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  4. Rectangular Plate Bending – Pinned at Edges

Rectangular Plate Bending – Pinned at Edges

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
  • Edge Boundary Supports: FFFRRR (3D Pin)
  • Pressure Load: 1 kPa normal to plate

pinned-at-edges-model

Results – 8×4 Structured Mesh

Result Location SkyCiv Third-Party Difference
Max Displacement Z (mm) Node 25 (center of plate) -0.53034 -0.56405 -5.98%
Max Von Mises Stress (MPa) Element 20 Top 4.71616 4.82904 -2.34%
Reaction Y (kN) Node 21 0.12062 0.12961 -6.94%
Max Shear Force XZ (kN/m) Element 1 0.35016 0.33767 3.70%

Results – 16×8 Structured Mesh

Result Location SkyCiv Third-Party Difference
Max Displacement Z (mm) Node 120 (center of plate) -0.55578 -0.56542 -1.70%
Max Von Mises Stress (MPa) Element 72 Top 5.13836 5.17574 -0.72%
Reaction Y (kN) Node 71 0.06206 0.06307 -1.60%
Max Shear Force XZ (kN/m) Element 1 0.40466 0.40086 0.95%

Results – Unstructured Mesh

Result Location SkyCiv Third-Party Difference
Max Displacement Z (mm) Node 182 (center of plate) -0.55725 -0.56293 -1.01%
Max Von Mises Stress (MPa) Element 170 Top 5.23330 5.25876 -0.48%
Reaction Y (kN) Node 59 0.04126 0.04217 -2.16%
Max Shear Force XZ (kN/m) Element 1 0.55652 0.49276 12.94%

pinned-at-edges-results

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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