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
  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

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