Consider the bar with two elements shown in Figure P7.10. Perform a patch test using the...

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 m⁴. 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.

(3.1.14))

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.