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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": 170,
"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. ]])"
]
},
"execution_count": 170,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import numpy as np\n",
"fea_arrays = np.load('./fea_arrays.npz')\n",
"K=fea_arrays['K'] #K in m\n",
"K[:3] #part of K"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In this project we are solving the problem, $\\mathbf{F}=\\mathbf{Ku}$, where $\\mathbf{F}$ is measured in Newtons, $\\mathbf{K}$ `=E*A*K` is the stiffness in N/mm, `E` is Young's modulus measured in MPa (N/mm^2), and `A` is the cross-sectional area of the beam measured in mm^2. \n",
"\n",
"There are three constraints on the motion of the joints:\n",
"\n",
"i. node 1 displacement in the x-direction is 0 = `u[0]`\n",
"\n",
"ii. node 1 displacement in the y-direction is 0 = `u[1]`\n",
"\n",
"iii. node 7 displacement in the y-direction is 0 = `u[13]`\n",
"\n",
"We can satisfy these constraints by leaving out the first, second, and last rows and columns from our linear algebra description. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 1. Calculate the condition of `K` and the condition of `K[2:13,2:13]`. \n",
"\n",
"a. What error would you expect when you solve for `u` in `K*u = F`? \n",
"\n",
"b. Why is the condition of `K` so large?\n",
"\n",
"c. What error would you expect when you solve for `u[2:13]` in `K[2:13,2:13]*u=F[2:13]`"
]
},
{
"cell_type": "code",
"execution_count": 180,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"condition of K is: 7.803794730603666e+16\n",
"condition of K[2:13,2:13] is: 52.23542514351013\n"
]
}
],
"source": [
"K = K #convert K matrix to m, will be using for all calcs\n",
"\n",
"#to find condition of matrix K\n",
"cond1 = np.linalg.cond(K)\n",
"print('condition of K is:',cond)\n",
"\n",
"cond2 = np.linalg.cond(K[2:13,2:13])\n",
"print('condition of K[2:13,2:13] is:',cond2)"
]
},
{
"cell_type": "code",
"execution_count": 181,
"metadata": {},
"outputs": [],
"source": [
"# Condition of K is very large b/c it is an ill conditioned matrix"
]
},
{
"cell_type": "code",
"execution_count": 182,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"expected errors solving for u:\n",
"error in K is: 6.640986594413594\n",
"error in K[2:13,2:13] is: 5.2235425143510105e-15\n"
]
}
],
"source": [
"# error = 10^(c-t)\n",
"# Cond(K) = 10^c\n",
"# assume t = 16 again\n",
"\n",
"t = 16\n",
"c1 = np.log(cond1)/np.log(10)\n",
"error1 = 10**(c1-t)\n",
"\n",
"c2 = np.log(cond2)/np.log(10)\n",
"error2 = 10**(c2-t)\n",
"\n",
"print('expected errors solving for u:')\n",
"print('error in K is:',error1)\n",
"print('error in K[2:13,2:13] is:',error2)"
]
},
{
"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": 183,
"metadata": {},
"outputs": [],
"source": [
"def solveLU(L,U,b):\n",
" '''solveLU: solve for x when LUx = b\n",
" x = solveLU(L,U,b): solves for x given the lower and upper \n",
" triangular matrix storage\n",
" uses forward substitution for \n",
" 1. Ly = b\n",
" then backward substitution for\n",
" 2. Ux = y\n",
" \n",
" Arguments:\n",
" ----------\n",
" L = Lower triangular matrix\n",
" U = Upper triangular matrix\n",
