LE1: Elliptic Membrane

CalculiX FEM/FEA, Gmsh, NetGen, Structural Analysis (FEM/FEA)

Description

Calculate the tangential edge stress (σyy) at point D (as indicated in the figure below) of an elliptical membrane under uniform outward pressure.

Reference

  1. Test LE1 from NAFEMS Publication NNB, Rev. 3, NAFEMS Linear Benchmarks, 5 Oct 1990.

Analysis type

Linear Static Analysis

Technologies used

  • Meshing: Gmsh, NetGen
  • Solver: Calculix

Geometry

LE1 Elliptic membrane
Figure 1: Elliptic membrane

Load assumptions

Uniform outward pressure of 10 MPa at outer edge BC, Inner curved edge AD unloaded.

Boundary conditions

  • Edge AB, symmetry about Y axis, e.g. zero x displacement
  • Edge CD, symmetry about X axis, e.g. zero y displacement

Material properties

E = 210 GPa, ν = 0.3

Computation target

Tangential edge stress (σyy) at point D = 92.7 MPa

Results

LE1: Elliptic Membrane meshed with Gmsh, calculated with CalculiX
Figure 2: LE1: Elliptic Membrane meshed with Gmsh, calculated with CalculiX
LE1: Elliptic Membrane meshed with NetGen, calculated with CalculiX
Figure 3: LE1: Elliptic Membrane meshed with NetGen, calculated with CalculiX

Summary

TheoryGmsh+CalculiXError
92.7 MPa91.248 MPa-1.566 %
Table 1: Tangential edge stress (σyy) meshed with Gmsh, calculated with CalculiX
TheoryNetGen+CalculiXError
92.7 Mpa92.943 MPa0.262 %
Table 2: Tangential edge stress (σyy) meshed with NetGen, calculated with CalculiX

Conclusion

CalculiX results are comparable with theoretical results.

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