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Question 1: 2-D Four-node Plane Finite Element Method (30 marks) Consider a first-order four-node rectangular plane element shown in Figure 1, made of titanium alloy (E = 110 GPa, v = 0.3). y 4(x4, )4) 3(x3, )3) X 1(x1, y1) 2(x2, y2) Figure 1: 2-D Four-node Plane Finite Element Tutorial Assignment 2 (100 marks, weighted 10%) MECH4002 CAE, Spring 2025 The coordinates of each node in mm are: (x1, VI) = (0, 0) (x2, 12) = (2, 0) (x] , )'3) = (2, 1) ( x4, 14) = (0, 1) The dispalcements at each node are found in the FEA as follows: (1), V,) = (0+0.00q, 0 +0.00q) mm (12, V2) = (0.002 +0.00q, 0.003 +0.00q) mm (U3, 13) = (0.006 +0.00q, 0.0032 + 0.00q) mm (14, V4) = (0 +0.00q, 0+0.00q) mm You are required to a) determine the displacements u and v at the centroid (s = 0,t = 0) b) determine its B matrix of this element at the centroid (s = 0,t =0)