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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

• Analysis Type
3-D static analysis
• Dimension
• 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)
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

### Results

X-displacements of the structure (Node 1)

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%

### Reference

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