" b = output vector\n",
" \n",
" returns:\n",
" ---------\n",
" x = solution of LUx=b '''\n",
" n=len(b)\n",
" x=np.zeros(n)\n",
" y=np.zeros(n)\n",
" \n",
" # forward substitution\n",
" for k in range(0,n):\n",
" y[k] = b[k] - L[k,0:k]@y[0:k]\n",
" # backward substitution\n",
" for k in range(n-1,-1,-1):\n",
" x[k] = (y[k] - U[k,k+1:n]@x[k+1:n])/U[k,k]\n",
" return x"
]
},
{
"cell_type": "code",
"execution_count": 184,
"metadata": {},
"outputs": [],
"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"
]
},
{
"cell_type": "code",
"execution_count": 185,
"metadata": {},
"outputs": [],
"source": [
"from pretty_print import array_print as AP \n",
"import matplotlib.pyplot as plt\n",
"import pandas as pd\n",
"from matplotlib import rcParams\n",
"from scipy.linalg import lu"
]
},
{
"cell_type": "code",
"execution_count": 203,
"metadata": {},
"outputs": [],
"source": [
"#use m,pa,N for all units\n",
"A = 1e-7 #m^2\n",
"Es = 200e9 #Mpa\n",
"Ea = 70e9 #Mpa\n",
"\n",
"#create matrix\n",
"Am = K[2:13,2:13] \n",
"\n",
"#2 methods, both work so I chose to proceed with lu(Am)\n",
"P,L,U = lu(Am) \n",
"L2,U2 = LUNaive(Am)\n",
"\n",
"#print('L')\n",
"#AP([L], ['[L]'])\n",
"#print('U')\n",
"#AP(([U]), ['[U]'])"
]
},
{
"cell_type": "code",
"execution_count": 204,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Displacements of Steel:\n",
"ux1 =0.000 mm\n",
"uy1 =0.000 mm\n",
"ux2 =1.949 mm\n",
"uy2 =-2.125 mm\n",
"ux3 =0.433 mm\n",
"uy3 =-4.000 mm\n",
"ux4 =1.083 mm\n",
"uy4 =-5.375 mm\n",
"ux5 =1.732 mm\n",
"uy5 =-4.000 mm\n",
"ux6 =0.217 mm\n",
"uy6 =-2.125 mm\n",
"ux7 =2.165 mm\n",
"uy7 =0.000 mm\n",
"\n",
"Displacements of Aluminum:\n",
"ux1 =0.000 mm\n",
"uy1 =0.000 mm\n",
"ux2 =5.567 mm\n",
"uy2 =-6.071 mm\n",
"ux3 =1.237 mm\n",
"uy3 =-11.429 mm\n",
"ux4 =3.093 mm\n",
"uy4 =-15.357 mm\n",
"ux5 =4.949 mm\n",
"uy5 =-11.429 mm\n",
"ux6 =0.619 mm\n",
"uy6 =-6.071 mm\n",
"ux7 =6.186 mm\n",
"uy7 =0.000 mm\n"
]
}
],
"source": [
"#displacements\n",
"# use solveLU\n",
"F = np.zeros(len(L))\n",
"F[5] = -100 #100 N force down \n",
"\n",
"# 7 nodes each with x and y displacement, need displacement arr of length 14\n",
"# node 1 is constrained x and y (displacements will be 0)\n",
"# node 7 is constrained in y (disp will be 0)\n",
"\n",
"#trick to print x y alternating\n",
"xy={0:'x',1:'y'}\n",
"\n",
"#steel\n",
"bs = F*(1/(Es*A))\n",
"usteel = solveLU(L,U,bs) #only nonzero values\n",
"us = np.zeros(14)\n",
"us[2:13] = usteel\n",
"print('Displacements of Steel:')\n",
"for i in range (len(us)):\n",
" print('u{}{} ={:.3f} mm'.format(xy[i%2],int(i/2)+1,us[i]*1000))\n",
" \n",
"#aluminum\n",
"ba = F*(1/(Ea*A))\n",
"ualum = solveLU(L,U,ba) #only nonzero values\n",
"ua = np.zeros(14)\n",
"ua[2:13] = ualum\n",
"print('\\nDisplacements of Aluminum:')\n",
"for i in range (len(ua)):\n",
" print('u{}{} ={:.3f} mm'.format(xy[i%2],int(i/2)+1,ua[i]*1000))"
]
},
{
"cell_type": "code",
"execution_count": 205,
"metadata": {
"scrolled": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Forces of Steel:\n",
"Fx1 =0.00 N\n",
"Fy1 =50.00 N\n",
"Fx2 =0.00 N\n",
"Fy2 =-0.00 N\n",
"Fx3 =-0.00 N\n",
"Fy3 =0.00 N\n",
"Fx4 =-0.00 N\n",
"Fy4 =-100.00 N\n",
"Fx5 =-0.00 N\n",
"Fy5 =-0.00 N\n",
"Fx6 =-0.00 N\n",
"Fy6 =0.00 N\n",
"Fx7 =0.00 N\n",
"Fy7 =50.00 N\n",
"\n",
"Forces of Aluminum:\n",
"Fx1 =0.00 N\n",
"Fy1 =50.00 N\n",
"Fx2 =0.00 N\n",
"Fy2 =-0.00 N\n",
"Fx3 =0.00 N\n",
"Fy3 =0.00 N\n",
"Fx4 =0.00 N\n",
"Fy4 =-100.00 N\n",
"Fx5 =0.00 N\n",
"Fy5 =-0.00 N\n",
"Fx6 =-0.00 N\n",
"Fy6 =-0.00 N\n",
"Fx7 =0.00 N\n",
"Fy7 =50.00 N\n"
]
}
],
"source": [
"#rxn forces\n",
"xy={0:'x',1:'y'}\n",
"\n",
"#steel\n",
"fsteel = K*Es*A@us\n",
"print('Forces of Steel:')\n",
"for i in range(len(fsteel)):\n",
" print('F{}{} ={:.2f} N'.format(xy[i%2],int(i/2)+1,fsteel[i]))\n",
"\n",
"#aluminum\n",
"falum = K*Ea*A@ua\n",
"print('\\nForces of Aluminum:')\n",
"for i in range(len(falum)):\n",
" print('F{}{} ={:.2f} N'.format(xy[i%2],int(i/2)+1,falum[i]))"
]
},
{
"cell_type": "code",
"execution_count": 206,
"metadata": {},
"outputs": [],
"source": [
"us*=1000\n",
"ua*=1000"
]
},
{
"cell_type": "code",
"execution_count": 207,
"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": [
"rcParams['font.family'] = 'sans'\n",
"rcParams['font.size'] = 16\n",
"rcParams['lines.linewidth'] = 3\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",
"\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",
"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",
"\n",
"# label the nodes\n",
"for n in nodes:\n",
" if n[2]>0.8*l: offset=0.1\n",
" else: offset=-l/5\n",
" plt.text(n[1]-l/3,n[2]+offset,'n {}'.format(int(n[0])),color='b')\n",
" \n",
" \n",
"# label the elements\n",
"#for e in elems:\n",
"# n1=nodes[e[1]-1]\n",
"# n2=nodes[e[2]-1]\n",
"# x=np.mean([n2[1],n1[1]])\n",
"# y=np.mean([n2[2],n1[2]])\n",
"# # ----------------->need elem labels<-----------------\n",
"# plt.text(x-l/5,y-l/10,'el {}'.format(int(e[0])),color='r')\n",
"s=5\n",
"plt.plot(r[ix]+us[ix]*s,r[iy]+us[iy]*s,'-',color=(1,0,0,1))\n",
"plt.quiver(r[ix],r[iy],fsteel[ix],fsteel[iy],color=(1,0,0,1),label='applied forces')\n",
"plt.quiver(r[ix],r[iy],us[ix],us[iy],color=(0,0,1,1),label='displacements')\n",
"\n",
"plt.title('Steel structure: Scale = 5x')\n",
"plt.xlabel('x (mm)')\n",
"plt.ylabel('y (mm)')\n",
"plt.axis(l*np.array([-0.5,3.5,-1,1.5]));\n",
"plt.legend(bbox_to_anchor=(1,0.5));"
]
},
{
"cell_type": "code",
"execution_count": 208,
"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": [
"rcParams['font.family'] = 'sans'\n",
"rcParams['font.size'] = 16\n",
"rcParams['lines.linewidth'] = 3\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",
"\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",
"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",
"\n",
"# label the nodes\n",
"for n in nodes:\n",
" if n[2]>0.8*l: offset=0.1\n",
" else: offset=-l/5\n",
" plt.text(n[1]-l/3,n[2]+offset,'n {}'.format(int(n[0])),color='b')\n",
" \n",
" \n",
"# label the elements\n",
"#for e in elems:\n",
"# n1=nodes[e[1]-1]\n",
"# n2=nodes[e[2]-1]\n",
"# x=np.mean([n2[1],n1[1]])\n",
"# y=np.mean([n2[2],n1[2]])\n",
"# # ----------------->need elem labels<-----------------\n",
"# plt.text(x-l/5,y-l/10,'el {}'.format(int(e[0])),color='r')\n",
"s=5\n",
"plt.plot(r[ix]+ua[ix]*s,r[iy]+ua[iy]*s,'-',color=(1,0,0,1))\n",
"plt.quiver(r[ix],r[iy],falum[ix],falum[iy],color=(1,0,0,1),label='applied forces')\n",
