Reference:

R. H. Macneal, R. L. Harder, A proposed standard set of problems to test finite element accuracy, North-Holland, Finite elements in analysis and design, 1, 1985, p. 3-20.

Problem description:

A rectangular isotropic plate of constant thickness t is subjected to displacements of the outer edges, providing conditions for constant stresses on the middle surface.

Problem sketch:

Type of created problem:

Spatial construction (X, Y, Z, UX, UY, UZ).

Geometric characteristics:

a = 0.12 m; b = 0.24 m; t = 0.001 m;

Coordinates of points: 1 (0.04, 0.02, 0.00); 2 (0.18, 0.03, 0.00); 3 (0.16, 0.08, 0.00); 4 (0.08, 0.08, 0.00).

Material properties:

Isotropic elastic: E = 1·10⁶ kPa; μ = 0.25.

Boundary conditions:

Along the outer edge: Z = UX = UY = UZ = 0.

Loads:

Node offset: u = (x + y/2)·10^-3 m; v = (x/2 + y)·10^-3 m.

Model description:

The system is modeled by 5 shell elements (FE type is 44).

Analytical solution:

Calculation results: