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  4. Rectangular Plate Bending – Pinned at Corners

Rectangular Plate Bending – Pinned at Corners

Model Details and Parameters

The purpose of this test case is to validate the plate/shell element solver in SkyCiv Structural 3D (S3D). The results were compared against a third-party analysis software. In this test case the following model parameters were used:

  • Analysis Type: Linear Static
  • Material: Structural Steel
  • Young’s Modulus: 200,000 MPa
  • Poisson’s Ratio: 0.27
  • Plate Type: Mindlin Plane Stress
  • Plate Size: 2m x 1m
  • Plate Thickness: 10 mm
  • Corner Supports: FFFRRR (3D Pin)
  • Pressure Load: 1 kPa normal to plate

pinned-at-corners-model

Results – 8×4 Structured Mesh

Result Location SkyCiv Third-Party 1 Difference 1 Third-Party 2 Difference 2
Max Displacement Z (mm) Node 8 (center of longer edge) -13.004 -13.111 -0.82% -13.004 0.00%
Max Von Mises Stress – Element (MPa) Element 28 Top 28.687 28.834 -0.51% 28.687 0.00%
Reaction Z (kN) Node 1 0.500 0.500 0.00% 0.500 0.00%
Max Moment X – Element (kN-m/m) Element 24 0.167 0.167 0.00% 0.167 0.00%

Results – 16×8 Structured Mesh

Result Location SkyCiv Third-Party 1 Difference 1 Third-Party 2 Difference 2
Max Displacement Z (mm) Node 12 (center of longer edge) -13.171 -13.220 -0.37% -13.171 0.00%
Max Von Mises Stress – Element (MPa) Element 120 Top 30.087 30.129 -0.14% 30.087 0.00%
Reaction Z (kN) Node 1 0.500 0.500 0.00% 0.500 0.00%
Max Moment Y – Element (kN-m/m) Element 120 0.510 0.510 0.00% 0.510 0.00%

Results – Unstructured Mesh

Result Location SkyCiv Third-Party 1 Difference 1 Third-Party 2 Difference 2
Max Displacement Z (mm) Node 14 (center of longer edge) -13.20518 -13.23577 -0.23% -13.20589 -0.01%
Max Von Mises Stress – Element (MPa) Element 99 Top 30.48232 28.78667 5.89% 30.33762 0.48%
Reaction Z (kN) Node 1 0.50002 0.50000 0.00% 0.50000 0.00%
Min Moment XY – Element (kN-m/m) Element 198 -0.19865 -0.19126 3.86% -0.20028 -0.81%

Extra Considerations

  • This verification model was created and checked on 28 February 2020. Since this date, the plate solver and S3D software may have been further improved to achieved greater accuracy.
  • Plates are not exact elements like beam and frame elements and therefore the mesh plays a huge role in the results. Always try to use a structured mesh when it is possible to do so.
  • Results between software will never be exactly the same since different elements are used and the nature of plates are approximate
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