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  4. Rectangular Plate Bending – Fixed at Edges

Rectangular Plate Bending – Fixed 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: FFFFFF (Fixed)
  • Pressure Load: 1 kPa normal to plate

fixed-at-edges-model

Results – 8×4 Structured Mesh

Result Location SkyCiv Third-Party 1 Difference 1 Third-Party 2 Difference 2
Max Displacement Z (mm) Node 25 (center of plate) -0.14645 -0.12737 14.98% -0.14645 0.00%
Max Von Mises Stress – Element (MPa) Element 20 Top 1.66868 1.61767 3.15% 1.66875 0.00%
Max Shear Force YZ – Element (kN/m) Element 24 0.18906 0.24271 -22.10% 0.18906 0.00%
Max Moment XY – Element (kN-m/m) Element 26 0.00703 0.00533 31.89% 0.00703 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 79 (center of plate) -0.14254 -0.13768 3.53% -0.14254 0.00%
Max Von Mises Stress – Element (MPa) Element 120 Top 2.89678 2.87609 0.72% 2.89676 0.00%
Max Shear Force YZ – Element (kN/m) Element 64 0.31696 0.35256 -10.10% 0.31697 0.00%
Max Moment XY – Element (kN-m/m) Element 98 0.01057 0.01008 4.86% 0.01057 0.00%

Results – Unstructured Mesh

Result Location SkyCiv Third-Party 1 Difference 1 Third-Party 2 Difference 2
Max Displacement Z (mm) Node 79 (center of plate) -0.14207 -0.13815 2.84% -0.14195 0.08%
Max Von Mises Stress – Element (MPa) Element 105 Top 3.40034 3.09604 9.83% 3.38262 0.52%
Max Shear Force YZ – Element (kN/m) Element 130 0.39549 0.40303 -1.87% 0.39374 0.44%
Max Moment XY – Element (kN-m/m) Element 225 0.01090 0.01078 1.11% 0.01092 -0.18%

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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