"plt.quiver(r[ix],r[iy],ua[ix],ua[iy],color=(0,0,1,1),label='displacements')\n",
"\n",
"plt.title('Aluminum structure: Scale = 5x')\n",
"plt.xlabel('x (mm)')\n",
"plt.ylabel('y (mm)')\n",
"plt.axis(l*np.array([-0.5,3.5,-1,1.5]));\n",
"plt.legend(bbox_to_anchor=(1,0.5));"
]
},
{
"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": 263,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Minimum area of steel is 2.690mm^2\n",
"Minimum area of aluminum is 7.690mm^2\n",
"\n",
"Displacements of Steel:\n",
"ux1 =0.0000 mm\n",
"uy1 =0.0000 mm\n",
"ux2 =0.0724 mm\n",
"uy2 =-0.0790 mm\n",
"ux3 =0.0161 mm\n",
"uy3 =-0.1487 mm\n",
"ux4 =0.0402 mm\n",
"uy4 =-0.1998 mm\n",
"ux5 =0.0644 mm\n",
"uy5 =-0.1487 mm\n",
"ux6 =0.0080 mm\n",
"uy6 =-0.0790 mm\n",
"ux7 =0.0805 mm\n",
"uy7 =0.0000 mm\n",
"max steel deformation is 0.1998mm\n",
"\n",
"Displacements of Aluminum:\n",
"ux1 =0.0000 mm\n",
"uy1 =0.0000 mm\n",
"ux2 =0.0724 mm\n",
"uy2 =-0.0790 mm\n",
"ux3 =0.0161 mm\n",
"uy3 =-0.1486 mm\n",
"ux4 =0.0402 mm\n",
"uy4 =-0.1997 mm\n",
"ux5 =0.0644 mm\n",
"uy5 =-0.1486 mm\n",
"ux6 =0.0080 mm\n",
"uy6 =-0.0790 mm\n",
"ux7 =0.0804 mm\n",
"uy7 =0.0000 mm\n",
"max aluminum deformation is 0.1997mm\n"
]
}
],
"source": [
"#aluminum to keep deflections less than 0.2mm, copy code above and change area\n",
"#new area values\n",
"AnewSt = 2.69e-6 #m^2\n",
"AnewAl = 7.69e-6 #m^2\n",
"\n",
"print('Minimum area of steel is {:.3f}mm^2\\nMinimum area of aluminum is {:.3f}mm^2'.format(AnewSt*1e6,AnewAl*1e6))\n",
"\n",
"#displacements\n",
"# use solveLU\n",
"F = np.zeros(len(L))\n",
"F[5] = -100 #100 N force down \n",
"\n",
"# 7 nodes each with x and y displacement, need displacement arr of length 14\n",
"# node 1 is constrained x and y (displacements will be 0)\n",
"# node 7 is constrained in y (disp will be 0)\n",
"\n",
"#trick to print x y alternating\n",
"xy={0:'x',1:'y'}\n",
"\n",
"#steel\n",
"bs = F*(1/(Es*AnewSt))\n",
"usteel = solveLU(L,U,bs) #only nonzero values\n",
"us = np.zeros(14)\n",
"us[2:13] = usteel\n",
"print('\\nDisplacements of Steel:')\n",
"for i in range (len(us)):\n",
" print('u{}{} ={:.4f} mm'.format(xy[i%2],int(i/2)+1,us[i]*1000))\n",
"print('max steel deformation is {:.4f}mm'.format(np.amax(abs(us))*1000))\n",
" \n",
"#aluminum\n",
"ba = F*(1/(Ea*AnewAl))\n",
"ualum = solveLU(L,U,ba) #only nonzero values\n",
"ua = np.zeros(14)\n",
"ua[2:13] = ualum\n",
"print('\\nDisplacements of Aluminum:')\n",
"for i in range (len(ua)):\n",
" print('u{}{} ={:.4f} mm'.format(xy[i%2],int(i/2)+1,ua[i]*1000))\n",
"print('max aluminum deformation is {:.4f}mm'.format(np.amax(abs(ua))*1000))\n"
]
},
{
"cell_type": "code",
"execution_count": 269,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"weight aluminum truss is 0.061332 N\n",
"weight steel truss is 0.060958 N\n"
]
}
],
"source": [
"l=0.3\n",
"g=9.81\n",
"\n",
"valum = AnewAl*l\n",
"vsteel = AnewSt*l\n",
"\n",
"palum = 2710 #kg/m^3\n",
"psteel = 7700 #kg/m^3\n",
"\n",
"massalum = palum*valum\n",
"masssteel = psteel*vsteel\n",
"\n",
"weightalum = massalum*g\n",
"weightsteel = masssteel*g\n",
"\n",
"print('weight aluminum truss is',round(weightalum,6),'N')\n",
"print('weight steel truss is',round(weightsteel,6),'N')"
]
},
{
"cell_type": "code",
