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{ | |
"cells": [ | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"# CompMech04-Linear Algebra Project\n", | |
"\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": "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": "code", | |
"execution_count": 1, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"import numpy as np\n", | |
"import pandas as pd\n", | |
"import random\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": "code", | |
"execution_count": 2, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"fea_arrays = np.load('./fea_arrays.npz')\n", | |
"K=fea_arrays['K']" | |
] | |
}, | |
{ | |
"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": [ | |
"We look at the smallest value we can perform computations with and in this case it is of the order of $10^{-16}$, thus t = 16" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 3, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"2.220446049250313e-16\n" | |
] | |
} | |
], | |
"source": [ | |
"print(np.finfo(float).eps)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 4, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"The condition of K: 1.4577532625238035e+17\n", | |
"Expected Error of K is 10 m.\n" | |
] | |
} | |
], | |
"source": [ | |
"#Part A:\n", | |
"print('The condition of K:', np.linalg.cond(K))\n", | |
"print('Expected Error of K is', 10**(17-16), 'm.')" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"**Part B:**\n", | |
"\n", | |
"The condition is large because it is ill-conditioned because the boundary conditions are not being considered. Thus, because we are not taking into account Newton's second law (m*a) then we end up with linearly dependent equations and thus incorrect results." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 5, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"52.23542514351006\n", | |
"Expected Error of K[2:13,2:13] is 1e-15 m.\n" | |
] | |
} | |
], | |
"source": [ | |
"#Part C:\n", | |
"print(np.linalg.cond(K[2:13,2:13]))\n", | |
"print('Expected Error of K[2:13,2:13] is', 10**(1-16), 'm.')" | |
] | |
}, | |
{ | |
"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": 6, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"#Given:\n", | |
"E_al = 70e3 #MPa\n", | |
"E_ss = 200e3 #MPa\n", | |
"A = 0.1 #mm^2" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 7, | |
"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\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" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 8, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"L:\n", | |
"[[ 1. 0. 0. 0. 0. 0.\n", | |
" 0. 0. 0. 0. 0. ]\n", | |
" [ 0. 1. 0. 0. 0. 0.\n", | |
" 0. 0. 0. 0. 0. ]\n", | |
" [-0.16666667 0.28867513 1. 0. 0. 0.\n", | |
" 0. 0. 0. 0. 0. ]\n", | |
" [ 0.28867513 -0.5 0.12371791 1. 0. 0.\n", | |
" 0. 0. 0. 0. 0. ]\n", | |
" [-0.66666667 0. -0.17857143 -0.09622504 1. 0.\n", | |
" 0. 0. 0. 0. 0. ]\n", | |
" [ 0. 0. -0.18557687 -0.72222222 -0.08247861 1.\n", | |
" 0. 0. 0. 0. 0. ]\n", | |
" [ 0. 0. -0.42857143 0.12830006 -0.23809524 0.33425542\n", | |
" 1. 0. 0. 0. 0. ]\n", | |
" [ 0. 0. 0. 0. 0.24743583 -0.78947368\n", | |
" 0.18426072 1. 0. 0. 0. ]\n", | |
" [ 0. 0. 0. 0. -0.57142857 -0.09116057\n", | |
" -0.24822695 -0.21650635 1. 0. 0. ]\n", | |
" [ 0. 0. 0. 0. 0. 0.\n", | |
" -0.23339692 -0.875 -0.32768529 1. 0. ]\n", | |
" [ 0. 0. 0. 0. 0. 0.\n", | |
" -0.53900709 0.24056261 -0.59459459 0.28867513 1. ]]\n", | |
"U:\n", | |
"[[ 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": [ | |
"#Part A:\n", | |
"L,U = LUNaive(K[2:13,2:13])\n", | |
"print('L:')\n", | |
"print(L)\n", | |
"\n", | |
"print('U:')\n", | |
"print(U)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 9, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"X, Y Displacements for Aluminum\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", | |
"\n", | |
"X, Y Displacements for Steel\n", | |
"[ 1.94855716 -2.125 0.4330127 -4. 1.08253175 -5.375\n", | |
" 1.73205081 -4. 0.21650635 -2.125 2.16506351]\n" | |
] | |
} | |
], | |
"source": [ | |
"F = np.zeros([11,1])\n", | |
"F[5,0] = -100\n", | |
"\n", | |
"u_al = solveLU(L,U,F*(1/(E_al*A)))\n", | |
"u_ss = solveLU(L,U,F*(1/(E_ss*A)))\n", | |
"\n", | |
"print('X, Y Displacements for Aluminum')\n", | |
"print(u_al, '\\n')\n", | |
"\n", | |
"print('X, Y Displacements for Steel')\n", | |
"print(u_ss)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 10, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"Aluminum\n", | |
"[-2.42861287e-14 -3.03576608e-15 0.00000000e+00 -2.12503626e-14\n", | |
" 2.12503626e-14 -1.00000000e+02 -2.42861287e-14 -1.21430643e-14\n", | |
" -2.12503626e-14 0.00000000e+00 0.00000000e+00] \n", | |
"\n", | |
"Steel\n", | |
"[ 0.00000000e+00 -1.08420217e-14 0.00000000e+00 -2.16840434e-14\n", | |
" 1.73472348e-14 -1.00000000e+02 -5.20417043e-14 1.73472348e-14\n", | |
" 6.50521303e-15 0.00000000e+00 0.00000000e+00]\n" | |
] | |
} | |
], | |
"source": [ | |
"#Part C:\n", | |
"print('Aluminum')\n", | |
"print(K[2:13,2:13]@u_al*E_al*A, '\\n')\n", | |
"\n", | |
"print('Steel')\n", | |
"print(K[2:13,2:13]@u_ss*E_ss*A)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 11, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"#Part D:\n", | |
"#Storing locations of nodes and elements\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", | |
"#x and y coordinates\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", | |
"\n", | |
"#Coordinates of structure\n", | |
"r = np.block([n[1:3] for n in nodes])\n", | |
"\n", | |
"scale = 5\n", | |
"\n", | |
"Ff = np.zeros(2*len(nodes) - 3)\n", | |
"Ff[5] = -100\n", | |
"\n", | |
"uf = np.linalg.solve(E_ss*A*K[2:13,2:13],Ff)\n", | |
"u = np.zeros(2*len(nodes))\n", | |
"u[2:13] = uf\n", | |
"\n", | |
