1. For a 3-node triangular element with all lengths equal to 1, show how the shape...

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1. For a 3-node triangular element with all lengths equal to 1, show how the shape functions will vary over the surface of the element. Show that at any location (x, y) N + N + N3 = 1. 3 y (0, 1) (0, -1) 2 1 (2,0) Figure 1: Triangular element 2. For the element shown in Fig, 1, calculate the element stiffness matrix. The coordinates are in mm. Take E = 70 GPa, v = 0.25, and t = 5 mm. If the nodal displacements (in mm) are U = 0; V1 = 0.01; 0.005; v2= 0; uz = 0; v3 = 0.01 compute the element stresses (assuming plane stress conditions). a 3 2 Po Px = Po [ Figure 2: Triangular element with quadratically varying traction. 1. For a 3-node triangular element with all lengths equal to 1, show how the shape functions will vary over the surface of the element. Show that at any location (x, y) N + N + N3 = 1. 3 y (0, 1) (0, -1) 2 1 (2,0) Figure 1: Triangular element 2. For the element shown in Fig, 1, calculate the element stiffness matrix. The coordinates are in mm. Take E = 70 GPa, v = 0.25, and t = 5 mm. If the nodal displacements (in mm) are U = 0; V1 = 0.01; 0.005; v2= 0; uz = 0; v3 = 0.01 compute the element stresses (assuming plane stress conditions). a 3 2 Po Px = Po [ Figure 2: Triangular element with quadratically varying traction.