑚 2.687999999999815\n"
]
}
],
"source": [
"max_y1 = 100 \n",
"new_area1 = 0.1;\n",
"while (max_y1>0.2):\n",
" new_area1 = new_area1 + 0.001\n",
" F_new_st = F*(1/(E_st*new_area1))\n",
" u_int_st = solveLU(L, U, F_new_st)\n",
" max_y1 = max(abs(u_int_st))\n",
"steel_min = new_area1 \n",
"print(' the minimum cross-sectional area to keep total y-deflections <0.2 𝑚𝑚', steel_min)"
]
},
{
"cell_type": "code",
"execution_count": 46,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The weight of the aluminum truss is: 0.06867329700000806\n",
"The weight of the steel truss is: 0.06830207999999531\n",
"The cost of the aluminum truss is $0.1061.\n",
"The cost of the steel truss is $0.032512.\n",
"Steel is the cheaper material\n"
]
}
],
"source": [
"p_st= 7700*(1/1000)**3 \n",
"p_al= 2710*(1/1000)**3 \n",
"l=300\n",
"V_st= steel_min*l*11\n",
"V_al= alum_min*l*11\n",
"st_weight= p_st*V_st\n",
"al_weight= p_al*V_al\n",
"print('The weight of the aluminum truss is:', al_weight)\n",
"\n",
"print('The weight of the steel truss is:', st_weight)\n",
"\n",
"\n",
"al_price= 1545/1000\n",
"st_price= 476/1000 \n",
"al_cost= price_al*weight_al\n",
"st_cost= price_st*weight_st\n",
"print('The cost of the aluminum truss is ${:.5}.'.format(al_cost))\n",
"print('The cost of the steel truss is ${:.5}.'.format(st_cost))\n",
"print('Steel is the cheaper material')"
]
},
{
"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": 60,
"metadata": {},
"outputs": [],
"source": [
"import random as random\n",
"\n",
"steel=np.loadtxt('../data/steel_price.csv',skiprows=1,delimiter=',')\n",
"al = np.loadtxt('../data/al_price.csv',skiprows=1,delimiter=',')\n",
"\n",
"\n",
"yr_st=(steel[:,0]-np.min(steel[:,0]))/(np.max(steel[:,0])-np.min(steel[:,0]))\n",
"price_st=steel[:,1]\n",
"\n",
"\n",
"yr_al=(al[:,0]-np.min(al[:,0]))/(np.max(al[:,0])-np.min(al[:,0]))\n",
"price_al=al[:,1]\n",
"\n",
"np.random.seed(103)\n",
"i_rand_st = random.sample(range(0,len(yr_st)),len(yr_st))\n",
"\n",
"i_rand_al = random.sample(range(0,len(yr_al)),len(yr_al))\n",
"\n",
"train_per=0.7\n",
"yr_st_train=yr_st[i_rand_st[:int(len(yr_st)*train_per)]]\n",
"price_st_train=price_st[i_rand_st[:int(len(yr_st)*train_per)]]\n",
"yr_al_train=yr_al[i_rand_al[:int(len(yr_al)*train_per)]]\n",
"price_al_train=price_al[i_rand_al[:int(len(yr_al)*train_per)]]\n",
"yr_st_test=yr_st[i_rand_st[int(len(yr_st)*train_per):]]\n",
"price_st_test=price_st[i_rand_st[int(len(yr_st)*train_per):]]\n",
"yr_al_test=yr_al[i_rand_al[int(len(yr_al)*train_per):]]\n",
"price_al_test=price_al[i_rand_al[int(len(yr_al)*train_per):]]"
]
},
{
"cell_type": "code",
"execution_count": 68,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"Z_st=np.block([[yr_st_train**0]]).T\n",
"Z_st_test=np.block([[yr_st_test**0]]).T\n",
"max_N=20\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,yr_st_train.reshape(-1,1)**i))\n",
" Z_st_test=np.hstack((Z_st_test,yr_st_test.reshape(-1,1)**i))\n",
" A_st = np.linalg.solve(Z_st.T@Z_st,Z_st.T@price_st_train)\n",
" St_st=np.std(price_st_train)\n",
" Sr_st=np.std(price_st_train-Z_st@A_st)\n",
" r2_st=1-Sr_st/St_st\n",
" SSE_train_st[i]=np.sum((price_st_train-Z_st@A_st)**2)/len(price_st_train)\n",
" SSE_test_st[i]=np.sum((price_st_test-Z_st_test@A_st)**2)/len(price_st_test)\n",
" if i==2:\n",
" order_2_price_st=Z_st@A_st\n",
" if i==3:\n",
" order_3_price_st=Z_st@A_st\n",
" if i==4:\n",
" order_4_price_st=Z_st@A_st\n",
" if i==5:\n",
" order_5_price_st=Z_st@A_st\n",
" if i==6: \n",
" order_6_price_st=Z_st@A_st\n",
" if i==7:\n",
" order_7_price_st=Z_st@A_st\n",
" if i==8:\n",
" order_8_price_st=Z_st@A_st\n",