"F = E_ss*A*K@u" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 12, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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JfCEinjxLydgO/psAz9A1L2ADo++cBImx2JbWrQTR58kxEXvjRz9s/7/Psf226mD7MrbCnpc/i33kJfMwcLbYxKKbscfo+fzaTV4iWbfPsJ8xDcnf6jQU24dxktiEtp7hTtKBacYYbw4m50ffm9iW9j6uy973Y1sBHxORRcaY70vlKJUqb8J9O14oJ+wdbEOxd95swAZHB7Efzq8ATfysUxf7C+wv7AdFvtuysV/kd2CbtfdifxH/hk2C2B+I8tleCvYuoJ+csnuxX+avA118ygZ9S7FTPhLbx8NwdH6hm5z5vxew7kZ8bkN35g/H3iac5aw/1Zmf5n7us06BywrY92Ly30Z9xDnfK7Ctd50KWf8s4N/Y4PcI9sttGTaY9b11v8Bzir3T7AXsl5BnO9OBhsGeryDOZ6Dzdp2z7Dqf+Vdh0xccdOo0FdsCs9j+Cx+1nRuxAUWm7/EWdPzYIGCuc96PYAOYx4EqRah/0K87NtB5xalnBrAf+z8xBleeJZ//3enYoOeI81p/BFzsKiPY/0XP/9bv2OCpqr/Xg8CpMfpgfyzscc7jZuxlp9tw5R4K9YT9wbUAGyQedI5zrXOcqQWsszHAcdbDXu780znOn4FBuHJMOeVeoYC8TNgg8rCzbnxJj1EnncrjJMaEoo9qfiJyEbY1pg02APkFGGqM+dxZXgObNLIHtq/BUuBeY8wPPtuJw/Zv6IttiVgJ3G+MKexOEKWUUkqpoIS8z5KIDMD2QVmBvcRxJbZVIMFZLth+Ct2AO7G380djm+Dr+WzudWyK/RHYO9m2AQtFpBVKKaWUUqUgpC1Lzu20P2M7Bz5bQJlLsZew/mGM+cKZl4S9bPaGMeYuZ15LbEvSDcaYKc68KGyz/lpjzD/9bV8ppZRSqihC3bJ0A/ay28sByvwT2OoJlMB758b75E/m+E9sP5p3XOWysUnpLvB3x4hSSimlVFGFOljqgB2HrbeIrBeRbBFZJyJ3uMo0xabt97UaaCAiVVzlNhhjDvopF0PBydaUUkoppYIW6tQBdZ3paexAjuuxfZZeEJEoY8xz2FuCN/pZ15M/pgb2zplk7J0qBZVL9rMMsPmWgFsAEhMT0085pSR36yulVOWyYsWKXcaYmoWXVOrYEOpgKQJ7G+91xhhPNt7Pnb5Mw0VkAvb2X38dqXwHpQy23FGMMZOASQBt27Y1y5cXZ9xapZSqnERkU7jroFQohfoynGe8tU995n+CzRtTB9sy5K9VqIbz6GlNKqzcbj/LlFJKKaWKJNTB0uoC5ntag3KdMk39lDkNm4nYM17TaqChZzgRn3KepHpKKaWUUiUS6mDpXefxAp/5FwB/GGO2Y3MspYqIZ5R5z/hOlzjLPOZj8y9d6SoXhR0s9hNTslHolVJKKaWA0PdZ+hA7hMArziCavwFXYEcUv94pMx+bsfsNERmCvew2HNv65B2jyhiz0hkr61lngMgN2KEIGpI3BppSSimlVImENFgyxhgR6YEdG+0RbP+iNdiBGd9yyuSKSHdgLHZU+Ths8NTZGPO7zyavx44l9Rh2uJNVQDdjzHehOB6llFJKHfvCMjZceaJ3wymlVNGIyApjTNtw10OpUAn52HBKKaWUUhWJBktKKaWUUgFosKSUUkopFYAGS0oppZRSAWiwpJRSSikVgAZLSimllFIBaLCklFJKKRWABktKKaWUUgFosKSUUkopFYAGS0oppZRSAWiwpJRSSikVgAZLSimllFIBaLCklFJKKRWABktKKaWUUgFosKSUUkopFYAGS0oppZRSAWiwpJRSSikVgAZLSimllFIBaLCklFJKKRWABktKKaWUUgFosKSUUkopFYAGS0oppZRSAWiwpJRSSikVgAZLSimllFIBaLCklFJKKRWABktKKaWUUgFosKSUUkopFYAGS0oppZRSAWiwpJRSSikVgAZLSimllFIBaLCklFJKKRWABktKKaWUUgFosKSUUkopFYAGS0oppZRSAWiwpJRSSikVgAZLSimllFIBaLCklFJKKRWABktKKaWUUgFosKSUUkopFYAGS0oppZRSAWiwpJRSSikVgAZLSimllFIBaLCklFJKKRWABktKKaWUUgFosKSUUkopFUDYgyUR+VhEjIg85jO/hoi8JiK7ROSAiCwSkeZ+1o8TkadFZJuIHBKRpSJybuiOQCmllFLHsrAGSyJyNdDSz3wB5gPdgDuBy4Fo4AsRqedT/HXgZmAE0B3YBiwUkVZlWHWllFJKVRJhC5ZEpDowHhjkZ/E/gQ5AP2PM28aYj515EcBQ1zZaAtcA9xpjXjXGfAZcBWwGRpfxISillFKqEghny9JTwGpjzNt+lv0T2GqM+cIzwxiTAbwPXOpTLgt4x1UuG5gJXCAisWVRcaWUUkpVHmEJlkSkA9AfuL2AIk2BH/3MXw00EJEqrnIbjDEH/ZSLAU4qheoqpZRSqhILebAkItHAK8BYY8zaAoolA3v8zN/tPNYIslxyAXW4RUSWi8jynTt3BldxpZRSSlVK4WhZuh+IB8YEKCOAKWB+ccrlY4yZZIxpa4xpW7NmzUBFlVJKKVXJRYVyZyLSAHgQuAmI9elTFOt0+t6HbRny1yrkaVHytCbtBhoEKLfbzzKllFJKqaCFumXpRCAOeAMb8HgmgMHO382xfY6a+ln/NGCzMWa/83w10FBEEvyUOwKsK9XaK6WUUqrSCXWwtBLo7GcCG0B1xgY484FUEenoWVFEqgGXOMs85mPzL13pKhcF9AI+McZkltmRKKWUUqpSCOllOGPM38Bi3/k2ByWbjDGLnefzgaXAGyIyBNviNBzbF+kp1/ZWisg7wLNOx/ENwG1AQ6BPWR6LUkoppSqHsA934o8xJhebjftT4CXgXSAH6GyM+d2n+PXAFOAxYAFQH+hmjPkudDVWSiml1LFKjPF3M1nl0bZtW7N8+fJwV0MppSoMEVlhjGkb7nooFSrlsmVJKaWUUqq80GBJKaWUUioADZaUUkoppQLQYEkppZRSKgANlpRSSimlAtBgSSmllFIqAA2WlFJKKaUC0GBJKaWUUioADZaUUkoppQLQYEkppZRSKgANlpRSSimlAtBgSSmllFIqAA2WlFJKKaUC0GBJKaWUUioADZaUUkoppQLQYEkppZRSKgANlpRSSimlAogqrICIxACXAd2AM4G6QBzwF7AW+BJ4xxjzUxnWUymllFIqLAoMlkQkARgCDARqAD8D/wV2AoeAZKAhcAfwkIh8DTxgjFlS1pVWSimllAqVQC1L64HtwAhgljHmr4IKisjZQF9goYjcZ4x5pXSrqZRSSikVHoGCpduMMfOC2YjTmrREREYBaaVQL6WUUkqpcqHAYCnYQMlnnR3AjhLVSCmllFKqHNG74ZRSSimlAij0bjgPEekGXAnUx94N52aMMR1Ls2JKKaWUUuVBUC1LIjIU+BDoDiQCOT5TbllVUCmllFIqnIJtWRoIvAIMNMbklGF9lFJKKaXKlWD7LFUD/q2BklJKKaUqm2CDpYXY7N1KKaWUUpVKUS7DvSsiBvgE2ONbwBjzW2lWTCmllFKqPAg2WDLAPmAM8FgBZSJLpUZKKaWUUuVIsMHSVKA9MB5YAxwpqwqpissYg4iEuxrHDD2fSilVPgQbLHXC3gk3teyqoiqqzZs307VLF35dt46LL76Y1q1bh7tKFdratWuZPXs2xhiGDh1KTExMuKtUoWVmZvLT0qX0GzCAXn37hrs6SqkKSIwxhRcS2YgdK+6jMq9RiLVt29YsX7483NWo0Nq1a4eeQ1URfPfdd8TEtObUUyFCxy8oNhFZYYxpG+56KBUqwX5cTABuFxH9eFH5GGPYv39/uKuhVFB69BhNu3YaKCmliibYy3A1gGbATyLyKUffDWeMMSNLtWaqQli4cCFr1qzxPj8bmAE0BK6lJ3+RQM9rY8lOjCMzNpbMOPto9NvKr3HjxpGRkXHU/NGjR4ehNhWL5OQQe+QIsYcPE5eZyfrv97J66RtUA9oC64GXNs8jJWUJ9p2qlFLBCfYyXGHDmRhjTIW8G04vwxVfdnY2rVq1YvXq1d55hb+bHImJkJQE1arZx4L+DrQ8Ph6OoQ7QCxYsoHv37n6XLVmyhPbt24e4RiFiDBw6BBkZsHevfSzo70DLDxwodFf/Ap6odgZ//71UO8+XgF6GU5VNUC1LxhhtBlBHmTp1qjdQqlKlCuc0agSrVgW38oEDdtq6tfgViIoqXrDlnle1qt1OOXDjjTe6niUB2YANAPr06cOGDRvCUa3AsrNtoFLUwMb3MTs7JNW9Axi39xtmzZpFr169QrJPpVTFVz6+JVSFs3//fh5++GHv89ath9H/q2+Bo4OlJbSnfrUMGiQ5X4779tnWhJLKzobdu+1UEr6tXMUJwErYyjV+/Hh27NjhfX4co9hFJHAXABs3bmT69On079+/ZMfq4W7NKU4rThFac0JGxAa/SUms27mTHYcP0wwbdnpUBZ4Chg0bRo8ePYiNjQ1PXZVSFUpQl+G8hW27dR0gzndZRc3grZfhimfkyJHefjSpqamse/FF4nr0OKpcNhEks5sDEUkcOQKRkUBuLuzfX/yWCM/fmZkhPuoA3K1cRbycmJ2YyAnNm7Pj8GFygBPj4rjg8NNMZCDVqE0mO8gEkpKS2L17NxG5uf5bZ4py7kLYmhOU2NiSX5atUgUiIli8eDGdO3fmOGA7/rPldgT+OXYs9913X2iP8xihl+FUZRNsn6UU4EWgJwW0Rmmfpcpjy5YtNG7cmEOHDgEwY9Ik+j75JKxfD8BchEsx3i+pWVxBL/7NtdfC1KmlWJHMzOL1cXHPK61WrlKyH4iJjiYiK4co8roK/oxtITkuOpqYrKxwVe9oIjZQKUmrXLVqNlgqJQ0aNOD333/nfcDTAyybSD7iQi7hAwB+AjolJfHz+vWkpKSU2r4rCw2WVGUT7GW414HOwAtoBu9Kb8SIEd5AqVWrVvTZvNkbKFG9Or/fdhvzn3iCnk75y5lDdXbzxhvJvP6607pUGmJjoWZNOxWXu5Ur2ADL39+l1MpVBcBPMHSq54/SDJQ8rTkluQTptOaUF5MmTeL333+nNnCRa/67Mb2498iT/CNiMYm5+zkNuDEjg8cee4zx48eHqbZKqYoi2JalDODuYzGDt7YsFc2qVato3bo1nvfN0ilTOPOWW/K+xF9+GQYMoHFKCmt27/a2Ls3jUnoyj4ED4fnnw1P3MuVu5SpCC9eGVauI3L+fakA1gkt8lgtElKQVpwxac8qD3NxckpKS2L9/Px8DF3gWREXxyD17GDW2Cu92fJYeX94LwCGgVVQUC37+mZNOOilMta6YtGVJVTrGmEInYANwYTBlK9qUnp5uVHByc3NN165dDTZDgLn4oouM6dzZGHshy5gzzzQmJ8cYY8zcuXPNTM98MDlgjmOHiYoK80GUIz/++KP3XALmmt69jcnIMKZBg7xz6poeBlMFTASYTZs2hbv65c6gQYMMYFKd95v33F13ncnMNCYy0pjPFmaZ3FatvMs+AHP5ZZeFu+oVDrDclIPPb510CtUUXCEYBLyH0xJ1LE0aLAXvo48+8n6xR0REmD/+9S/j/UKKjDRm5cp85Vs3amSyXF9ae87uZlJSjBk9OkwHUM40a9bMez5jYmLMoUOHjDl0yBgR7znLdZ2//WCinPJnnnlmuKtfruzbt89ERUUZwHzmDpSioow5cMAYY8yVVxqTlWWMWbbM5LrOcU8wX3/9dXgPoILRYEmnyjYF1dnAGPMM8Cs2g/fzIjLaZ3qk1Jq6VLmUnZ3N4MGDvc/v7t+f1GeeyStw993QsmW+dSbPns1M1/NqSz5m1/+2cscdZVzZCmDBggX8+OOP3ufDhg0jLi4O+vb1djg3wI286k30