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Hemispherical shell under concentrated loads

Model Details and Parameters

Determine the displacements of a hemispherical shell subjected to concentrated tensile and compressive loads in two orthogonal radial directions.
Only a quarter model may be analyzed due to symmetry.


Structural geometry and analysis model

Structural geometry


  • Analysis Type
    3-D static analysis
  • Dimension
    Radius: 10.0 in
  • Plate Type
    Mindlin Plane Stress
  • Material
    Structural Steel
    Young’s Modulus: 68250 ksi
    Poisson’s Ratio: 0.3
  • Element Property
    Plate Thickness: 0.04 in
  • Boundary Supports
    Nodes 1 – 9: Constrain Dy, Rx and Rz. (Symmetric about X-Z plane)
    Nodes 73 – 81: Constrain Dx, Ry and Rz. (Symmetric about Y-Z plane)
    Node 37: Constrain Dz. (To prevent the rigid body motion in the Z direction)
  • Loads
    A concentrated load, 1.0 lbf is applied to the node 1 in the X direction
    A concentrated load, 1.0 lbf is applied to the node 73 in the -Y direction



Analysis model


X-displacements of the structure (Node 1)2

X-displacements of the structure (Node 1)

Von Mises Stress of the structure (Element 2)

Von Mises Stress of the structure (Element 2)

Comparison of Results

Result Location SkyCiv Theoretical Difference 1 Third-Party 2 Difference 2
Max Displacement X (in) Node 1 0.094795 0.094000 0.85% 0.094789 0.01%
Max Von Mises Stress – Element (ksi) Element 1 Top 4.944245     4.989211 0.90%


MacNeal, R. H. and Harder, R. C., “Proposed Standard Set of Problems to Test Finite Element Accuracy”, Finite Elements in Analysis and Design 1, 1985, pp. 3-20, NorthHolland.

Extra Considerations

  • This verification model was created and checked on 26 April 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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