Question 1 The displacement vector of the plane stress 4-node bilinear finite element shown in Figure Q1 is as follows:

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Question 1 The Displacement Vector Of The Plane Stress 4 Node Bilinear Finite Element Shown In Figure Q1 Is As Follows 1 (52.82 KiB) Viewed 41 times

Question 1 The displacement vector of the plane stress 4-node bilinear finite element shown in Figure Q1 is as follows: {d} = [u. V uz V2 u v 14 va]"= [0 0 0 0 0.002 0.002 0.001 0.001]" (m) (a) Determine the shape functions of the element giving short statements to describe each stage of the derivation (b) Determine the displacements at the centroid of the element. (c) Determine the strain vector {8) at the centroid of the element. (d) Determine the stress vector (o) at the centroid of the element if the elastic modulus is equal to E = 200 GPa and Poisson's ratio v=0.3. Recall that for plane stress conditions the constitutive [D] matrix is given by: 1 Vp 1-w Vp 0 E [D] = 1 0 (1- Y(m) 1m X(m) (0,0) Im 2m 2m Figure Q1 Answers u(0,0)=1:6/8 103=0.75-10m v(0,0)=1:6/8-10-3 =0.75-10'm Ex = 0.125 . 10-3, y = 0.75 . 10-3 Yxy = 0.875. 10-3 (0.0769 {g} = 0.1731 GPa 0.0673)