C Page < 2 > of 3 - ZOOM + Question 2 (10 marks): As indicated in Fig 2, we assume that there is one quadrilateral element (No. 63) with 4 corner nodes (Q4). After finite element meshing and solution, the nodal coordinates, and displacements for the element No 63 in the global coordinate system are given in Table 1, respectively. Let the material Young's modulus E = 125GPa and Poisson's ratio u = 0.25. As shown in Fig 3, using the isoparametric element and 1-node Gaussian quadrature (5=0, n=0), calculate (hand calculation) (1). The strain {8} of the element. (2). The stress {6} of the element. Displacement Displacement 2 Force: 10000 N A 250 265 63 1 251 266 Fig 2: A structural mesh for a 2-D plan stress analysis problem Node Number Table 1. Nodal coordinates and displacements for element No 63 Coordinates (Ansys meshing) Displacements (Ansys solution) X location (m) Y location (m) X Displacement Y Displacement 250 1.7443 251 1.8581 0.0649 0.0389 0.2985E-9 -0.8085E-11 0.3461E-9 -0.4778E-11 266 1.9775 0.1577 0.3954E-9 -0.1972E-10 265 1.8125 0.2319 0.3212E-9 -0.2847E-10 n. 2 C Page 3 > of 3 - ZOOM + Node Number X location (m) Y location (m) Table 1. Nodal coordinates and displacements for element No 63 Coordinates (Ansys meshing) Displacements (Ansys solution) Y Displacement X Displacement 250 1.7443 0.0649 0.2985E-9 -0.8085E-11 251 1.8581 0.0389 0.3461E-9 -0.4778E-11 266 1.9775 0.1577 0.3954E-9 -0.1972E-10 265 1.8125 0.2319 0.3212E-9 -0.2847E-10 (-1,1) (1,1) (-1,-1) =n=0 Fig 3: Isoparametric element using 1-by-1 rule for Gaussian quadrature 3