From d36fc3b8f88cc3108ffff6151e376b619b9abb01 Mon Sep 17 00:00:00 2001 From: kinitrupti Date: Fri, 12 May 2017 18:40:35 +0530 Subject: Revised list of TBCs --- Mechanical_Metallurgy/Chapter_2.ipynb | 251 ---------------------------------- 1 file changed, 251 deletions(-) delete mode 100755 Mechanical_Metallurgy/Chapter_2.ipynb (limited to 'Mechanical_Metallurgy/Chapter_2.ipynb') diff --git a/Mechanical_Metallurgy/Chapter_2.ipynb b/Mechanical_Metallurgy/Chapter_2.ipynb deleted file mode 100755 index 535881a6..00000000 --- a/Mechanical_Metallurgy/Chapter_2.ipynb +++ /dev/null @@ -1,251 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Chapter 2: Stress and Strain Relationships for Elastic Behavior" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "collapsed": true - }, - "source": [ - "### Example 2.1, State of Stress in two dimensions, Page No. 25" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "sigma_x= -12.5 MPa\n", - "sigma_y= -2.5 MPa\n", - "T_xy= 57.5 MPa\n", - "sigma_y`= -65 MPa\n" - ] - } - ], - "source": [ - "\n", - "from math import sin\n", - "from math import cos\n", - "from math import radians\n", - "from numpy.linalg import inv\n", - "import numpy as np\n", - "\n", - "#variable declaration\n", - "sigma_x=25;\n", - "sigma_y=5;\n", - "theta=45;\n", - "sigma_x_=50;\n", - "T_x_y_=5;\n", - "\n", - "#calculation\n", - "theta=radians(theta);\n", - "A=[[(sigma_x+sigma_y)/2+(sigma_x-sigma_y)/2*cos(2*theta),sin(2*theta)],[(sigma_y-sigma_x)/2*sin(2*theta),cos(2*theta)]];\n", - "B=[[sigma_x_],[T_x_y_]];\n", - "X=np.dot(inv(A),B);\n", - "p=X[0];\n", - "T_xy=X[1];\n", - "sigma_x1=sigma_x*p;\n", - "sigma_y1=sigma_y*p;\n", - "sigma_y_=sigma_x1+sigma_y1-sigma_x_;\n", - "\n", - "#result\n", - "print ('\\nsigma_x= %g MPa\\nsigma_y= %g MPa\\nT_xy= %g MPa\\nsigma_y`= %g MPa') %(sigma_x1,sigma_y1,T_xy,sigma_y_);\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Example 2.2, State of Stress in three dimensions, Page No. 29" - ] - }, - { - "cell_type": "code", - "execution_count": 22, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "sigma0 = 360 MPa\n", - "\n", - "sigma1 = -280 MPa\n", - "\n", - "sigma2 = -160 MPa\n" - ] - } - ], - "source": [ - "import numpy as np\n", - "\n", - "#variable declaration\n", - "A=[[0,-240,0],[-240,200,0],[0,0,-280]];\n", - "\n", - "#calcualtion\n", - "p=[1, -(A[0][0]+A[1][1]+A[2][2]), (A[0][0]*A[1][1]+A[1][1]*A[2][2]+A[0][0]*A[2][2]-A[1][0]**2-A[2][1]**2-A[2][0]**2), -(A[0][0]*A[1][1]*A[2][2]+2*A[1][0]*A[2][1]*A[2][0]-A[0][0]*A[2][1]**2-A[1][1]*A[2][0]**2-A[2][2]*A[1][0]**2)];\n", - "X=np.roots(p);\n", - "\n", - "#result\n", - "for i in range (0,3):\n", - " print('\\nsigma%i = %g MPa')%(i,X[i]);\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Example 2.3, Calculation of