mQi85vy9bNky/vOf/4SyyuVa3759yc7O5gRs50qvG26AhAQA3njDSal1xhnIrbd6i0wAHr7nHowpPx39lVLlTDARFbav5CFsdwl/U06Q27kCmANscra3FngCqOpTrgb2e2EXNivfIqC5n+3FAU8D25ztLQXOLUq0qC1LwZk0aZK3FaRKlSrmQP/+xvvrvV49Y/bu9bveheecY464fukfPvfcENe8fMoswZwAACAASURBVDr++OO957NGjRomJyfHmDVr8rUqGTCQaxZzrvd5DpgGznppaWnhPoxyYd26dUZEDGC+dLcqxcTYljp/9uwx2Skp3rLjwMycOTO0Fa/A0JYlnSrZFFwhewfc/wHNgehi7wyWAbOAPthUJ/cAfzvzI5wyAnwF/AFcDXQDvnQCp3o+23vTWf9moAsw1wmaWgVbJw2WCrdv3758X+6TBwzI/6U+d26B6+7YscNMdn2B5YIxlby/zbhx4/L1VXrrrbfsgtNOM+5AyYCJjThiktlpsoj0zlvhWnfatGnhPZhyID093QCmkc9lSzNwYOAV33zTWzYbzEV16pjDhw+HptIVnAZLOlW2KbhCcBA4v8Q7g5p+5vV3Pvj/4Ty/1Hne2VUmCdgNTHDNa+mUu941L8pprZofbJ00WCrciBEjvF/ODerWNTnNmxvvF1L37sbk5gZc/+a+fU2m60tsbyU+51lZWSY+Pt57Phs1amQXzJxpjE+gZMA0StxqwJhnuMc7LxfMRc76SUlJtlWqkvriiy+85/I/7nMXG2tMZmbglXNzzZGOHb3rLAMz7qmnQlLvik6DJZ0q2xRcIVgCXFcmFbApZAzQz3n+OrDFT7lpwCbX84ex+Z4SfMo9AmQCscHsX4OlwP744498X+7/vfpq4/1Cio83ZsOGQreRmZlpJkXmtYzkgjG//Vb2lS+HBgwYkK9V6ZtvvrF3EFarlndeo6O9f9/d+H3nzxyTEZHknb/TtY0HHngg3IcVNvXq1TOAOdW3VWnQoOA2sHatyXa9N++Njze7du0q20ofAzRY0qmyTcFmk7sLGCwiZwdZvig6Oo8/O49NgR/9lFsNNBCRKq5yG4wxB/2UiwE0cUopePjhh70JKC847TTazp+ft3DECEhLK3QbMTEx7B45Ek/aRgF2XXRRoFWOSbt37+a1117zPj/77LM5/fTT4d57be4lj9NO43POZRfVeajpe87MCG5hkrez93HAo87fTz/9NAcP+v4bHPsmTZrEH3/8AdhfUt6R+eLi4Mkng9vIySfDsGHepyMOHWK867lSSgFBtyz9DmQAOcBeYLPPtKk4kRqQCvwJfOqa9wsw00/Zm7C/pOs7zz8Blvkp19Upd06A/d4CLAeWN2jQwCj/Vq5c6e04C5gd55xjvL/cTzut8MscPl6Ji/Ounwu2Q3Mlcv7553vPpYiYLVu2GPPnnzbtgue8tmljTJcu5gVuNZBrhJx8V+Z+IK9f0xEw1ZztXXnlleE+vJDKyckxVapUMYBp4duqNGxY0TZ26JDZV7u2d/03Rcwvv/xSNhU/RqAtSzpVsinY4U4+cz7kS43TQvQekA1c715UwL58h3QPttxRjDGTgElgM3gHU9/KxhjD4MGDMcaenlFt21Lrq6/yCkycCDExRdpmzalTOdy7N3HYF+mPrl2p9/vvpVfpcmz16tV88skn3ue9e/embt26cO65kJNjZ4rAu+/CDTdwBy8zmHEcJiHfdnryLms5hQgM0cA7wIXA7Nmz2bx5Mw0aNAjZMYXTkCFD2L9/PwBTcf3Tx8fDmDFF21hcHIlTp0K3bgBcYwyP3HgjI//v/0qptpXTihUrGkdFRT0gIi2NMdUJLkG9UqGWKyLbs7OzH2nTps3CggoFNdxJaROROOBDoBXQ0Rjzg2vZN8DfxpgLfNYZCjyJTTOwX0Tewd711sSn3FXY75BmxpjVhdVFhzvx7+OPP+bCCy8EIFGE3XXqELN1q114/fUweXKxtjs5OZkb9uwBbKSb9f33xLRqVRpVLteaNWvG6tX27RgTE0NGRgZxy5fDOefkFfKMNNy1K3z2Ge9xMT14H9/4f27UlfTMng3Yc9gW+A4488wzWbp0aSgOJ6z27dtHcnIy2dnZtAX+i+sMjRwJo0YVa7t/nX8+KZ9+Ctjm7V2ffUb7f/yj5BU+BhU23MmKFSsujI2NnVC7dm2qVat2IDo6Oluk0N+xSoVcbm6uHDp0KG7jxo0xmZmZAwsKmEIe6YtINDbX0unARe5AybEa2x/J12nAZmPMfle5hiKS4KfcEWBd6dW6cvFNQDm7Zcu8QCk5GZ56qtjbbvPJJxxy/hZgS5cuxa9oBbFgwQJvoAQwfPhwm4Cyd++8QgkJ4OrPBHApC0iKOrov0tDaM7zjugnwb2f+smXLWLJkSWlXv9zp168f2dnZAEzBFSglJtp+dMWUMm0aB6OjATgZ+LF/f8LxY/JYEB0dPTQtLS3ruOOOy4iJidFASZVbERERJjEx8VBaWtqRqKiokQWWK2iBiPQsaFmAdeqIyJkBlkdgcyN1AS41xizzU2w+kCoiHV3rVQMucZa5y0UDV7rKRQG9gE+MMaUzDHwlNGXKFO+Xe9v4eC5wZZrm6afhuOOKve1Wbdsyx3WpKG33bnYtWlTs7VUEN954o/fvGjVqMGLECBg3DrZsySv0zDNOeun8Pv/H6KPmJdeNy3ep6URsojGwmayPZevXr2e+c5PBWfj8qnrwQYgowe+/OnU49NBD3qf9t2zhw+eeK/72KjFjTFpiYmLlu+tAVVjx8fGHjTG1C1oe6JPlRRFZJSK3ikhyoJ2IyDkiMgnbmtMi0Daxwc1Y4ICInOma6jll5mMzcb8hIr1F5AJnngDeJg1jzErs5bZnReQmEekCzAQaAgVGhyqw/fv38/DDDwP2hM+pVQtxfsXToQNcd12J93H+N99wwPlbgD09epR4m+XVM888w44dO7zPX3zxRSKOHLFf7B4NG8KAAX7Xb5O8mbp188876STgvvsgNdU7bzz2n3njxo1Mmzat9A6gnOnVq5e3tWcyrlalqlXh/vtLvP2UBx/k99r28zIOqDZ8OJmHD5d4u5WQaGuSqkgiIiIMAWKiQMHSSdjLZaOBHSLyPxGZISLPiMgTIvKyiHwiIruBxUBj4Dyn83RBLnQeH8QGRO7pJgBjTC7QHfgUeAl4F3sXXmdjjG9v4OuxLfGPAQuA+kA3Y8x3AeqgAnj66ae9X+73VK9Og02b7IKoKNupuyS/3B21atfmE1c/pZMOHGDNjBkl3m55k52dzUOulopGjRpx9dVXQ79+kOlq+Jw9O+B2vvkm//N27Zw/ZuaNvOceN+7uu+8mNze3+BUvpxYvXsyKFSsAOBfI11lx5MhSeW8SGUn1t9/G6XLPOYcP8+lNN5V8u0qpCq3ATxdjzEFjzGjs7f19sbfapwM3APdiL4tFAs8BTY0xnY0xAUf2NMakGWOkgGmUq9xuY8wNxphkY0yCMaaLMWaVn+0dMsYMMsbUNsbEGWPOMMYsLvppUABbtmzh6aefBiAZeNzTogS2JaNZs1Lb18VLl+LpfCZAxDH4hTRw4EBvjiqAt99+G375BebMySt0/vnQpk3A7dSrB6eemvf8vPOcPzp0yNdB/FqgAZCRkZEvSDtW9OvXz/v3ZJG8VqXq1e37s5RU7dSJHzp6ewHQ9q232L1hQ6ltXylV8RT6U8wYk2WMeccJXk4zxlR3ApNUJ4h5xBizJhSVVWXLnYDyteRk4pxbsznhBHAuzZWWmLg4lp9/vvd54yNH+Pyxx0p1H+HkLwFlu3btoGdPm80HbGvdO+8Etb3//jfv76bujjpz50JkJGD/mec6s8eOHXtMJap0J6DsApzo7ng9+uh+XSXVdM4cdjjntbYx/NizyF04VUFE0sM6VTBr166NEZH0CRMmpHjmXX755WmpqanNS2sfgwYNqitBnJu9e/dG9OjRo2FycnJLEUm/4YYb6pdWHco7zXuhAFi1ahVTp04F4Gyg5+7deQtfeMHeaVTKOn30EZ681QLUH3nsdDW7+uqryXHyJ4kIs2bNglmz4Kef8goNHWpbRYJQpUr+LANexx0Hd9zhfdoGuAjIysriulLoX1Ye5Obmcp+r5WhyZGReq1JyMtx5Z6nvMzolhU333ut93mHVKjbPnRtgDaVCZ/To0dtmzZoV8ju+n3rqqZoffPBB8ujRo/9YtGjRmmHDhu0ofK1jgwZLKl8CyijgzSpV8hb27Andu5fNjiMi2Oj6Qj8pN5cZN9xQNvsKId8ElFdffTV1a9eGW27JK5SSAo8+6mftgn3+uQ2ajjJ+PCQlATbonOrM9iSqrOjcCSgvAup7kngCPPFEme233ZNPsqxGDcB+UGbdeGNeAlGlwqhp06aZZ5999qHCS5auNWvWxNesWfPIwIED/+rSpcuBk08++UhJtnfo0KEKcxeABkuKhQsXssi5fX+QCCd4Lr8lJkIZ3zrdYsoU9jodcwU4a8oUjhwp0f9f2PXq1cv7d0xMDK+//rrtU5ORkVdo6tQid0iOioLvv/ezICICXnnF+7QmdjRpYwxXXXVVkfZR3uzbt48JEyZ4n78eHZ3XqlSzZv4AtJRJRAQJr7/uzQvW6O+/WV+KfaNUxfLjjz/G9ujRo2FqamrzuLi4NvXq1Wvep0+fBjt37ox0l7v88svTjj/++BaffvppYrNmzU6NjY1tk5qa2nzMmDG13OUmTJiQIiLpH330UZWuXbs2SkhIaF29evVW/fr1a7B///6AQYS/y3D79u2LuO2221JTU1ObR0dHt0lNTW1+//33187xCfCXLFkSn56e3iQ2NrZNrVq1WgwZMqROMPnERCR9zpw5Kdu3b48RkXQRSf/ggw+qAqxatSr2vPPOa1S1atVWcXFxbVq2bHnK7Nmzq7nX91zq+/bbb+M6dOjQOCEhoXX37t1P9CyfPn169TZt2pySkJDQukqVKq2bN29+6ptvvpnkWZ6VlcXw4cNrN2zYsGlMTEybWrVqtbj55pvrHTx4UNxl7r777rr169dvFhsb26ZGjRot09PTmyxcuNDfz8wiCXa4E3WMciegPAF4NDISPB27H3kE6pf9JemMIUOo5gx82ggYe/HFDHEyKVc0H3zwwdEJKPfvh+efzyvUunWxW+tOKmh46F69bN8d5zLfMOBp4JtvvmHJkiWcfXZZjIFd9twJKC8Damdl5S10bkYoSy169mRWixZc9b//AVD7+ecxQ4YgrrQNqnL4/fffo1NTU49cccUVv6ekpGT/+uuvsc8880yd8847L2HlypX5+u0eOHAgsl+/fo3uuuuubSeffHLm22+/nfzQQw/Vr1q1as5dd931l7vsDTfc0PCSSy7Zc/vtt69ftmxZ4vjx4+scPHgwYs6cORuDrVtWVhadOnVqvH79+vhBgwZtbdmy5aH//Oc/ic8++2zd3bt3R7366qt/AGzbti3qwgsvbHLcccdlvfDCCxvi4uLM+PHja2/durXQsasWLVq0ZtSoUXXXrFkTP3PmzPUArVu3PrRx48boTp06nZKYmJj75JNPbq5evXrOxIkTa/Xq1avx22+//etVV121172dyy677KQ+ffrsGjp06PYI5wfjmDFjaj300EP1u3bt+vdLL720vWrVqrnLly9P2LBhQ6xnvZ49e5742WefJd1xxx3bO3TosH/16tXx//rXv+pu3rw5duHChesBHnroodqvvvrq8cOHD9/Spk2bgxkZGZHffvtt4q5du/IFtMUS7sHpwj2lp6ebymzSpEnewV0/dA/o2qKFMUeOhKwef0dFeff9G5ht27aFbN+l6fjjj/eezxo1apicnBxjzj0377yKGLNxY+CNdOmSV7537+B3vmaN3b6z7odOPdLS0kp2UGGybt26fAM573INxGxq1w5ZPTasWWN+dp3XTWeeGbJ9l1cUMpDuypUrNxpjlvud3IMeh2MqqF5FnI4cObL8448/XgOYr7/+erVn/mWXXbYLMK+88sp6d/mzzjoro06dOpk5OTnLjTHLn3vuuQ2Aufrqq/90lxs6dOgfERERZtWqVT8YY5avWbPmf4B57rnnNrj3Ubdu3UzP8xdeeOE3wHz44YdrfLcVFRWV+8cff6w0xiwfOHDgtqioqNxffvnlf54yGRkZ31WvXj2LIM7NP//5z7/c+zXGLL/55pu3R0ZGmh9++OEHz7ysrKzlJ5xwwuFTTz31gGfevffeuxUwo0eP3uxe/6+//vouISEh57zzzttT0H4/+uijNYB5/vnnN7jnv/TSS78BZsmSJauNMcs7der0d6DtFDY571u/72m9DFeJuRNQXgpc6G6uffllcIZ+CAmnZQkgDXi2a9fQ7buU+E1AuXQpuAdk7dfP3l1YFpo0gcsu8z7thh18saImqnQnoLwmIoIUd3LI8eNDVo+0Jk340nVptcGyZRx5//2Q7V+VD4cPH5Zhw4bVbtiwYdO4uLg2MTEx6d26dWsCsHr16jh32cjISK699tq/3fOuvPLKPdu2bYvZsGFDvg/W3r1773E/79+//57c3Fy+/vrroO+qWbhwYVLdunWPdO3adX9WVhae6aKLLtqbnZ0tixcvTgT49ttvE1u2bHmgcePG3r4O1apVy+3SpUtGwVsPbOnSpVVbtmy5v1mzZt7kcVFRUVx22WW716xZk7B79+58cUbv3r3znZfPP/+8ysGDByNuueWWnQXtY8GCBUnR0dGmf//+e9zHd+mll+51tlEVoE2bNge+/PLLpDvvvDN14cKFVQ4fPlxqfaKCCpZEZImI9BOR2MJLq4rCk4AyEXgp0tVKecstcNZZIa1L0qBB7I2znzcC3L56Nd99V3FyixaYgNL1JUt8PLz6atlW5I038o0b50l3WdESVX7xxRfeBJQAE+Nc30V16+YfVy8Eek2cyDsxeVcqDl53HRwKef9aFUZ33nln6rhx4+peeeWVu2fNmvXr4sWLf542bdp6gMOHD+f7Lq1atWp2bGxsvo5AtWvXzgLYtGlTvktedevWzXI/r1evXhbAli1bCr005rFr166orVu3xsTExKS7p06dOp3qWQ7w559/RtesWTPLd/1atWodNS9YGRkZkf7Wr127dpYxxrtvjwYNGuQru3PnziiAE044ocDOqjt37ozKysqSpKSk1u7jS01NbQnw119/RQE8/vjj2wcPHrx14cKFSd26dWuSkpLS6oorrkjbtm1bibscBbuBLGAadmiRacAko7mVKjR3AspRQF1Pq1LNmmV6h1EgCS++CM44ag2Ap7p3p41nAN9yzm8CymeeyT/+27hxEBP051/xxMXBY4/BkCGA7QN2E/Cak6jy8ccfL9v9l5L+/ft7/74lNpZq7pxRL7wQ8vpUr16dfSNHsufBB6kBVN+9m4MPP0zC2LEhr4sKj/feey/5sssu++upp57a5pn3/vvv++0Ls2/fvqjMzExxB0zbt2+PhqODgq1bt0YD3mbTP/74IxogNTU16DtdkpOTc1JTU4+89dZb6/0t97Qk1apVK2vnzp1HXTL4888/i30ZISkpKcff+tu3b48WEWrWrJntnu8MK+JVq1atbIDNmzfHtGvXzu/YQsnJydmxsbHmk08+8Rt3eAKw2NhYM2bMmO1jxozZvnnz5qjZs2dXHzFiRP2bbropYsGCBb8V9xghyJYlY0wn4FRswNQfWC0ii0Wkl4iE8FqNKi2eBJQtgHvcC8aNs7lrwiDqhhvY77o3fvi2bcwuZCiQ8sBvAsrmzeGBB/IKpaXBbbeFpkKDB+MeUO5Z7D96RUlU6U5ACfCs+3Jw/fo2nUUYXDtkCM/UyruhKWb8eFijvxkri8OHD0dERUXl+6KfPHlyir+yOTk5TJs2LV8StX//+9816tSpc6Rhw4b5WlZmzpxZw/18+vTpNSIiIujQocMBgnT++ednbN++Pbpq1aq555577kHfqU6dOtkA7dq1O7Bq1arEdevWef+p9u7dG/HZZ58lFbz1wNq3b79v1apViWvXrvX+EszOzmbevHk1Tj311IM1atQI2KT9j3/8Y39CQkLupEmTahZU5qKLLtqbmZkpe/bsifR3fGlpaUe1bDVo0CB70KBBu9q3b7937dq18cU9Po+gm6aMMWuBQSIyHLgKuAV4C9glIlOwrU0litxUaHgSUArwMq43QadOEOZR66u89pr3Eksq8Mn113PFFVeEtU6F8ZuAsn///OO//fvfoa3U22+DM2RHIvAqcKOTqHLWrFmhrUsR+CagHFqjBvF7XF06Jk4MQ62s6Oho0idOZOnll3MWEJWby8HrriNh6VLQQWOPeR07dsyYO3duyr/+9a9DJ598cubs2bOrr1ixwu8t6YmJibkjR46st2vXrqgmTZpkvvXWW8lLly6tNmHChI0RPilDvvjii6QBAwbU69at295ly5YlPPPMM3V79uz5V4sWLTL9bdufAQMG7J4xY8ZxF1xwwcm33377jtatWx/MzMyUdevWxS5YsKD6xx9/vL5q1aq5DzzwwI5p06bVPP/8808ePnz4Vs/dcL6XDIti+PDhO2bNmpXi2WZSUlLOyy+/XHPTpk1x77zzzq+FrV+jRo3cBx988I8HH3ywwQUXXNDommuu+atatWq53333XXxcXJx58MEH/+zevfu+7t277+7Xr1+jAQMG7DjzzDMPRERE8Ntvv8V8/PHHSePGjfujRYsWmV26dGnUvHnzQ+np6QeTk5OzV6xYkfDVV19Vu+aaa3YV9/g8inwdzxiTCcwQkdXAM9gxLYcCg0XkXeBOY8z2klZMlQ1j8hJQ3gx4eyZFR9svonB/6PfqxaHbbyfeySA+ev9+xowZw4MPPhjeehXAbwLKAwfyD4573nnQtm1oK3buuXbsuK+/Buy4cSPJS1TZoEGD0NYnSO4ElACPuccnbNgQLr44DLXKc2nPntzQujXtvv+eKCDhm29sPzHXuHWqEMasKLxQ+TNp0qTfb775Znn88cdTATp16pQxY8aM3zz9gtwSExNzpk+f/tu9997b4Ndff41PSUnJevTRR3+/8847//ItO3ny5A1jx449vk+fPo2io6NN7969d02cONF30PiAYmNjzZdffvnLQw89VGfatGnHPf7447Hx8fG59evXzzz//PMz4uLicgHq1KmT/eGHH/5y99131x84cGDDpKSk7GuvvXZndna2PPvss3WKc17S0tKyFi9evOa+++6rN2TIkAZHjhyJOOWUUw6+8847v15xxRV7C98CPPDAAzvr1KmTPX78+OMHDBhwYlRUlDnxxBMPDR8+3HvJc968eRsef/zxWm+88cZxEyZMqBMTE5Nbt27dI507d96bmpqaDdChQ4f98+bNqzF16tRahw8fjqhdu/aR2267bccTTzyxreC9B0c8d5sEVVgkHrgauBU7qO4abOPEv7ED644C1hhjupS0YqHStm1bs3z58nBXI2Q++ugjLrroImoCawFv++9DDxU5o3SZefddzGWXeZMP3hQZyUsHDxJT1v19iqFZs2bevEoxMTFkZGQQ17YteHItRUXBzp1BD2sCQNeu8Nln9u/evW0rUXH8+ae9HOe0ei0H2gFnnHEGy5YtK942y9DevXtJSUnx5lV6sl49hroux/HJJ65RhMPn22+/5cvTT2ew8/xI9erErF8ftsvX4SAiK4wxBf4CWLVq1caWLVuW+Nd8RXT55Zenff3119V27Njxv0DlJkyYkHL33Xen/fDDDz+67yRT4bNq1arjWrZsmeZvWbB3wzUXkReArdjgaBPQ1RjT1BjzvDFmuzHmVWwQVTGz31UC7gSUY3EFSieemL9/Tbj17ElW7drep0/k5HBLGWZqLi6/CSjnz88LlMB2tC5KoFSaatWC22/3Pk3HphPwJKosb/r37+8NlAS4z53xvHHjchEoAbRr146frrwSz0//mL//xgwfHtY6KaXKVrB5llYBPbB9RU8wxlxpjPnCT7l1wNLSqpwqXVOmTOGnn36iE7aXvteLL9rb2suRmNdfx9PmWROImzaN7dvL19Xdm266yft3jRo1GPHQQ/mH30hOtnemhdOzz0I1O+qAANOd2X3D3DfN1/r165k/f773+etNmxK5b19egbJOuVBEI556ikFReb0YZNIkWKoffUodq4INlq7EBkmPGGMKvPZnjPnZGNO5dKqmSpMnAWUMkK+L7FVXQbduYapVABddRK6rX80YoHeIc+sE4puA8qWXXiJiyJASj/9W6iIiYNIk71PPuHHlLVHlVVdd5U1AGRURwXWbNuUtPOUUb2f18iItLY0T772X+a55uQMG5A0VpCqtOXPmbCzsEhzAXXfd9ZcxZoVegqsYgk0dMMcYo8Nth8vatSXehCcB5WDgFM/MqlVDmgm5qCJfe83bupQCNP/yy3KRqNJfAsreXbsePf7bJZeEoXZ+9OoFp+b1QR0GVKH8JKr84osv8r2u8886C3F18mby5DDUqnDDH3iAEdWr47m/O+KHH8A16G+x7KqU3XyUKvd0uJPyLjcXevQo0SY8CShPBB5yLxgzJl8+nnLnvPMwrpFjHwWudmfEDhO/CSivuMLbkRoRePfdMNWuAO++673TMQZ4B8hwElWGmzsBZdXERLqtXJm3sFmzkGeTD1b16tW56dFHecQ1z4wYAb8X6Uam/LTvk1LlkgZL5d3cuTbxnfuuoCLyJKB8AfD2TEpPz9f5t7yKcPVdqg50X7curIkq/SagPHIEvvwyr1DfvmU3/ltxNWmSL5njhUBLwp+o0jcB5eLOnZEDrlx8U6aEoVbBGzBgAB+cdBI/Os/lwAG4++7ibWzHDnj9ddi4sbSqp5QqJRoslXevvGIfi3m5zJOA8grsFyRgWxhefhki/WbqL1/OPRc5xXvhkJHArWG8M85vAkp3X6r4eHAFU+XKjBn5xo2bA2RlZXHttdeGpTq+CSjrp6bSxpMyAaBVq9Dnpyqi6OhoHn/6aW51z3z3XSjOQLsLFoAxxVtXKVWmNFgq7zx32MybV+RVPQkoqxjDc+4Ft99e7r+E8pk82du6VA0YsGcPY8aMCXk1/CagnDkzf6tfKMZ/K66EhHy5tBoBNwBz5sxh8+bNIa+ObwLKrzt2zD84bTnqgB7IpZdeSsQ555AvRL7zTjgQ9GgVlidI0mBJqXJHg6Xy7Mcf8z5wpvhkGAAAIABJREFUN2yAI0GPqwjAxx9/zKJFi3gU8PZMql3b9lWqSM46C2ne3Pt0OPDoI49wpIjno6R6ufpLxcTE8PqLL4I7s/gJJ4Ru/LfiGjIE6uQl6n0OEGO46qqrQlqNvXv3MsHVGbpd69Y0mDs3r0DbttCiRUjrVFwiwrhx47gf8HbP3rSpaEleDx+GTz+1fy9eDHuDSnyslAoRDZbKs2eeyfvbmCL13/AkoGwDDHQvGD8ekoo9ZmL4uFqXqgDDs7JCmqjSbwLKW2+1X3IeoR7/rbhmzvT+WQWYROgTVeZLQCnCJ61b5z+X06cXsGb51K5dO7pdc403qzeAGTfO/uAJxuLFeT+MsrJstnKlVLmhwVJ59vHH+Z9PnRr0qlOmTGHNTz/xMuDtmXTeefY28oqobVukVSvv0yHAjBAmqjwqAeXVV4N7QNrzzoN27UJSlxLzjBvnuA6oB/Tp0ycku/dNQHn5JZdQ/Y038gqceWa+VAcVxZgxY5gZE4Onq79kZ9uWxmDSM/heejuGL8WJkB7OqbSP5/TTT29y+umnNwH44IMPqopI+gcffFC1tPdTltuuqGbMmFF91KhRx4diXxoslVd//w3bfPJ/fv99UKt6ElDeih0LDLAde198MfwD5ZbEtGne1qUEQpeo0jcB5cSJE4m44grb2gd2/Dd34FQRzJnj7eAfCcwFNm3aFJJElfkSUEZF8Wbt