"execution_count": 272,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Cost of Steel: $ 0.03\n",
"Cost of Aluminum: $ 0.09\n",
"steel truss is cheaper\n"
]
}
],
"source": [
"priceal = 1545/1000 #$/kg\n",
"pricest = 476/1000 #$/kg\n",
"\n",
"costal = weightalum*priceal\n",
"costst = weightsteel*pricest\n",
"\n",
"print('Cost of Steel: $',round(costst,2))\n",
"print('Cost of Aluminum: $',round(costal,2))\n",
"print('steel truss is cheaper')"
]
},
{
"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": 329,
"metadata": {},
"outputs": [],
"source": [
"steel = pd.read_csv('../data/steel_price.csv')\n",
"aluminum = pd.read_csv('../data/al_price.csv')\n",
"\n",
"tst = steel['Year']\n",
"pst = steel['dollars/MT']\n",
"tal = aluminum['Year']\n",
"pal = aluminum['dollars/MT']\n",
"\n",
"# randomize testing/training indices\n",
"np.random.seed(100)\n",
"strand=np.random.randint(0,len(tst),size=len(tst))\n",
"alrand=np.random.randint(0,len(tal),size=len(tal))\n",
"train_per=0.7\n",
"\n",
"np.random.seed(100)\n",
"tsttrain=np.sort(tst[strand[:int(len(tst)*train_per)]])\n",
"psttrain=np.sort(pst[strand[:int(len(tst)*train_per)]])\n",
"taltrain=np.sort(tal[alrand[:int(len(tal)*train_per)]])\n",
"paltrain=np.sort(pal[alrand[:int(len(tal)*train_per)]])\n",
"\n",
"tsttest=np.sort(tst[strand[int(len(tst)*train_per):]])\n",
"psttest=np.sort(pst[strand[int(len(tst)*train_per):]])\n",
"taltest=np.sort(tal[alrand[int(len(tal)*train_per):]])\n",
"paltest=np.sort(pal[alrand[int(len(tal)*train_per):]])"
]
},
{
"cell_type": "code",
"execution_count": 344,
"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": [
"max_N=46\n",
"St_train=np.block([[tsttrain**0]]).T\n",
"\n",
"for i in range(1,max_N+1):\n",
" St_train=np.hstack((St_train,tsttrain.reshape(-1,1)**i))\n",
" \n",
"A = np.linalg.solve(St_train.T@St_train,St_train.T@psttrain)\n",
"plt.plot(tsttrain,psttrain,'o',label='data')\n",
"plt.plot(tsttrain,St_train@A,label='Order Fit: {}'.format(max_N),lw=3)\n",
"plt.legend(loc='center left', bbox_to_anchor=(1, 0.5));\n",
"plt.title('Cost of Steel')\n",
"plt.xlabel('Time (Years)')\n",
"plt.ylabel('Cost ($)');"
]
},
{
"cell_type": "code",
"execution_count": 345,
"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": [
"max_N=46\n",
"Al_train=np.block([[taltrain**0]]).T\n",
"\n",
"for i in range(1,max_N+1):\n",
" Al_train=np.hstack((Al_train,taltrain.reshape(-1,1)**i))\n",
" \n",
"A1 = np.linalg.solve(Al_train.T@Al_train,Al_train.T@paltrain)\n",
"plt.plot(taltrain,paltrain,'o',label='data')\n",
"plt.plot(taltrain,Al_train@A1,label='Order Fit: {}'.format(max_N),lw=3)\n",
"plt.legend(loc='center left', bbox_to_anchor=(1, 0.5));\n",
"plt.title('Cost of Aluminum')\n",
"plt.xlabel('Time (Years)')\n",
"plt.ylabel('Cost ($)');"
]
},
{
"cell_type": "code",
"execution_count": 346,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"---- n=1 -------\n",
"the coefficient of determination for this fit is 0.576\n",
"the correlation coefficient this fit is 0.759\n",
"---- n=2 -------\n",
"the coefficient of determination for this fit is 0.728\n",
"the correlation coefficient this fit is 0.853\n",
"---- n=3 -------\n",
"the coefficient of determination for this fit is 0.728\n",
