LE4: Axisymmetric hyperbolic shell under uniform internal pressure

Description

Find the meridional stress and the hoop stress at point B shown in Figure 1.

Reference

1. NAFEMS Finite Element Methods & Standards, The Standard NAFEMS Benchmarks, Test No. LE4. Glasgow: NAFEMS, Rev. 3, 1990.

Analysis type

Linear Static Analysis

Technologies used

• Meshing: Gmsh, NetGen
• Solver: Calculix

Geometry

Load assumptions

Uniform internal pressure of 1.0 MPa.

Boundary conditions

Axisymmetric about rq plane at y=0, i.e. around the waist circle through B:

• zero displacement in y direction

Material properties

Isotropic, E = 210 GPa, ν = 0.3

Computation target

On the midsurface at point B, the meridional stress is –50.0 MPa and the hoop stress is 50.0 MPa.

Results

Summary

	Theory	Gmsh+CalculiX	Error
Meridional stress	-50.0 MPa	-50.202 MPa	0.40 %
Hoop stress	50.0 MPa	50.337 MPa	0.67 %

	Theory	NetGen+CalculiX	Error
Meridional stress	-50.0 MPa	-51.584 MPa	3.17 %
Hoop stress	50.0 MPa	48.469 MPa	-3.06 %

Conclusion

CalculiX results are comparable with theoretical results.