2vkvMVewViWPtLQ07r7nHm4Hsjwzv/668B85/jp1f/hhXioKVWG0b9/+wKJFi9a0b9++iB3WVHHMmzev+sSJEzVYqtReeOHoeZmZ8H//V+iqTz31FLJjB4+7Zz7wgB1fqyJr0QJxdUy/G/iqjBNV+ktA2SsyMv/llcGDwzf+W3HVqpWvf1Vb4ALKPlHl559/nu/1GjxwIDHuy8vnnFOh36fDhw9nR0oKY90zhwwJnGzyf/87OjfTrl3wzTdlUUVVhpKTk3O7dOlyIDk5OfzZXlWp0mCpvCqopaKQDMFbtmxh7NixPAN4eyadfDLcf39p1i58pk/3ti7FA09j70orK0cloHzzTbj55rwCyckVr8O8x3PPHTVuXFknqnSnKahatSpj9u2zfXQ8KsgdcAWpXr06o0aN4lFgg2fm7t0wdGjBK33wgf/5x/CluIpq0qRJNRo2bNg0JiamzUknndR0+vTp+X4l+btUNmfOnGqtW7c+pWrVqq0SEhJap6WlNRs8eLD3LotBgwbVFZH0//73v/FnnHHGyfHx8a1r1qzZ4p577qmbU0jr4ty5c6t17NjxpJo1a7aIj49v3bhx46YjR448PtvPsDvjxo077rTTTjs1Li6uTbVq1Vq1a9euyaeffproWb5v376I2267LTU1NbV5dHR0m9TU1Ob3339/bXcdPMc3Y8aM6tdcc80JSUlJrapVq9bqxhtvrJ+dnc2XX36ZkJ6e3iQ+Pr71SSed1HTOnDnVfOuxYMGCKmedddbJiYmJrePj41t36NCh8bfffhvnLnP66ac3SU9PbzJv3ryqp5122qmeY5sxY4b3fF9++eVpc+fOTfnzzz+jRSRdRNJTU1ObA2RkZERce+219evUqdM8JiamTUpKSsv27duf/P3338f51idYGiyVR7m58NNP/pd94W/84jwPP/wwHQ4dIl/48NJL3vw6Fd6ppyKujM53AL/98kuZJKr0m4DynXfsJVKPKVPCP/5bcUVE2HxbjlrYPFZllajSNwHls088QYQ7OOrcGRo2LPX9htqAAQOo17hx/hsrpkyBr77yv4InKIpzPsdjY+3lcg2WypV58+ZVvfXWW09s2LBh5vTp09ffdddd2++///76GzZsKPDD9aeffoq5+uqrT6pfv37mlClTfps5c+a6O+64Y/uBAweO+tC4/PLLG3Xq1Gnvm2++ub5Hjx67n3vuuTpDhgwJOMTCunXrYjt16rTvxRdf3Dhr1qx1vXv33jV27Ni6d911V6q73C233FJv8ODBJzRv3vzg5MmT10+aNGlD+/bt923YsCEGbL61Tp06NX777bdrDhgwYMfs2bN/7du3785nn3227q233lrPd7/Dhg2rn5CQkDN16tTfrr/++j8nT55c68Ybb6x//fXXN+zXr9+uN954Y31SUlJ23759G23bts074vTMmTOTLr300iYJCQk5r7zyyoZXX311w4EDByK7dOlyyrp166Ld+9i8eXPs4MGDGwwcOHDHjBkz1tesWfPI9ddf3+jHH3+MBRg9evS2jh07ZtSoUSN70aJFaxYtWrRm1qxZ6wAGDBhQ/4MPPkgeOnTotvfee++X8ePHb2rWrNnB3bt3Fz+5oDGmUk/p6emm3HnvPWMaNTLmk0+MiY01BoypU8eYqVPt45YtfldbuXKliQPzi+0FYac+fUJc+RD45Ze84wPzPJiUlJRS3835559vAAMYETFbf/jBmMjIvH23alXq+zTGGNOlS94+evcum324nXKKd3+ZYKqAueKK/2/vzsOjqs4Hjn/f7EGSQAgIwQRkcyeyCW5oLYsgixtFKOrPUgUXRMGqKFpQEUpxqYIWCi4FQYuASrVQUVxaRYsWjKggWpBNIKwBQpLJnN8f985kMpmZLCQzc5P38zz3ycy5d2beM1nmzbnnvufaGn2JkpIS07BhQ+/7mZWVZcyNN5b2U8SYbdtq9DUjadmyZQYwr/v+Lp51ljGFhWUP3L3bmGuvNWbdOmN69bKO697dmA0brO/9li2R6UAFgLUmxN/VdevWbTHGrA20+b4lkdiCxVXR1qlTpyNt2rQpcLlc3rb33nvvW8B069Yt3xizdvny5RsBs3z58o3GmLUvvPDCD4DZt2/fl8Ge9+67794JmAkTJmz3bR86dOjeBg0alOzdu/e/gZ7bfyspKVlbVFS09t57792ekpLi8sSZm5ubGxMTY0aOHPlzsBhmzpz5I2Deeeed73zb77333u1xcXHu7du3r/ON4dprr83zPe6MM844CpgVK1Z4H79mzZoNgHnmmWf+52nLyso63qNHj8O+j923b9+XjRo1Kr7pppt2e9q6deuWHxsb6/7qq69yPW3bt29fFxMTY+677z7v+3T11VfnNWvWrMi/P+3atSsI1d9gm/1zG/Bn2qH/EtdxAwbA5s3WFVa+brwRdu60aiX5McYqQHkf4J3xkZZmFUmsa9q3t+a22G4B8vftq9FClV9//XW5ApQtxowpu/5bNQqFRiWf+kYJwKvUfKHKe+65p0wByoVz5oDvFXC9e8Mp5f6BdazBgwdz8cUXMxbI9zRu2FC+En/TplbJiZycsu1nngmLFkF2dhiiVRVxuVzk5uY2GDhw4IFYn5UPLrvssqOZmZlBC75169btWFxcnLnqqqvavPjii4137NgRF+zYESNG7Pe9P2zYsP3Hjh2L+eKLL5KDPWbr1q3xw4cPb5WZmXlOQkJC54SEhC7Tp09vmZ+fH+t5rXfeeSfV7XZz++23B504t3LlyrTMzMyiXr16HSkuLsaz9e/f/7DL5ZIPPvjgJN/j+/Xrd8j3ftu2bY8nJye7+/bt6/0lz8nJOQ6wbdu2BIDc3NzEbdu2JQ4dOnSf72ukpKS4O3XqdHTNmjUNfZ+zVatWheecc06h537Lli1d6enpxT/99FOFVX9zcnKOLl68OOP+++9v/tFHHzUIdFqyqjRZikYVndYJsH/FihVsXbWKMstwTpsGJ4flQoHwmz/fezMBeBZ49NFHa6xQpe9VdgkJCcwbOdKqheMxfHjNr//WrBlcdlnZS83dbmsh2ZYtgz/uRJ1xRpl14/oD55iaK1R5+PBhnn32We/9Ll26cNH8+WUTT4fPVfLnKVS5A3jYd8fkyWXXfqvo6lQnX71ah+zatSvO5XLJySefXOy/LyMjo1ybx9lnn124dOnS791ut9x6662nZmVl5XTs2PH0t99+u6H/saecckqZT/TMzMxigJ9++ine/1iAkpISrrjiinarVq1KGz9+/K6///3vmz788MNvx4wZswugoKAgBmDfvn2xAG3atAn6xzEvLy9u586dCQkJCV18t0svvfQMz37f49PT08vEmpCQYFJSUspMsEpKSjIAx48fF7DeQ4C77767tf/rrF69Ou3gwYNlXqNRo0blMpyEhARTWFhYYd4yb968n0aMGLF34cKFGZdccskZGRkZ544cOTIrPz+/2jlP0CxXOYfL5eKe8eN5DvCePO/eHSK4hlqta9XKSizefx+Am4CxhYXcfPPNJ3z5e8AClL7rpyUnwwsvnNBrBJSeXn5Ommeif48eNf96vhYssF6/sNC7blz7zz7jX//6Fxf51GSqDv8ClEvmzbMWcvbo3z/gaKnTdevWjeHDh/PswoXcCJwL1nIud9xhzUfSRMgxWrRo4YqLizO7d+8ul7jk5eXFt2zZMmgiMnDgwPyBAwfmFxQUyLvvvttw8uTJmUOGDGn/ww8/5LZo0cKbEGzfvj3uzDPP9D7Pzp074wGys7MDJmPffPNN4oYNGxrMmjXrf7fddpt3VGrZsmVlJp1nZGS4ALZs2RKfk5NT6P88AOnp6SUtW7YsWrhw4Q+B9rdv3/6E/wtt2rRpCcCECRN2XH755eVK1CcmJpryj6qetLQ096xZs3bMmjVrx6ZNmxJeeeWVxlOmTGmZkJDgfv7553dU5zl1ZKkOePHFF8n59lt62feNZ+KuUyceV9bLL3s/cOKB54EFCxaccKHKcgUoU1PLrv82Y0btrP/29NPB93kWVK4tDRrAI49477bDSkBHjBhxQk/rX4DyyiuvpNVjj5WOKsXEVKnYqtNMmTKFuMRERgHe8cK33647p3Dribi4OM4555xjy5cvb+x7ddj7779/0s6dOyv1xyA5OdkMGjQof9y4cT8XFBTEbNq0qczjFixYkO57f9GiRekNGjRwd+nSpYAAjhw5EgMQHx/vTTIKCwtlyZIlZZ6nf//++TExMcycObNpsNj69Olz6Oeff45PSUlx9+zZ85j/5pvUVVdOTs7xzMzMom+++SY50Gt07949YD9DSUxMrHCkqUOHDkWTJ0/e3aFDh4Jvv/026CnNiujIksMdOXKEGQ8+iG/1JRk71lqxva475RTo0wdWrgRgBHC72811113HB76nzKrgiSeeKFOAcvaf/kSM7whdq1bWQsS14fLLA7eLhGedtHvvtRI2uxjqM0CaXajS95L/qvAvQPnXp58ue8XboEGQkXGikUet1q1bM3bsWKZPn85swFvZ6s47oVcvSNFizE7x8MMP77j66qs79O7du90tt9yyd8+ePXHTpk3LDHUabvr06U0//vjjhv369TvUqlWror1798bNmDGjRdOmTYv9k6D58+dnuN1uunfvfuwf//hH6muvvZYxbty4nRkZGQHrB3Tq1Ol4ZmZm0aOPPtoyLi6O+Ph488wzz5Sbd3HWWWcVjhw5cvfcuXNPPnLkSOygQYMOxsbGms8+++yk008//fjNN998YNSoUfvnz5+f0bdv3w633Xbb7k6dOh0rLCyUzZs3J7799tuNVqxY8UNKSsoJ1Y6KiYnhySef/OnXv/512yuuuEKGDBmyv2nTpq5du3bFf/LJJw2zs7OLJk2atLviZyp1xhlnFCxatCjjD3/4Q9MePXocTU5ONuedd17Bueeee3q/fv0OduzYsSAlJcW9evXqhhs3bmwwbNiwbRU/a2CaLDnc9OnTGbt3L57fEHdmJjGTJ0c0prB66SXIzARjiMNa52yEXaiyc+fOVXoql8vFQw895L3ftm1bhrzzTnjXf8vIKF/AMJwTnxcutC7hx1o3bjZWocrrr7+emCqOVPoXoLzrrrtoeOedpXOyYmJg3rwaCjx6PfDAA8ybN48H9u3jarB+V7dvh0mT6uYFGBUwhi8iHUN1XHnllfnPP//8/6ZOnZp5ww03tM3Ozi6cNm3atpkzZwadGNq5c+djK1euTH3kkUdO2b9/f1xaWpqra9euR1555ZUf7atDvZYuXbr5jjvuyH766aczGzZsWHLnnXfumj59+q5gz52UlGQWL168ecyYMdm33XZb69TU1JJhw4blZWdnF40fP77MhMo5c+Zsb9euXeHcuXObLlmypElycrL7tNNOK+jXr99hsEZoPvzww00TJ05s8fLLL2c8/vjjicnJye6srKzCPn36HEpKSqqRIptDhw491KRJk41Tpkxpceedd7YuLCyMycjIKO7UqdPR4cOH76/4GcoaO3Zs3ueff37SlClTWubn58dmZmYW7dixI/f888/Pf+ONN9JnzpyZ4HK5JCsrq3Dy5MnbJk6cuKe6sYvnv776qmvXrmbt2rWRDiO4pCSrcneLFtaVcD527NjB8LZtWV1YWHo+9fXX4Zprwh5mRA0YYJ3aAFxAE6B5hw5s3LixSk8zevRoZvuc7lq3ZAk5vsua9OpVujJ8bXngAZg6tWzb7NnhnX920UVgL6pbAmQDN9x/P1P946pAVlaWt65SSkoKBzdtIsZObAEYMsR5y8RU08yZMxkzZgzDgVc8jbGxsHZt6Shw796wapU133DNmghFWjki8oUxpmuw/evXr9+Sk5MTomy58hg3blzmU0891aKoqOiL+PiAc7lVmKxfvz4jJyendaB9dXxSS932+wcf5GmfRMn06wdXXx3RmCLipZe887PigLnApioWqgxUgDJn0qSy67/V9qgSlJk35BXuifpLl3rfz1hgGdbpyaoUqvQvQPnUU08RM3Jk6fsZGws+73ddN2rUKNq3b89C4D1PY0kJjB5duYV2lVIRpcmSQ61fv56Ul1+mk32/JCEBcfpCudWVkQGDB3vvXg00xhopqqxhw4bhmbgpIrx5442Qm1t6wLhx4Vn/LS6utJIzeJcjCatmzawPcVs34BfFxZWet+R2uxk/frz3flZWFiP79YN//KP0oOuui0zfIiQ+Pp7p06cDcBvgvSTps8/gL3+JVFhKqUrSZMmBjDFMu+MOfMcgYidNqhNLRVTbCy+UGQ15AdhXyUKV5QpQDh1KE9+1vNLTy58aq032nCGgTP2jsHr2We/kYwHmU/lClf4FKBcsWGAVVPUdpfNZZqW+GDx4MD179mQTMM13x/33w+4qzWtVdciTTz650xijp+CinCZLDrRixQqu+de/8FxHU9imDfj8J18vNWpkzYGxDQIyqFyhSv8ClC81axbZ9d98azhFKqmIiYHZs72LFjcDHq5EocpABSh7tm4N771XetD110PDcjX56jwRYcaMGQBMBTZ7dhw8CPfcE6mwlFKVoMmSw7hcLt4aNYprfdoSX3yxdur+OM2cOdZcGKwf7JeBQrtQZTD+BSgnjx1L/KxZpQfk5FiXt4dT8+ZWP+Ljy56SC7dhw5DTT/fefQDItQtVBuNfgHLx4sXlR5Wee642o45qnkKVhVin47wWLID9Vb4YSCkVJposOcxf//xn7t1WWiqiYOhQ6NkzghFFkdRUGDbMe/dyoAWhC1X6F6C89z//KbsMx7JltRhwCB06lK1yHSlLl3pHlxKA1wheqDJQAcpTjSm7TMzIkZFNAKPA448/TmJiIu9ircPn9d13EYqoVpj6fqW1cha32y341I71p8mSg+Tn55N/3314ZiYdS04m2eeUh8K6zD7OKh/mGV1y24Uq/fkXoPzb3XcT47/+W6Tmgf3pT7VftbsyzjgD8Zk3dQWQaheq9FeuAOVf/wo33FB6QEICPPNMbUcc9Vq1asVdd90FwDjgsOeijCpcbRjtRGTL0aNHG0Q6DqUqq6CgIElEgi7/oMmSg7x0773c5vMHNfaJJ6xVy1WpBg2sOTG2XwJZwId2oUqPQAUoe/lelVRb679VVu/e4anaXRkLFkCiteqgZ924sWPH4va55D1gAcodO7z1mgAYNUpPF9smTJhAkyZN2AU84D8C41sE1aGKi4unb9myJS4vL69RUVFRnI4yqWjldrvl6NGjyVu2bElwuVxBKzprUUqHFKXc0bQpP+7bx8X2B9Se9u1p9t13dX/9t+o4ftw6JVdsrUKwGrgM6OBTqNK/AOWWceNo9eSTpc/x7LPWgqfKMm0aTJjgvfsb4GSfQpXlClAePEjMBRdYl8aDlWzl51vzsBRQWqgyBlgbG0snz+nftDQ4cCCqy4BUVJQS4IsvvmgfFxc3QURyjDGN0X/OVXRyi8jPLpdrcufOnVcGPcoY4+gNa+DgdeAQcBhYCmRX9vFdunQxUS0x0Rgwf4mPN8aaJmuKwJSsWxfpyKLb6NHe98sN5lQwgFm8eLHJy8szsbGxBrvtsgsuMCYpyXu8yc6OdPTRqXlz73uUDyYxNtYcPXrUzJ492/teAmbu3LnG5OaWvp9gzPjxkY4+6hQVFZn27dsbwHQGU+L7fr32WqTDCwlYa6Lg779uuoVri3gAJxQ8NAC+B74GrgQGA7nAD8BJlXkOJyRLX4HZ4/OHdMvQoZGOKvoVFhqTkOB9zz62P8ibNGlievfu7f1gFxFzdNAgU+aDfc2aSEcfnVavNm6f92kOmGuuucbYa1wZwGRlZVnHdu5c+n4mJRlTXBzZ2KPUsmXLvO/ds74/gy1aGHPwYKTDC0qTJd3q2+b0YdGbgTbAlcaYN4wxb2KV2GkFjIpoZDXEGMM2wDMzaU9yMq3qweKjJywhoUwV6guB9liFKt/1Wd/tzgEDaLB8eenjfvlLa20uVd6llyIXXOC9+xvg0yVLyheg/O9/wWf+EuPGeSfdq7I8hSoBHgTysE+97drFrt8+5L0wUykVWY6esyQi7wFJxpgL/do/BDDGXFLRc0TznCWXy8W/ExK4xOd79NH48aQGuXRb+XG56HjBBcTYc5fWAOf7HXKkbVtO+uEHAExsLLmrVuEOx7ImDhWXl8dZffsi9ty5z4Ae9r7s7GzefPNNOvzqVzT4/nsASpKSyP33v3VuXQhr16711gL7FVZ5BoASYri80WeccmVXBgyAPn28RdUjrjJzlpSqS5yeLP0MvGmMGeXX/hwwxBhT4aVi0Zws7fnxR5q1bVumrRg4YG/77e2A39dAbQfsx9Y304Hf2bcNcA7gKUF5FdaVXZ5ptH8A7g9rdM40E7jdvm2AvoBnrK4r8Dml7+nDwKNhjS46xGOtT5hub4FuB2vzHYP7mIvoyceANVh66aUwcCAMGACtW4elKwFpsqTqG6cnS0XAk8aY+/3aHwPuN8YEHPsXkVuAWwCys7O7bN26tdZjrY5PevXiAt9lIk7QEaqWYHluH66xCMIvBsjHmtwGsBZrYViw+tfYvr0Pa3kUVTmHAM8yuLuB5vbtXOBs+3a+zzFOlUrwxCZU4lNTi7kcIpVGHKQ0/bSKu198MTzwgFVhIhI0WVL1TV2YSBAo2wt5za0xZg4wB6yRpdoIqiac+vvfl1lTqyAmhmR30AKjFWpob9lVfJwLOBwbS35sLIfi4jgcG8vh2FgOxcZy2L5/yG7zv18cBadfXtm1i5v37AGgC3AuMJzSRMkAj7ZuTU5aWmQCdKDH9+1j6vbtCHAy8BBN2Nq2EWfZpzQBXmjenJyTT45YjB7xbjdpJSWklpSQ6nKRWlJCmr2llJSQ5nKV3vY5JrWkhNgIxFsQk0ieuym7OZknGA8IjRtDv37WqNLll1tLISqlwsfpydIBrH/m/DW29zlai4svBmPY9fHHpHXsSIO0NKuG0IED1rZ/f+lX39vB2qqZaMUB6SUlpJeUQAWL0pbToAGkp0PjxtbXYLf921JTa26ei9ttTfY4dgwBXqENHdgKWLNnpWNHnl6/vmZeqz45/XSw61ZN5DBHDjQq/S8lNZWxO3Ywtia/h4cPV/5n3bctEpWxY2PL/2xX4ufeldKYczsnsmkTnHaalRx9MAAuvFDnyCsVSU7/9dsAnBWg/UzgmzDHUmtaXHxx6Z2kJGjRwtqqwu22igJW9YNm/344erT6wR87Zm12wcJKi4mx/n2uSoLl+eq/9lhMDNx3H/z+9wCcyY+l+0TgjTeq37/6bMkSzNlnI0ACxaTvLx1VYtKkwMnu8eNVT/L374eDB6ud7J+Qhg0r/7PnezslpVpFJTestwqdDxwI7dvXQn+UUtXi9GTpLWCGiLQxxvwIICKtsa4U17m6vmJirMrAaWlVX++sqKj8h1dlP+yqe+2z2136XFWVnFz+Q6xRI+vDy3+OXnZ2mVOdqmqkQwfYtKn8jtxcuPLK8j8fBQXhDzIurvJJjv/PTJiXZ8nJsTalVHRx+gTvk4D1QAEwEXv6CZACdDTGHAnxcCC6r4ZzPGPgyJHqnTrJz4909CrapKRUfZQxPd0aHYripUOcSCd4q/rG0SNLxpijInIZ8BQwH2ti93vAXZVJlFQtE7E+4FJSoFWrqj22uNg69VKdRKu4PhZJcIj4+CrP4/GO8ui6ckqpCHF0sgRgjPkJuCbScagaFh8PTZtaW1UYY82xCpJUbZ74Iu2KvgVgbc5Iuur/xifu4EFYsgSAT+nOl62u4faJQRKfk07SUR6llOM4+jRcTdDTcPXL4MHw1luGRAq5pE8SK1fCww/DI49EOjJn+/RTuOSCIopJQMSacnb8ODz0EPzxj5GOTtU0PQ2n6pvIF8FRKgx69YKhQ+G88wCEQpL44gtr7u+0aZGOzvnOPx9ik6zJ0MbA734HJ58Ms2ZFODCllKoBmiypeqFDB/jb32DixNK2ffusi/UytHR3jbArMwAwY4ZVFqmwMHLxKKVUTdFkSdULzz0XfF+PHsH3qYo98YRVrWHq1PL7IlEaSSmlapomS6reOPvswO133RXeOOqa8eOtMl6HnbyIoFJKhaDJkqo33n03cHvPnuGNoy7avTv4RW5btoQ1FKWUqnGaLKl6o3lza8k5X1Gwzm+d0LAhrFsXeN+rr4Y3FqWUqmn6UaHqleefL3u/YcPIxFEXdewIs2eXb//44/DHopRSNUmTJVWvDB9uLQjvcdppkYulLrrlFrjxxrJt338ZMwxuAAALbklEQVQfmViUUqqmaLKk6p2rriq9PXx45OKoq156CTp1Kr2/d2/EQlFKqRqhyZKqdxYtKr09enTk4qjLvvzSWs4NrNVnlFLKyTRZUvVOXByceqp1OykpsrHUZXv3Wqc8Xa5IR6KUUidGkyVVLy1fXv7KOFWz4uJg8+ayc8SUUsqJNFlS9dJZZ8Hq1ZGOou5r3Ro++ijSUSil1InRZEnVW507RzqC+uH88yMdgVJKnRhNlpRSSimlQtBkSSmllFIqBE2WlFJKKaVC0GRJKaWUUioETZaUUkoppULQZEkppZRSKgRNlpRSSimlQtBkSSmllFIqBE2WlFJKKaVC0GRJKaWUUioETZaUUkoppULQZEkppZRSKgRNlpRSSimlQtBkSSmllFIqBE2WlFJKKaVC0GRJKaWUUioETZaUUkoppULQZEkppZRSKgRNlpRSSimlQtBkSSmllFIqBE2WlFJKKaVCEGNMpGOIKBHZC2yNdBwVyADyIh1ELdL+OZv2z7mq27dWxpimNR2MUtGq3idLTiAia40xXSMdR23R/jmb9s+56nLflKpJehpOKaWUUioETZaUUkoppULQZMkZ5kQ6gFqm/XM27Z9z1eW+KVVjdM6SUkoppVQIOrKklFJKKRWCJktKKaWUUiFoshSlRCRLRF4XkUMiclhElopIdqTjCkVErhWRJSKyVUQKRGSjiEwVkRS/4xqLyFwRyRORoyKySkTOCfB8SSLyRxHZZT/fpyLSM3w9qpiIrBARIyKP+bU7to8i0l9EPhKRI/bP3loRucxnv5P7dqGI/FNE9th9+1JEfuN3TNT3T0ROEZFn7dc8Zv8Mtg5wXI32RURiRGSCiGwRkeMisl5ErqmdXioVPTRZikIi0gB4HzgduBG4HmgPrBaRkyIZWwXuAUqAB4DLgeeBW4F3RSQGQEQEeMvePwa4BojH6tspfs83D7gZeBgYAOwCVorIubXflYqJyDAgJ0C7Y/soIqOAN4EvgKuAIcBioIG938l96wiswor3ZqzY/wPME5Fb7WOc0r92wK+AA8DHgQ6opb48CkwCZgL9gDXAYhHpf+JdUiqKGWN0i7INGIuVdLTzaTsVcAHjIh1fiLibBmi7ATDAZfb9wfb9X/gckwbsB57xacuxj7vJpy0O2Ai8FQV9bQT8DAyz43zMZ58j+wi0BgqAu0Ic48i+2a//OFAENPRrXwN86qT+ATE+t39rx9K6Nr9XQDOgEJjs9zrvAV9F4nuqm27h2nRkKToNAtYYYzZ7Gowx/wP+jfUHMCoZY/YGaP6P/bWl/XUQsNMYs9rncYeA5ZTt2yCgGHjN5zgX8CrQV0QSazD06pgObDDGLAqwz6l9/A3gBv4c4hin9g0gwY6pwK/9IKWj7I7onzHGXYnDarovfbHewwV+r7MAOEdETq1qP5RyCk2WotNZwNcB2jcAZ4Y5lhN1if31W/trqL5li0hDn+P+Z4w5FuC4BKzTEBEhIhdhjZjdFuQQp/bxIuA74DoR+UFEXCKyWURu9znGqX0DeMn++oyIZIpIIxG5Gfgl8JS9z8n981fTfTkLa2Rpc4DjwHl/m5SqNE2WolM61lwEf/uBxmGOpdpEpCXwCLDKGLPWbg7VNyjtX0XHpddUnFUhIvHAbGCGMWZjkMOc2