From 92cca121f959c6616e3da431c1e2d23c4fa5e886 Mon Sep 17 00:00:00 2001
From: hardythe1
Date: Tue, 7 Apr 2015 15:58:05 +0530
Subject: added books

---
 .../Chapter06.ipynb                                | 112 +++++++++++++++++++++
 1 file changed, 112 insertions(+)
 create mode 100755 Aircraft_Structures_for_Engineering_Students/Chapter06.ipynb

(limited to 'Aircraft_Structures_for_Engineering_Students/Chapter06.ipynb')

diff --git a/Aircraft_Structures_for_Engineering_Students/Chapter06.ipynb b/Aircraft_Structures_for_Engineering_Students/Chapter06.ipynb
new file mode 100755
index 00000000..5195a30b
--- /dev/null
+++ b/Aircraft_Structures_for_Engineering_Students/Chapter06.ipynb
@@ -0,0 +1,112 @@
+{
+ "metadata": {
+  "name": "",
+  "signature": "sha256:902d8cc266f9fb597a0d00273b10ab788d226cbd969bb1e960b465c84a750eef"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+  {
+   "cells": [
+    {
+     "cell_type": "heading",
+     "level": 1,
+     "metadata": {},
+     "source": [
+      "Chapter 06: Matrix methods"
+     ]
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 6.4 Pg.No.205"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "from __future__ import division\n",
+      "import math\n",
+      "import numpy as np\n",
+      "from sympy import solve, symbols, pprint\n",
+      "from sympy import diff\n",
+      "x,y=symbols('x,y')\n",
+      "\n",
+      "E=200000                #youngs modulus (N/mm^2)\n",
+      "nu=0.3                   #poissons ratio\n",
+      "u1=0.001\n",
+      "u2=0.003\n",
+      "u3=-0.003              #displacements of corners (m)\n",
+      "u4=0\n",
+      "v1=-0.004\n",
+      "v2=-0.002\n",
+      "v3=0.001\n",
+      "v4=0.001\n",
+      "\n",
+      "\n",
+      "a=np.array([[1,-2,-1,2],[1,2,-1,-2],[1,2,1,2],[1,-2,1,-2]])\n",
+      "b=np.array([u1,u2,u3,u4])\n",
+      "alpha=np.linalg.solve(a,b)\n",
+      "alpha1=alpha[0]\n",
+      "alpha2=alpha[1]\n",
+      "alpha3=alpha[2]\n",
+      "alpha4=alpha[3]\n",
+      "\n",
+      "a=np.array([[1,-2,-1,2],[1,2,-1,-2],[1,2,1,2],[1,-2,1,-2]])\n",
+      "b=np.array([v1,v2,v3,v4])\n",
+      "alpha=np.linalg.solve(a,b)\n",
+      "alpha5=alpha[0]\n",
+      "alpha6=alpha[1]\n",
+      "alpha7=alpha[2]\n",
+      "alpha8=alpha[3]\n",
+      "\n",
+      "u=alpha1+alpha2*x+alpha3*y+alpha4*x*y\n",
+      "v=alpha5+alpha6*x+alpha7*y+alpha8*x*y\n",
+      "\n",
+      "ex=diff(u,x)\n",
+      "ey=diff(v,y)\n",
+      "Yxy=diff(u,y)+diff(v,x)\n",
+      "\n",
+      "ex=-0.000125\n",
+      "ey=.002\n",
+      "Yxy=-0.0015\n",
+      "\n",
+      "sigma_x=E/(1-nu**2)*(ex+nu*ey)\n",
+      "sigma_y=E/(1-nu**2)*(ey+nu*ex)\n",
+      "print \"longitudinal stress in x direction = %3.1f N/mm^2\"%(sigma_x)\n",
+      "print \"longitudinal stress in y direction = %3.1f N/mm^2\"%(sigma_y)\n",
+      "\n",
+      "T_xy=E/2/(1+nu)*Yxy\n",
+      "print \"shear stress at the center of plate = %3.1f N/mm^2\"%(T_xy)"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "longitudinal stress in x direction = 104.4 N/mm^2\n",
+        "longitudinal stress in y direction = 431.3 N/mm^2\n",
+        "shear stress at the center of plate = -115.4 N/mm^2\n"
+       ]
+      }
+     ],
+     "prompt_number": 44
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [],
+     "language": "python",
+     "metadata": {},
+     "outputs": []
+    }
+   ],
+   "metadata": {}
+  }
+ ]
+}
\ No newline at end of file
-- 
cgit