C-04 (Cook Membrane Problem) |
  
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C-04 (Cook Membrane Problem) |
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Objective
To verify compatible and incompatible membrane formulations
Problem Description
The skewed cantilever plate shown below is subjected to a distributed shear of 1 lb at the end.
Material properties: E = 1.0 psi, ν = 0.333
Thickness t = 1 in
Finite Element Model
4 shell elements
Model type: 2D Plane Stress (using compatible and incompatible formulations)
Results
The best results are given by [Ref 1] as follows:
Displacement Dy @ C: 23.9 in
Principal stress S1 @ A: 0.236 psi
Principal stress S2 @ B: -0.201 psi
Units: displacement – in; stress - psi
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Compatible formulation |
Incompatible formulation |
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Displacement Dy @ C |
Principal Stress S1 @ A |
Principal Stress S2 @ B |
Displacement Dy @ C |
Principal Stress S1 @ A |
Principal Stress S2 @ B |
2 x 2 mesh |
11.85 |
0.1078 |
-0.07762 |
21.05 |
0.1789 |
-0.1694 |
64x64 |
23.92 |
0.2376 |
-0.2038 |
23.96 |
0.2368 |
-0.2035 |
[Ref 1] |
23.9 |
0.236 |
-0.201 |
23.9 |
0.236 |
-0.201 |
Comments
The results given by ENERCALC 3D are compared with the referenced values. For the 2 x 2 coarse mesh, the incompatible formulation is superior to the compatible one. For the 64 x 64 fine mesh, both compatible and incompatible formulations give satisfactory results.
Reference
[1]. Bergan & Filippa, “Triangular membrane element with rotational degrees of freedom”, Comput. Meth. Appl. Mech. Engng., 50: 25-69, 1985