sdMrLlxfwSmAX2Ad4GZIjLWJyYn9g1jzNfApVijKjuw4psFjDbGvOoTlyP7F0BN9yUdOGiM8S/OF019VqpWxEU6ABVUoGqhEvYoqsn+r/VNrHlWN/nuonJ9q+xx4XYfkAxMCXGMU/sYA6QA/2eMWWq3vW9fZTVBRJ7BuX1DRNoDS7BGQkZjnY4bDPxZRI4bY17Bwf0LoKb74oQ+K1UrNFmKTgcI/F9aYwL/BxhVRCQJ6yqcNsAlxpjtPrv3E7xvUNq//UCgUgmNffaHlVilGx7EmlCb6DcvJVFEGgH5OLeP+7BGlt71a/8n1hVVLXBu38Ca4F0MDDDGFNtt74lIE+BPIrIIZ/fPX033ZT/QWETEb3QpmvqsVK3Q03DRaQPW/AB/ZwLfhDmWKrFPUy0BzgP6G2Ny/Q4J1befjDFHfI471S6j4H9cEeXnTYRDGyAJa0LrAZ8NrLIJB4BzcG4fNwRp94wcuHFu38D63qz3SZQ8PgeaYF3t5eT++avpvmwAEoG2AY6DKP/bpNSJ0GQpOr0F9BCRNp4G+1TIhfa+qGTXUnoFa8LsYGPMmgCHvQW0FJFLfB6XCgykbN/ewqoJM8TnuDhgKPBPY0xhzfegQuuAXwTYwEqgfoH1weLUPi6zv/b1a+8LbDfG/Ixz+wZWqYdzRSTBr707cBxrZMTJ/fNX031ZgZU8/drvdUYAX9tX7CpVN0W6doFu5TfgJKwP3VysORWDgPXAj/jViImmDasIpQEeA3r4bafYx8QAnwDbgOuwPog/wPqgyvJ7vlexRmt+i5WAvY71odY50n31i9O/zpIj+4g1gvQ+1um40VgTvOfY/fs/J/fNjudauy8r7d+rPljFFQ3wpNP6Z/fnWp/fu1vt+5fUVl+wJv4fB8ZhTZZ/HmvEcWAkvqe66RauLeIB6BbkG2PNIVgCHMaaB/MGfkXnom0Dtth/tANtk3yOSwdesP9oH8MqapcT4PmSgSexRgSOA58Bl0a6nwHiLJMsObmPQCrWFWK7sUYRvgKG14W+2TH1sxOGvfbv1TqsEhCxTutfiN+1D2qrL0AsMBHYilVG4Cvg2kh+T3XTLRybGBPo4gallFJKKQU6Z0kppZRSKiRNlpRSSimlQtBkSSmllFIqBE2WlFJKKaVC0GRJKaWUUioETZaUUkoppULQZEmpMBGRk0Rkl4hcE+lYAETkKhH52V70WCmlVBCaLCkVPuOBPGBppAOxvYFVhPB3kQ5EKaWimSZLSoWBvR7ZGODPJkoqwdpxzAHuEJGkSMejlFLRSpMlpSrBPoX2nYh8LiLxPu19RMQtIrdX8BRXYS098Zrf874kIttFpKuIfCIiBSKyUUSusPePE5EtInJYRN4UkaZ+jzci8piIjBeRrSJyVETeFpFm9vY3ETkkIttE5L4Acf0NaARcXZ33RSml6gNNlpSqBGPMUWAYkAM8CiAizYC/An83xsyq4CkuB741xuQF2JdqP89crKRqD7BERJ4AfgHcDtxl3w70OtcDl2GtcTYGuNh+vmVYa3ddA7wDTBOR/n79ygO+teNTSikVQFykA1DKKYwx/xWR+4EnRGQVcA9QAvymEg/vAXwZZF8KMNoY8xGAiOwE1gMDgDONMSV2+9nAGBGJ9bTZCoHBxhiXz3F3Aw8ZYx6z2z7ASsSGYCVOvv5rx6eUUioATZaUqpqngd7A34EEoHeQ0SJ/mcDKIPuOehIl23f211V+SdF3WL+zLYDtPu3vehIlv8d7X88Y4xKRzUBWgNffa8enlFIqAD0Np1QV2JOi5wOJwHpjzHuVfGgS1ghQIAf9XqPIvnnA7zhPu/9k7GDHBWoPNJG7IEi7UkopNFlSqkpEpDnW6NKXQI6IjK3kQ/cBjWstsBOTjhWfUkqpADRZUqqSRESAl7FGaHpjJU1/EJGOlXj4d0CbWgzvRJwKbIx0EEopFa00WVKq8sYBvYARxpj9wP3AN8AiEUmu4LEfAV1FJKp+5+wEsBtWfEoppQKIqj/cSkUrEekEPA5MNcZ8CN65RcOA1sCTFTzFa0Aa1mX90eQCrNNwr0Y6EKWUilYSJcWElarz7Mv3NxtjfhvpWDxE5HngbGNMtCVxSikVNTRZUipMRORCYBXQzhizIwriaQ78CFzuV7pAKaWUDz0Np1SYGGP+jVUsslWkY7G1BsZroqSUUqHpyJJSSimlVAg6sqSUUkopFYImS0oppZRSIWiypJRSSikVgiZLSimllFIhaLKklFJKKRXC/wPXkbl+5XwFTwAAAABJRU5ErkJggg==\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"plt.plot(r[ix],r[iy],'-',color=(0,0,0,1))\n", | |
"plt.plot(r[ix]+u[ix]*scale,r[iy]+u[iy]*scale,'-',color=(1,0,0,1))\n", | |
"plt.quiver(r[ix],r[iy],F[ix],F[iy],color=(1,0,0,1),label='applied forces')\n", | |
"plt.quiver(r[ix],r[iy],u[ix],u[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 with Deformation scale = {:.1f}x'.format(scale))\n", | |
"plt.legend(bbox_to_anchor=(1,0.5));" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 13, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"uf = np.linalg.solve(E_al*A*K[2:13,2:13],Ff)\n", | |
"u = np.zeros(2*len(nodes))\n", | |
"u[2:13] = uf\n", | |
"\n", | |
"F = E_al*A*K@u" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 14, | |
"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": [ | |
"plt.plot(r[ix],r[iy],'-',color=(0,0,0,1))\n", | |
"plt.plot(r[ix]+u[ix]*scale,r[iy]+u[iy]*scale,'-',color=(1,0,0,1))\n", | |
"plt.quiver(r[ix],r[iy],F[ix],F[iy],color=(1,0,0,1),label='applied forces')\n", | |
"plt.quiver(r[ix],r[iy],u[ix],u[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('Alum with Deformation scale = {:.1f}x'.format(scale))\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": 15, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"Cross Sectional Area for Aluminum: 7.679 mm^2.\n", | |
"Cross Sectional Area for Steel: 2.688 mm^2.\n" | |
] | |
} | |
], | |
"source": [ | |
"#Part A-B:\n", | |
"u_aly = np.array([u_al[1],u_al[3],u_al[5],u_al[7],u_al[9]])\n", | |
"u_ssy = np.array([u_ss[1],u_ss[3],u_ss[5],u_ss[7],u_ss[9]])\n", | |
"\n", | |
"A_al = A * (abs(np.min(u_aly)) / 0.2)\n", | |
"A_ss = A * (abs(np.min(u_ssy)) / 0.2)\n", | |
"print('Cross Sectional Area for Aluminum:', round(A_al,3), 'mm^2.')\n", | |
"print('Cross Sectional Area for Steel:', round(A_ss,3), 'mm^2.')" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 16, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"Weight of Aluminum: 0.674 N\n", | |
"Weight of Steel: 0.683 N\n" | |
] | |
} | |
], | |
"source": [ | |
"#Part C:\n", | |
"n_elem = 11\n", | |
"L = 300 #mm\n", | |
"rho_al = 2710e-9 #kg/mm^3\n", | |
"rho_ss = 7850e-9 #kg/mm^3\n", | |
"g = 9.81 #m/s^2\n", | |
"W_al = rho_al*L*A_al*g*n_elem\n", | |
"W_ss = rho_ss*L*A_ss*g*n_elem\n", | |
"print('Weight of Aluminum:', round(W_al,3), 'N')\n", | |
"print('Weight of Steel:', round(W_ss,3), 'N')" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 17, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"Price of Al: $ 10206617.18159562\n", | |
"Price of Steel: $ 3188076.288530451\n" | |
] | |
} | |
], | |
"source": [ | |
"#Part D:\n", | |
"T_to_N = 9806.65 #Conversion Factor\n", | |
"\n", | |
"p_al = 1545 * W_al * T_to_N\n", | |
"p_ss = 476 * W_ss * T_to_N\n", | |
"\n", | |
"print('Price of Al:' , '$', p_al)\n", | |
"print('Price of Steel:' , '$', p_ss)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"We find that steel is the cheaper material to build the truss." | |
] | |
}, | |
{ | |
"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.d__?" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 18, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"#Importing Data and Normalizing:\n", | |
"al_prices = pd.read_csv('../data/al_price.csv')\n", | |
"ss_prices = pd.read_csv('../data/steel_price.csv')\n", | |
"\n", | |
"al_y = al_prices['Year'].values\n", | |
"al_yn = (al_y - al_y.min()) / (al_y.max() - al_y.min())\n", | |
"al_p = al_prices['dollars/MT'].values\n", | |
"\n", | |
"ss_y = ss_prices['Year'].values\n", | |
"ss_yn = (ss_y - ss_y.min()) / (ss_y.max() - ss_y.min())\n", | |
