v2.01.107 SDLD107 - Minimization of an error-type energy functional in relation to behavior in structural dynamics

Summary:

The field of application of this test concerns the dynamics of structures. It makes it possible to validate the calculation operator CALC_ERC_DYN [u4.53.41] which makes it possible to obtain the solution fields of a problem of minimizing an error-type energy functional in relation to behavior (ERC) under a modal formulation.

The aim is to solve the ERC problem for a system composed of 3 masses and 4 springs, embedded at its ends in free vibration. The springs and the masses are modelled by elements of the type “DIS_T”.

The verified results for the case studied were obtained semi-analytically. Its resolution, which acts as a reference, was carried out using the Matlab software.

• 1. Reference problem
  • 1.1. Geometry
  • 1.2. Material properties
  • 1.3. Boundary conditions
  • 1.4. Initial conditions
  • 1.5. Observation
  • 1.6. Error functional
• 2. Benchmark solution
  • 2.1. Calculation method used for the reference solution
  • 2.2. Benchmark results
  • 2.3. Uncertainty about the solution
• 3. Modeling A
  • 3.1. Characteristics of the mesh
  • 3.2. Tested sizes and results
• 4. Summary of results