e) For a 3-noded triangular element (dimension in mm) in Figure 2d, the displacements (in mm)...

Transcribed Image Text:

e) For a 3-noded triangular element (dimension in mm) in Figure 2d, the displacements (in mm) at the nodes are obtained as [ui vi u2 v2 U3 v3] = [-0.002 0.001 0.00 0.003 0.001 -0.002]. Calculate the strains and stresses of the element in plane stress state. (10 marks) 3 (0.3) E = 80 GPa v=0.25 Thickness t=0.1 mm 2 (2.1) 1 (0,0) Figure 2d Note: The shape functions for a 3-noded triangle element are given by: N = 24 (x23 x3 2 ) + (12 - 13 )x + (x3 x2 )y} - N2 = (x301 - 13 ) + (13 - 11 ) + (x x3 ]y} N 2.A 3 = {(x112 -231) + (31-32)x+(x2 x1)} N3 2.A = and A is the area of the triangular element. The [B] matrix is given by JN3 [B] = 0 aN aN3 21 21 22 22 2N3 dy The [D] matrix for plane stress state is given by 0N3 [D] = 1- E 1 v V 1 00 | 2. e) For a 3-noded triangular element (dimension in mm) in Figure 2d, the displacements (in mm) at the nodes are obtained as [ui vi u2 v2 U3 v3] = [-0.002 0.001 0.00 0.003 0.001 -0.002]. Calculate the strains and stresses of the element in plane stress state. (10 marks) 3 (0.3) E = 80 GPa v=0.25 Thickness t=0.1 mm 2 (2.1) 1 (0,0) Figure 2d Note: The shape functions for a 3-noded triangle element are given by: N = 24 (x23 x3 2 ) + (12 - 13 )x + (x3 x2 )y} - N2 = (x301 - 13 ) + (13 - 11 ) + (x x3 ]y} N 2.A 3 = {(x112 -231) + (31-32)x+(x2 x1)} N3 2.A = and A is the area of the triangular element. The [B] matrix is given by JN3 [B] = 0 aN aN3 21 21 22 22 2N3 dy The [D] matrix for plane stress state is given by 0N3 [D] = 1- E 1 v V 1 00 | 2.