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Cantilever Membrane

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: Quadrangle
  • Plate Corner 1 Coordinates:  0, 0, 0 m
  • Plate Corner 2 Coordinates:  1, 1, 0 m
  • Plate Corner 3 Coordinates:  1, 1.5, 0 m
  • Plate Corner 4 Coordinates:  0, 1, 0 m
  • Plate Thickness: 5 mm
  • Left-Edge Supports: FFFFFF (Fixed)
  • Point Load: 1 kN +Y vertical at Plate Corner 2

membrane-cantilever-model

Results – 5×5 Structured Mesh

Result Location SkyCiv Third-Party 1 Difference 1 Third-Party 2 Difference 2
Min Displacement X (mm) Node 3 -0.01557 -0.01389 12.10% -0.01557 0.00%
Max Displacement Y (mm) Node 3 0.01844 0.01541 19.66% 0.01844 0.00%
Max Von Mises Stress – Element (MPa) Element 5 Top 1.68643 1.91644 -12.00% 1.67746 0.53%
Max Membrane Force XY – Element (kN/m) Element 21 3.01272 2.70639 11.32% 2.91848 3.23%
Reaction Y Node 15 -0.33642 -0.29053 15.80% -0.33642 0.00%
Reaction X Node 15 -0.63959 -0.61917 3.30% -0.63959 0.00%

Results – 20×20 Structured Mesh

Result Location SkyCiv Third-Party 1 Difference 1 Third-Party 2 Difference 2
Min Displacement X (mm) Node 3 -0.01564 -0.01551 0.84% -0.01564 0.00%
Max Displacement Y (mm) Node 2 0.02020 0.02010 0.50% 0.02020 0.00%
Max Von Mises Stress – Element (MPa) Element 20 Top 5.52230 6.42078 -13.99% 5.49870 0.43%
Max Membrane Force XY – Element (kN/m) Element 381 5.84653 5.65927 3.31% 5.79700 0.85%

Results – Unstructured Mesh

Result Location SkyCiv Third-Party 1 Difference 1 Third-Party 2 Difference 2
Min Displacement X (mm) Node 3 -0.01556 ERR -0.01556 0.00%
Max Displacement Y (mm) Node 3 0.01982 ERR 0.01982 0.00%
Max Von Mises Stress – Element (MPa) Element 82 Top 3.68514 ERR 3.69233 -0.19%
Max Membrane Force XY – Element (kN/m) Element 112 5.01036 ERR 4.59800 8.97%

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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