TEST CASE 7.3 RECTANGULAR PLATE UNDER CONSTANT STRESSES ON THE MIDDLE SURFACE
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 = 1·10^{6} 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:
Target value |
Analytical solution |
LIRA 10 |
Deviation, % |
σ_{x}, kPa |
1333.33 |
1333.33 |
0.00 |
σ_{y}, kPa |
1333.33 |
1333.33 |
0.00 |
τ_{xy}, kPa |
400 |
400 |
0.00 |