"ss_p = ss_prices['dollars/MT']" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 19, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"#Part A:\n", | |
"train_per = 0.7\n", | |
"np.random.seed(100) #Help Create reproducible problems\n", | |
"\n", | |
"i_rand_al =random.sample(range(0,len(al_yn)),len(al_yn))\n", | |
"i_rand_ss =random.sample(range(0,len(ss_yn)),len(ss_yn))\n", | |
"\n", | |
"#Random indexes for testing and Training data\n", | |
"i_test_al = i_rand_al[int(len(al_yn)*train_per):]\n", | |
"i_train_al = i_rand_al[:int(len(al_yn)*train_per)]\n", | |
"i_test_ss = i_rand_ss[int(len(ss_yn)*train_per):]\n", | |
"i_train_ss = i_rand_ss[:int(len(ss_yn)*train_per)]\n", | |
"\n", | |
"al_y_train = al_yn[np.sort(i_train_al)]\n", | |
"al_y_test = al_yn[np.sort(i_test_al)]\n", | |
"al_p_train = al_p[np.sort(i_train_al)]\n", | |
"al_p_test = al_p[np.sort(i_test_al)]\n", | |
"\n", | |
"Z_train_al = np.block([[al_y_train**0]]).T\n", | |
"Z_test_al = np.block([[al_y_test**0]]).T\n", | |
"\n", | |
"ss_y_train = ss_yn[np.sort(i_train_ss)]\n", | |
"ss_y_test = ss_yn[np.sort(i_test_ss)]\n", | |
"ss_p_train = ss_p[np.sort(i_train_ss)]\n", | |
"ss_p_test = ss_p[np.sort(i_test_ss)]\n", | |
"\n", | |
"Z_train_ss = np.block([[ss_y_train**0]]).T\n", | |
"Z_test_ss = np.block([[ss_y_test**0]]).T" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 20, | |
"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": [ | |
"#Part B:\n", | |
"max_N = 11\n", | |
"SSE_train_al = np.zeros(max_N)\n", | |
"SSE_test_al = np.zeros(max_N)\n", | |
"\n", | |
"for i in range(1,max_N):\n", | |
" Z_train_al = np.hstack((Z_train_al,al_y_train.reshape(-1,1)**i))\n", | |
" Z_test_al = np.hstack((Z_test_al,al_y_test.reshape(-1,1)**i))\n", | |
" \n", | |
" A_al = np.linalg.solve(Z_train_al.T@Z_train_al,Z_train_al.T@al_p_train)\n", | |
" \n", | |
" SSE_train_al[i]=np.sum((al_p_train-Z_train_al@A_al)**2)/len(al_p_train)\n", | |
" SSE_test_al[i]=np.sum((al_p_test-Z_test_al@A_al)**2)/len(al_p_test)\n", | |
" \n", | |
"plt.plot(al_y_train, al_p_train, 'o', color ='black', label = 'data')\n", | |
"plt.plot(al_y_train, Z_train_al@A_al, color = 'red', label = 'Fit')\n", | |
"plt.title('Al Training Data & Fit')\n", | |
"plt.xlabel('Years (year 0 = 2016)')\n", | |
"plt.ylabel('Prices ($/ MT)')\n", | |
"plt.legend();" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 21, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"max_N = 11\n", | |
"\n", | |
"SSE_train_ss = np.zeros(max_N)\n", | |
"SSE_test_ss = np.zeros(max_N)\n", | |
"\n", | |
"for i in range(1,max_N):\n", | |
" Z_train_ss = np.hstack((Z_train_ss,ss_y_train.reshape(-1,1)**i))\n", | |
" Z_test_ss = np.hstack((Z_test_ss,ss_y_test.reshape(-1,1)**i))\n", | |
" \n", | |
" A_ss = np.linalg.solve(Z_train_ss.T@Z_train_ss,Z_train_ss.T@ss_p_train)\n", | |
" \n", | |
" SSE_train_ss[i]=np.sum((ss_p_train-Z_train_ss@A_ss)**2)/len(ss_p_train)\n", | |
" SSE_test_ss[i]=np.sum((ss_p_test-Z_test_ss@A_ss)**2)/len(ss_p_test)\n", | |
" \n", | |
"plt.plot(ss_y_train, ss_p_train, 'o', color ='black', label = 'data')\n", | |
"plt.plot(ss_y_train, Z_train_ss@A_ss, color = 'red', label = 'Fit')\n", | |
"plt.title('SS Training Data & Fit')\n", | |
"plt.xlabel('Years (year 0 = 2016)')\n", | |
"plt.ylabel('Prices ($ / MT)')\n", | |
"plt.legend();" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 22, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
}, | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"#Part C:\n", | |
"plt.figure(1)\n", | |
"plt.semilogy(np.arange(1,max_N),SSE_train_al[1:],label='training error')\n", | |
"plt.semilogy(np.arange(1,max_N),SSE_test_al[1:],label='testing error')\n", | |
"plt.title('Al Error')\n", | |
"plt.ylabel('Total Sum of Square error')\n", | |
"plt.xlabel('Polynomial Order')\n", | |
"plt.legend();\n", | |
"\n", | |
"plt.figure(2)\n", | |
"plt.semilogy(np.arange(1,max_N),SSE_train_ss[1:],label='training error')\n", | |
"plt.semilogy(np.arange(1,max_N),SSE_test_ss[1:],label='testing error')\n", | |
"plt.title('Steel Error')\n", | |
"plt.ylabel('Total Sum of Square error')\n", | |
"plt.xlabel('Polynomial Order')\n", | |
"plt.legend();" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 23, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"Price/MT for Aluminum: $ 2279.7\n" | |
] | |
} | |
], | |
"source": [ | |
"#Part D:\n", | |
"y_al = np.linspace(2016,2025,len(al_yn))\n", | |
"y_n = (y_al - y_al.min()) / (y_al.max() - y_al.min())\n", | |
"\n", | |
"train_per = 0.7\n", | |
"np.random.seed(100)\n", | |
"\n", | |
"i_rand_al =random.sample(range(0,len(y_n)),len(y_n))\n", | |
"i_train_al = i_rand_al[:int(len(y_n)*train_per)]\n", | |
"\n", | |
"Y_al = y_n[np.sort(i_train_al)]\n", | |
"Z_train_al = np.block([[Y_al**0]]).T\n", | |
"\n", | |
"max_N = 11\n", | |
"for i in range(1,max_N):\n", | |
" Z_train_al = np.hstack((Z_train_al,Y_al.reshape(-1,1)**i))\n", | |
" \n", | |
"print('Price/MT for Aluminum: $', round((Z_train_al@A_al)[-1],1))" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 24, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"Price/MT for Steel: $ 268.2\n" | |
] | |
} | |
], | |
"source": [ | |
"y_ss = np.linspace(0,9,len(ss_yn))\n", | |
"y_n = (y_ss - y_ss.min()) / (y_ss.max() - y_ss.min())\n", | |
"i_rand_ss = random.sample(range(0,len(y_ss)),len(y_ss))\n", | |
"\n", | |
"i_train_ss = i_rand_ss[:int(len(y_n)*train_per)]\n", | |
"y_ss = y_n[np.sort(i_train_ss)]\n", | |
"Z_train_ss = np.block([[y_ss**0]]).T\n", | |
"\n", | |
"max_N = 11\n", | |
"for i in range(1,max_N):\n", | |
" Z_train_ss = np.hstack((Z_train_ss,y_ss.reshape(-1,1)**i))\n", | |
" \n", | |
"print('Price/MT for Steel: $', round((Z_train_ss@A_ss)[-1],1))" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"**Part E:**\n", | |
"\n", | |
"Based on the results of the extrapolation, we find that the cost per metric ton for Steel is still cheaper than Aluminum as was found in part 3.d." | |
] | |
} | |
], | |
"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": 2 | |
} |