" if i==9:\n",
" order_9_price_st=Z_st@A_st\n",
" if i==10: \n",
" order_10_price_st=Z_st@A_st\n",
"fig = plt.figure(figsize=(12,8)) \n",
"plt.plot(yr_st,price_st,'b-',label='order 1')\n",
"plt.plot(yr_st_train, order_2_price_st,'.',label='order 2')\n",
"plt.plot(yr_st_train, order_3_price_st,'.',label='order 3')\n",
"plt.plot(yr_st_train, order_4_price_st,'.',label='order 4')\n",
"plt.plot(yr_st_train, order_5_price_st,'.',label='order 5')\n",
"plt.plot(yr_st_train, order_6_price_st,'.',label='order 6')\n",
"plt.plot(yr_st_train, order_7_price_st,'.',label='order 7')\n",
"plt.plot(yr_st_train, order_8_price_st,'.',label='order 8')\n",
"plt.plot(yr_st_train, order_9_price_st,'.',label='order 9')\n",
"plt.plot(yr_st_train, order_10_price_st,'o',label='order 10')\n",
"plt.xlabel('Year')\n",
"plt.ylabel('Price')\n",
"plt.title('Steel Polynominal Functions')\n",
"plt.legend(loc='best');"
]
},
{
"cell_type": "code",
"execution_count": 71,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"Z_al=np.block([[yr_al_train**0]]).T\n",
"Z_al_test=np.block([[yr_al_test**0]]).T\n",
"max_N=20\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,yr_al_train.reshape(-1,1)**i))\n",
" Z_al_test=np.hstack((Z_al_test,yr_al_test.reshape(-1,1)**i))\n",
" A_al = np.linalg.solve(Z_al.T@Z_al,Z_al.T@price_al_train)\n",
" St_al=np.std(price_al_train)\n",
" Sr_al=np.std(price_al_train-Z_al@A_al)\n",
" r2_al=1-Sr_al/St_al\n",
" SSE_train_al[i]=np.sum((price_al_train-Z_al@A_al)**2)/len(price_al_train)\n",
" SSE_test_al[i]=np.sum((price_al_test-Z_al_test@A_al)**2)/len(price_al_test)\n",
" if i==2:\n",
" order_2_price_al=Z_al@A_al\n",
" if i==3:\n",
" order_3_price_al=Z_al@A_al\n",
" if i==4:\n",
" order_4_price_al=Z_al@A_al\n",
" if i==5:\n",
" order_5_price_al=Z_al@A_al\n",
" if i==6: \n",
" order_6_price_al=Z_al@A_al\n",
" if i==7:\n",
" order_7_price_al=Z_al@A_al\n",
" if i==8:\n",
" order_8_price_al=Z_al@A_al\n",
" if i==9:\n",
" order_9_price_al=Z_al@A_al\n",
" if i==10: \n",
" order_10_price_al=Z_al@A_al\n",
"fig = plt.figure(figsize=(12,8)) \n",
"plt.plot(yr_al,price_al,'b-',label='order 1')\n",
"plt.plot(yr_al_train, order_2_price_al,'.',label='order 2')\n",
"plt.plot(yr_al_train, order_3_price_al,'.',label='order 3')\n",
"plt.plot(yr_al_train, order_4_price_al,'.',label='order 4')\n",
"plt.plot(yr_al_train, order_5_price_al,'.',label='order 5')\n",
"plt.plot(yr_al_train, order_6_price_al,'.',label='order 6')\n",
"plt.plot(yr_al_train, order_7_price_al,'.',label='order 7')\n",
"plt.plot(yr_al_train, order_8_price_al,'.',label='order 8')\n",
"plt.plot(yr_al_train, order_9_price_al,'.',label='order 9')\n",
"plt.plot(yr_al_train, order_10_price_al,'o',label='order 10')\n",
"plt.xlabel('Year')\n",
"plt.ylabel('Price')\n",
"plt.title('Aluminium Polynominal Functions')\n",
"plt.legend(loc='best');"
]
},
{
"cell_type": "code",
"execution_count": 81,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(8,8))\n",
"plt.plot(range(1, max_N+1),SSE_train_al, label='Train')\n",
"plt.plot(range(1, max_N+1),SSE_test_al, label='Test')\n",
" #plt.plot(3,SSE_train_al[2],'ks') #Finding order after first peak\n",
"plt.xlabel('Polynomial Function Order, n')\n",
"plt.ylabel('SSE')\n",
"plt.title('Aluminium Test and Training Error as Function of Polynominal Order')\n",
"plt.legend(loc='best');"
]
},
{
"cell_type": "code",
"execution_count": 82,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"#Problem 4.c Steel\n",
"plt.figure(figsize=(8,8))\n",
"plt.plot(range(1, max_N+1),SSE_train_st, label='Train')\n",
"plt.plot(range(1, max_N+1),SSE_test_st, label='Test')\n",