"the correlation coefficient this fit is 0.853\n",
"---- n=4 -------\n",
"the coefficient of determination for this fit is 0.728\n",
"the correlation coefficient this fit is 0.853\n",
"---- n=5 -------\n",
"the coefficient of determination for this fit is 0.728\n",
"the correlation coefficient this fit is 0.853\n",
"---- n=6 -------\n",
"the coefficient of determination for this fit is 0.728\n",
"the correlation coefficient this fit is 0.853\n",
"---- n=7 -------\n",
"the coefficient of determination for this fit is 0.727\n",
"the correlation coefficient this fit is 0.853\n",
"---- n=8 -------\n",
"the coefficient of determination for this fit is 0.727\n",
"the correlation coefficient this fit is 0.853\n",
"---- n=9 -------\n",
"the coefficient of determination for this fit is 0.733\n",
"the correlation coefficient this fit is 0.856\n",
"---- n=10 -------\n",
"the coefficient of determination for this fit is 0.731\n",
"the correlation coefficient this fit is 0.855\n",
"---- n=11 -------\n",
"the coefficient of determination for this fit is 0.749\n",
"the correlation coefficient this fit is 0.866\n",
"---- n=12 -------\n",
"the coefficient of determination for this fit is 0.738\n",
"the correlation coefficient this fit is 0.859\n",
"---- n=13 -------\n",
"the coefficient of determination for this fit is 0.737\n",
"the correlation coefficient this fit is 0.859\n",
"---- n=14 -------\n",
"the coefficient of determination for this fit is 0.712\n",
"the correlation coefficient this fit is 0.844\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"#Steel\n",
"Z=np.block([[tsttrain**0]]).T\n",
"Z_test=np.block([[tsttest**0]]).T\n",
"Z_train=np.block([[tsttrain**0]]).T\n",
"max_N=15\n",
"SSE_train=np.zeros(max_N)\n",
"SSE_test=np.zeros(max_N)\n",
"for i in range(1,max_N):\n",
" Z_train=np.hstack((Z_train,tsttrain.reshape(-1,1)**i))\n",
" Z_test=np.hstack((Z_test,tsttest.reshape(-1,1)**i))\n",
" A = np.linalg.solve(Z_train.T@Z_train,Z_train.T@psttrain)\n",
" St=np.std(psttrain)\n",
" Sr=np.std(psttrain-Z_train@A)\n",
" r2=1-Sr/St\n",
" print('---- n={:d} -------'.format(i))\n",
" print('the coefficient of determination for this fit is {:.3f}'.format(r2))\n",
" print('the correlation coefficient this fit is {:.3f}'.format(r2**0.5))\n",
" plt.plot(tsttrain,psttrain-Z_train@A,'--',label='order {:d}'.format(i))\n",
" SSE_train[i]=np.sum((psttrain-Z_train@A)**2)/len(psttrain)\n",
" SSE_test[i]=np.sum((psttest-Z_test@A)**2)/len(psttest)\n",
" \n",
"plt.legend(loc='center left', bbox_to_anchor=(1, 0.5),fontsize='10');\n",
"plt.title('Steel: Error in predicted vs measured values')\n",
"plt.xlabel('x')\n",
"plt.ylabel('error in y');"
]
},
{
"cell_type": "code",
"execution_count": 347,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"---- n=1 -------\n",
"the coefficient of determination for this fit is 0.835\n",
"the correlation coefficient this fit is 0.914\n",
"---- n=2 -------\n",
"the coefficient of determination for this fit is 0.853\n",
"the correlation coefficient this fit is 0.923\n",
"---- n=3 -------\n",
"the coefficient of determination for this fit is 0.853\n",
"the correlation coefficient this fit is 0.923\n",
"---- n=4 -------\n",
