49325 CAMD: Computer-Aided Mechanical Design Assignment 2 XXXXXXXXXX04 May 2017 Name: XXXXXXXXXXStudent ID: THIS ASSIGNMENT SHOULD TAKE AN AVERAGE STUDENT 5 HOURS TO COMPLETE. Question 1: Figure 1 shows a 2D mesh for a structural plan stress analysis problem. We assume that an element with No 15 is such a quadrilateral element with 4 corner nodes in the mesh, and its 4 node coordinates in the global coordinate system (in millimetres) are given in Figure 2. Let Young’s modulus E = 200GPa and Poisson’s ratio ? = 0.25. As indicated in Figure 3, using the isoparametric Q4 element and 4-node Gaussian quadrature (numerical integration to approximate the element stiffness matrix), calculate: 1 The stiffness matrix of the element 15 by using hand calculations 2 The stress of the element at the local location ?=0, ?=0. Figure 1: A structural mesh for a 2-D plan stress analysis problem 1Figure 2: The quadrilateral element in two dimensions ?Gauss point 1: ?? ?? , ??? 0.5773,?0.5773? 11 ? Gauss point 2: ?? ,?? 0.5773, 0.5773 ??? ? W? 1 ? 21? 1 ? Weights: ? Gauss point 3: ?? , ??0.5773,0.5773 ??? ? 12 W? 1 ? ? 2 ? Gauss point 4: ?? ,? 0.5773,0.5773 ??? ? 22 ? Figure 3: The isoparametric element using 2-by-2 rule for Gaussian quadrature 2
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