v2.03.007 SDLS07 - Eigenmodes of a thin spherical envelope

Summary:

This test from guide VPCS makes it possible to validate the algorithms of the CALC_MODES eigenvalue search operator with the stiffness and mass matrices corresponding to the following models:

1. three-dimensional shells: finite elements DKT (mesh size of a 1/8 sphere),

2. axisymmetric \(\mathrm{2D}\) finite elements TRIA6 and QUAD8 (mesh of a section),

3. three-dimensional shells: axisymmetric isoparametric finite elements SEG3 (linear mesh of the section),

4. three-dimensional shells COQUE_3D: finite element MEC3QU9H (1/8 sphere mesh),

5. 3D shells COQUE_3D: finite element MEC3TR7H.

The results obtained are compared with the analytical solution (HAYEK) and show differences of less than:

• \(\text{0,45\%}\) for axisymmetric continuous medium elements,

• \(\text{0,20\%}\) for DKT shell elements,

• \(\text{0,17\%}\) for isoparametric axisymmetric shell elements,

• \(\text{0,17\%}\) for COQUE_3D elements.

• 1. Reference problem
  • 1.1. Geometry
  • 1.2. Material properties
  • 1.3. Boundary conditions and loads
• 2. Benchmark solution
  • 2.1. Calculation method used for the reference solution
  • 2.2. Benchmark results
  • 2.3. Uncertainty about the solution
  • 2.4. Bibliographical references
• 3. Modeling A
  • 3.1. Characteristics of modeling
  • 3.2. Characteristics of the mesh
  • 3.3. Tested sizes and results
  • 3.4. notes
• 4. B modeling
  • 4.1. Characteristics of modeling
  • 4.2. Characteristics of the mesh
  • 4.3. Tested sizes and results
• 5. C modeling
  • 5.1. Characteristics of modeling
  • 5.2. Characteristics of the mesh
  • 5.3. Tested sizes and results
  • 5.4. notes
• 6. D modeling
  • 6.1. Characteristics of modeling
  • 6.2. Characteristics of the mesh
  • 6.3. Tested sizes and results
  • 6.4. notes
• 7. E modeling
  • 7.1. Characteristics of modeling
  • 7.2. Characteristics of the mesh
  • 7.3. Tested sizes and results
  • 7.4. notes
• 8. Summary of results