v2.03.001 SDLS01 - Thin square plate, free or embedded at the edge

Summary:

The field of application of this test case concerns the dynamics of structures, and more particularly modal calculation and harmonic response calculation.

For the modal calculation, it is a question of calculating the natural modes of bending of a thin square plate in two configurations:

• Plate embedded on one edge,

• Free plate.

The plate is meshed in triangular elements to which DKT elements are assigned.

Four different models are tested:

• Modal calculation— Edges of the plate oriented according to the axes of the coordinate system,

• Modal calculation— Any orientation of the plate and harmonic response for the embedded plate,

• Modal calculation by classical and cyclic dynamic substructuring,

• Modal calculation following a Guyan condensation.

The reference results of modal calculations are derived from analytical calculations. On the one hand, they validate the tools for creating mass and stiffness matrices, as well as the classical and cyclic dynamic substructuring operators implemented in Code_Aster. On the other hand, this test case validates the modal calculation following a Guyan condensation (condensation of the mass matrix).

• 1. Reference problem
  • 1.1. Geometry
  • 1.2. Material properties
  • 1.3. Boundary conditions and loads
  • 1.4. Initial conditions
• 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 B modeling
  • 4.2. Characteristics of the mesh
  • 4.3. Tested sizes and results
  • 4.4. notes
• 5. C modeling
  • 5.1. Characteristics of modeling
  • 5.2. Characteristics of the mesh
  • 5.3. Tested sizes and results
• 6. D modeling
  • 6.1. Characteristics of modeling
  • 6.2. Characteristics of the mesh
  • 6.3. Tested sizes and results
  • 6.4. notes
• 7. Summary of results