Consider the bar with two elements shown in Figure P7.10. Perform a patch test using these two elements. Let E = 200 GPa, and A = 1 × 10-4 m2. Use the standard bar element stiffness matrix [Eq. (3.1.14)] derived using the shape functions N1 (x) = x / L and N2 (x) = 1 - x/L.

a. For the rigid body motion test, set u1 = 1 m and u3 = 1 m and verify that u2 = 1 m by using the direct stiffness method.

b. For the constant strain test, assume linear displacement function u(x) = x for the nodes at the boundaries, such that u1 = 0 and u3 = 2 m, and verify that u2 = 0.6 m.

Figure P7-10

-1.4 m- 0.6 m