" #plt.plot(3,SSE_train_st[2],'ks') #Finding order after first peak\n",
"plt.xlabel('Polynomial Function Order, n')\n",
"plt.ylabel('SSE')\n",
"plt.title('Steel Test and Training Error as Function of Polynominal Order')\n",
"plt.legend(loc='best');"
]
},
{
"cell_type": "code",
"execution_count": 96,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Predicted price of aluminum in 2025 from a 10th degree polynomial: -32723.1277 $/MT.\n",
"Predicted price of aluminum in 2025 from a 40th degree polynomial: -31854.3829 $/MT.\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"\n",
"year_ext= np.linspace(2016,2025,100)\n",
"Z_ext=np.block([[year_ext**0],[year_ext**1]]).T\n",
"Z_al= np.block([[year_al**0],[year_al**1]]).T\n",
"max_N=46\n",
"plt.figure(figsize=(8,8))\n",
"for i in range (2, max_N+1):\n",
" Z_al=np.hstack((Z_al,year_al.reshape(-1,1)**i))\n",
" Z_ext=np.hstack((Z_ext,year_ext.reshape(-1,1)**i))\n",
" A = np.linalg.solve(Z_al.T@Z_al,Z_al.T@price_al)\n",
" if i==10: \n",
" plt.plot(year_ext,Z_ext@A,label='order {}'.format(i))\n",
" price_10al= (Z_ext@A)[-1]\n",
" if i == 40:\n",
" plt.plot(year_ext,Z_ext@A,label='order {}'.format(i))\n",
" price_40al= (Z_ext@A)[-1]\n",
"plt.plot(year_al,price_al,label='Current Data')\n",
"plt.ylabel('Price')\n",
"plt.xlabel('Year')\n",
"plt.title('Future Predicted Price of Aluminum')\n",
"plt.legend();\n",
"print('Predicted price of aluminum in 2025 from a 10th degree polynomial: {:.4f} $/MT.'.format(price_10al))\n",
"print('Predicted price of aluminum in 2025 from a 40th degree polynomial: {:.4f} $/MT.'.format(price_40al))"
]
},
{
"cell_type": "code",
"execution_count": 98,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Predicted price of steel in 2025 from a 10th degree polynomial: 63.4928 $/MT.\n",
"Predicted price of steel in 2025 from a 40th degree polynomial: 168.8289 $/MT.\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"year_ext= np.linspace(2014.7,2025,100)\n",
"Z_ext=np.block([[year_ext**0],[year_ext**1]]).T\n",
"Z_st= np.block([[year_st**0],[year_st**1]]).T\n",
"max_N=46\n",
"plt.figure(figsize=(8,8))\n",
"for i in range (2, max_N+1):\n",
" Z_st=np.hstack((Z_st,year_st.reshape(-1,1)**i))\n",
" Z_ext=np.hstack((Z_ext,year_ext.reshape(-1,1)**i))\n",
" A = np.linalg.solve(Z_st.T@Z_st,Z_st.T@price_st)\n",
" if i==10: #or i==5 or i==7 or i==20 or i == 46: \n",
" plt.plot(year_ext,Z_ext@A,label='order {}'.format(i))\n",
" price_10st= (Z_ext@A)[-1]\n",
" if i == 40:\n",
" plt.plot(year_ext,Z_ext@A,label='order {}'.format(i))\n",
" price_40st= (Z_ext@A)[-1]\n",
"plt.plot(year_st,price_st,label='Current Data')\n",
"plt.ylabel('Price ($/MT)')\n",
"plt.xlabel('Year')\n",
"plt.title('Future Predicted Price of Steel')\n",
"plt.legend();\n",
"print('Predicted price of steel in 2025 from a 10th degree polynomial: {:.4f} $/MT.'.format(price_10st))\n",
"print('Predicted price of steel in 2025 from a 40th degree polynomial: {:.4f} $/MT.'.format(price_40st))"
]
},
{
"cell_type": "code",
"execution_count": 99,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"d.\n",
"based upon this pricing model I would change my answer in part b because the function must be modified. The price based on the function eventually goes below zero which is not possible.\n"
]
}
],
"source": [
"print('d.')\n",
"print('based upon this pricing model I would change my answer in part b because the function must be modified. The price based on the function eventually goes below zero which is not possible.')"
]
},
{
"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
},
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