v2.02.010 SDLL10 - Beam with variable rectangular cross section (recessed and embedded)

Summary:

This flat problem consists in looking for the frequencies and modes of vibration of a mechanical structure composed of a recessed and embedded beam whose area of the straight section varies exponentially. This Structural Mechanics test corresponds to a dynamic analysis of a linear model with linear behavior. It includes a single model.

By means of this problem, we test the Timoshenko flexure beam element of variable cross section as well as the calculation of the frequencies and modes of vibration by the Lanczos method. The « standard to 1. » functionality is also tested at the point of maximum translational amplitude » of the vibration modes.

By using fine spatial discretization, the results obtained are in good agreement with the analytical results given in guide VPCS.

• 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. Summary of results