"the coefficient of determination for this fit is 0.853\n",
"the correlation coefficient this fit is 0.923\n",
"---- n=5 -------\n",
"the coefficient of determination for this fit is 0.853\n",
"the correlation coefficient this fit is 0.923\n",
"---- n=6 -------\n",
"the coefficient of determination for this fit is 0.853\n",
"the correlation coefficient this fit is 0.923\n",
"---- n=7 -------\n",
"the coefficient of determination for this fit is 0.853\n",
"the correlation coefficient this fit is 0.923\n",
"---- n=8 -------\n",
"the coefficient of determination for this fit is 0.853\n",
"the correlation coefficient this fit is 0.923\n",
"---- n=9 -------\n",
"the coefficient of determination for this fit is 0.853\n",
"the correlation coefficient this fit is 0.923\n",
"---- n=10 -------\n",
"the coefficient of determination for this fit is 0.853\n",
"the correlation coefficient this fit is 0.924\n",
"---- n=11 -------\n",
"the coefficient of determination for this fit is 0.852\n",
"the correlation coefficient this fit is 0.923\n",
"---- n=12 -------\n",
"the coefficient of determination for this fit is 0.852\n",
"the correlation coefficient this fit is 0.923\n",
"---- n=13 -------\n",
"the coefficient of determination for this fit is 0.853\n",
"the correlation coefficient this fit is 0.924\n",
"---- n=14 -------\n",
"the coefficient of determination for this fit is 0.856\n",
"the correlation coefficient this fit is 0.925\n"
]
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"#Aluminum\n",
"Z=np.block([[taltrain**0]]).T\n",
"Z_test=np.block([[taltest**0]]).T\n",
"Z_train=np.block([[taltrain**0]]).T\n",
"max_N=15\n",
"SSE_train=np.zeros(max_N)\n",
"SSE_test=np.zeros(max_N)\n",
"for i in range(1,max_N):\n",
" Z_train=np.hstack((Z_train,taltrain.reshape(-1,1)**i))\n",
" Z_test=np.hstack((Z_test,taltest.reshape(-1,1)**i))\n",
" A = np.linalg.solve(Z_train.T@Z_train,Z_train.T@paltrain)\n",
" St=np.std(paltrain)\n",
" Sr=np.std(paltrain-Z_train@A)\n",
" r2=1-Sr/St\n",
" print('---- n={:d} -------'.format(i))\n",
" print('the coefficient of determination for this fit is {:.3f}'.format(r2))\n",
" print('the correlation coefficient this fit is {:.3f}'.format(r2**0.5))\n",
" plt.plot(taltrain,paltrain-Z_train@A,'--',label='order {:d}'.format(i))\n",
" SSE_train[i]=np.sum((paltrain-Z_train@A)**2)/len(paltrain)\n",
" SSE_test[i]=np.sum((paltest-Z_test@A)**2)/len(paltest)\n",
" \n",
"plt.legend(loc='center left', bbox_to_anchor=(1, 0.5),fontsize='10');\n",
"plt.title('Aluminum: Error in predicted vs measured values')\n",
"plt.xlabel('x')\n",
"plt.ylabel('error in y');"
]
},
{
"cell_type": "code",
"execution_count": 363,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Cost of Steel in 2025 : $ 1625950064.89\n",
"Cost of Aluminum in 2025: $ 245131054.52\n"
]
}
],
"source": [
"for i in range(0,len(A)):\n",
" pricest=A[i]*2025**i\n",
"print('Cost of Steel in 2025 : $',round(pricest,2))\n",
"for i in range(0,len(A)):\n",
" priceal = A1[i]*2025**i\n",
"print('Cost of Aluminum in 2025: $',round(priceal,2))\n"
]
},
{
"cell_type": "code",
"execution_count": 360,
"metadata": {},
"outputs": [],
"source": [
"#now steel is more expensive"
]
},
{
"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
}