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.
- Analysis Type
3-D static analysis
Radius: 10.0 in
- Plate Type
Mindlin Plane Stress
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
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%|
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.
- 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