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| author | hardythe1 | 2015-04-07 15:58:05 +0530 |
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| committer | hardythe1 | 2015-04-07 15:58:05 +0530 |
| commit | 92cca121f959c6616e3da431c1e2d23c4fa5e886 (patch) | |
| tree | 205e68d0ce598ac5caca7de839a2934d746cce86 /sample_notebooks/ApurvaBhushan/Chapter_3.ipynb | |
| parent | b14c13fcc6bb6d01c468805d612acb353ec168ac (diff) | |
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added books
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diff --git a/sample_notebooks/ApurvaBhushan/Chapter_3.ipynb b/sample_notebooks/ApurvaBhushan/Chapter_3.ipynb new file mode 100755 index 00000000..777522bb --- /dev/null +++ b/sample_notebooks/ApurvaBhushan/Chapter_3.ipynb @@ -0,0 +1,195 @@ +{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 3: Elements of the Theory of Plasticity"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Example 3.1, True Stress and True Strain, Page No. 76"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ "Engineering Stress at maximum load = 99852.1 psi\n",
+ "True Fracture Stress = 112785 psi\n",
+ "True Strain at fracture = 0.344939\n",
+ "Engineering strain at fracture = 0.411903\n"
+ ]
+ }
+ ],
+ "source": [
+ "from math import pi\n",
+ "from math import log\n",
+ "from math import exp\n",
+ "\n",
+ "#variable declaration\n",
+ "D_i=0.505;\n",
+ "L=2;\n",
+ "P_max=20000;\n",
+ "P_f=16000;\n",
+ "D_f=0.425;\n",
+ "\n",
+ "#calculation\n",
+ "E_St= P_max*4/(pi*D_i**2);\n",
+ "T_fr_St= P_f*4/(pi*D_f**2);\n",
+ "e_f=log(D_i**2/D_f**2);\n",
+ "e=exp(e_f)-1;\n",
+ "\n",
+ "#result\n",
+ "print('\\nEngineering Stress at maximum load = %g psi\\nTrue Fracture Stress = %g psi\\nTrue Strain at fracture = %g\\nEngineering strain at fracture = %g')%(E_St,T_fr_St,e_f,e);\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Example 3.2, Yielding Criteria for Ductile Metals, Page No. 78"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "\n",
+ "\n",
+ "from math import sqrt\n",
+ "\n",
+ "#variable declaration\n",
+ "sigma00=500;\n",
+ "sigma_z=-50;\n",
+ "sigma_y=100;\n",
+ "sigma_x=200;\n",
+ "T_xy=30;\n",
+ "T_yz=0;\n",
+ "T_xz=0;\n",
+ "\n",
+ "#calculation\n",
+ "sigma0=sqrt((sigma_x-sigma_y)**2+(sigma_y-sigma_z)**2+(sigma_z-sigma_x)**2+6*(T_xy**2+T_yz**2+T_xz**2))/sqrt(2);\n",
+ "s=sigma00/sigma0;\n",
+ "\n",
+ "#result\n",
+ "print('\\nSince the calculated value of sigma0 = %g MPa, which is less than the yield strength of the aluminium alloy\\nThus safety factor is = %g')%(sigma0,s);\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Example 3.3, Tresca Criterion, Page No. 81"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "\n",
+ "\n",
+ "#variable declaration\n",
+ "sigma00=500;\n",
+ "sigma_z=-50;\n",
+ "sigma_y=100;\n",
+ "sigma_x=200;\n",
+ "T_xy=30;\n",
+ "T_yz=0;\n",
+ "T_xz=0;\n",
+ "\n",
+ "#calculation\n",
+ "sigma0=sigma_x-sigma_z;\n",
+ "s=sigma00/sigma0;\n",
+ "\n",
+ "#result\n",
+ "print('\\nSince the calculated value of sigma0 = %g MPa, which is less than the yield strength of the aluminium alloy\\nThus safety factor is = %g')%(sigma0,s);\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+ "source": [
+ "Example 3.4, Levy-Mises Equation, Page No. 91"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "\n",
+ "Plastic Strain = 0.199532\n"
+ ]
+ }
+ ],
+ "source": [
+ "from math import sqrt\n",
+ "\n",
+ "#variable declaration\n",
+ "r_t=20;\n",
+ "p=1000;\n",
+ "\n",
+ "#calculation\n",
+ "sigma1=p*r_t;\n",
+ "sigma1=sigma1/1000; #conversion to ksi\n",
+ "sigma=sqrt(3)*sigma1/2;\n",
+ "e=(sigma/25)**(1/0.25);\n",
+ "e1=sqrt(3)*e/2;\n",
+ "\n",
+ "#result\n",
+ "print('\\nPlastic Strain = %g')%(e1);\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
+}
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