Consider the thin plate supported on three springs and subjected to a uniformly distributed load...

Consider the thin plate supported on three springs and subjected to a uniformly distributed load as shown in Fig. 14.5. Solve this problem using one quadratic quadrilateral element as shown in the figure. Given E = 200 GPa, ν = 0.3, t = 0.01 m, k = 4000 kN/m, and w = 5000 kN/m^{2}, determine:

1. the global stiffness matrix for the structure.

2. the horizontal and vertical displacements at nodes 1, 2, 3, 6, 7, and 8.

3. the reactions at nodes 9, 10, and 11.

4. the stresses in the element.

5. the principal stresses and principal angle for the element.

6. the force in each spring.

Compare your answers with those obtained for Problem 11.3 and Problem 13.3.

Problem 13.3

Consider the thin plate supported on three springs and subjected to a uniformly distributed load as shown in Fig. 13.10. Given E = 200 GPa, ν = 0.3, t = 0.01 m, k = 4000 kN/m, and w = 5000 kN/m^{2}, determine:

1. the global stiffness matrix for the structure.

2. the horizontal and vertical displacements at nodes 1, 2, 3, 4, 5, and 6.

3. the reactions at nodes 7, 8, and 9.

4. the stresses in each element.

5. the principal stresses and principal angle for each element.

6. the force in each spring.

Use two bilinear quadrilaterals to solve this problem. Compare your answers with those obtained for Problem 11.3.

Problem 11.3

Consider the thin plate supported on two springs and subjected to a uniformly distributed load as shown in Fig. 11.9. Given E = 200 GPa, ν = 0.3, t = 0.01 m, k = 4000 kN/m, and w = 5000 kN/m^{2}, determine:

1. the global stiffness matrix for the structure.

2. the horizontal and vertical displacements at nodes 1, 2, 3, and 4.

3. the reactions at nodes 5 and 6.

4. the stresses in each element.

5. the principal stresses and principal angle for each element.