Stresses from elastic strains, Page No. 52" - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "sigma1 = 971.833 MPa\n", - "sigma2 = 520.705 MPa\n", - "\n", - "\n", - "Note: Slight calculation errors in Book\n" - ] - } - ], - "source": [ - "\n", - "\n", - "#variable declaration\n", - "E=200;\n", - "nu=0.33;\n", - "e1=0.004;\n", - "e2=0.001;\n", - "\n", - "#calculation\n", - "sigma1=E*(e1+nu*e2)/(1-nu**2);\n", - "sigma2=E*(e2+nu*e1)/(1-nu**2);\n", - "sigma1=sigma1*1000; #conversion to MPa\n", - "sigma2=sigma2*1000; #conversion to MPa\n", - "\n", - "#result\n", - "print('\\nsigma1 = %g MPa\\nsigma2 = %g MPa\\n')%(sigma1,sigma2);\n", - "print('\\nNote: Slight calculation errors in Book')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Example 2.4, Elastic Anisotropy, Page No. 60" - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "For Iron:\n", - "\n", - "\n", - "E_111 = 2.72727 x 10^11 Pa\n", - "E_100 = 1.25 x 10^11 Pa\n", - "\n", - "\n", - "\n", - "\n", - "For Tungten:\n", - "\n", - "\n", - "E_111 = 3.84615 x 10^11 Pa\n", - "E_100 = 3.84615 x 10^11 Pa\n", - "\n", - "Therefore tungsten is elastically isotropic while iron is elasitcally anisotropic\n" - ] - } - ], - "source": [ - "\n", - "\n", - "#variable declaration\n", - "from math import sqrt\n", - "S11_Fe=0.8;\n", - "S12_Fe=-0.28;\n", - "S44_Fe=0.86;\n", - "S11_W=0.26;\n", - "S12_W=-0.07;\n", - "S44_W=0.66;\n", - "D_100_l=1;\n", - "D_100_m=0;\n", - "D_100_n=0;\n", - "D_110_l=1/sqrt(2);\n", - "D_110_m=1/sqrt(2);\n", - "D_110_n=0;\n", - "D_111_l=1/sqrt(3);\n", - "D_111_m=1/sqrt(3);\n", - "D_111_n=1/sqrt(3);\n", - "\n", - "#calculation\n", - "Fe_E_111=1/(S11_Fe-2*((S11_Fe-S12_Fe)-S44_Fe/2)*(D_111_l**2*D_111_m**2+D_111_n**2*D_111_m**2+D_111_l**2*D_111_n**2));\n", - "Fe_E_100=1/(S11_Fe-2*((S11_Fe-S12_Fe)-S44_Fe/2)*(D_100_l**2*D_100_m**2+D_100_n**2*D_100_m**2+D_100_l**2*D_100_n**2));\n", - "W_E_111=1/(S11_W-2*((S11_W-S12_W)-S44_W/2)*(D_111_l**2*D_111_m**2+D_111_n**2*D_111_m**2+D_111_l**2*D_111_n**2));\n", - "W_E_100=1/(S11_W-2*((S11_W-S12_W)-S44_W/2)*(D_100_l**2*D_100_m**2+D_100_n**2*D_100_m**2+D_100_l**2*D_100_n**2));\n", - "\n", - "#result\n", - "print '\\nFor Iron:\\n\\n'\n", - "print 'E_111 = %g x 10^11 Pa\\nE_100 = %g x 10^11 Pa\\n' %(Fe_E_111,Fe_E_100)\n", - "print '\\n\\n\\nFor Tungten:\\n\\n'\n", - "print 'E_111 = %g x 10^11 Pa\\nE_100 = %g x 10^11 Pa\\n\\nTherefore tungsten is elastically isotropic while iron is elasitcally anisotropic' %(W_E_111,W_E_100)\n" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 2", - "language": "python", - "name": "python2" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 2 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython2", - "version": "2.7.9" - } - }, - "nbformat": 4, - "nbformat_minor": 0 -} -- cgit