u2.06.04 Instructions for the construction of dynamic scale models

Summary:

The models used for linear dynamic response calculations are getting bigger and bigger. To significantly improve calculation times, it is possible to build a small-sized subspace that makes it possible to project the complete problem, and thus accelerate the various response calculations. These reduced component models can also be used in sub-structuring approaches, and certain non-linear analyses (shocks, non-linear behavior). A methodology is also proposed to « condense » internal variables for linear dynamic analysis. This manual aims to help users build dynamic scale models and provides a framework for evaluating the quality of built scale models.

We emphasize the value of the process of orthogonalization of projection bases (operator DEFI_BASE_MODALE , keyword ORTHO_BASE ) making it possible to eliminate vectors that are too collinear, resulting from the concatenation of several families of vectors. A family containing almost collinear vectors will lead, in the worst case, to singular projected matrices and to a poorly posed problem.

• 1. Introduction
• 2. Model reduction: principle of static correction
  • 2.1. Description and ratings
  • 2.2. Model reduction and static correction
  • 2.3. Model reduction hypothesis
  • 2.4. Definition of static correction
  • 2.5. Test cases illustrating the use of static corrections
  • 2.6. Indications for the subsequent control of the quality of the scale model
• 3. Taking into account external efforts, shocks, and non-linear behaviors
• 4. Model reduction for dynamic substructuring.
  • 4.1. Classic methods: Craig&Bampton and MacNeal&Rubin.
  • 4.2. Use of interface modes.
  • 4.3. Calculating interface modes
• 5. Construction of a base adapted to the dissipative problem
  • 5.1. Construction of a complete database on the static correction model for hysteretic and/or viscous damping.
  • 5.2. Taking into account the particularity of the problem
  • 5.3. Filtering the reduction base
  • 5.4. Iterations on residues
  • 5.5. Reduction of models including internal variables (or intermediate variables)
• 6. Code_Aster test case
  • 6.1. Note on the studies presented
  • 6.2. Numerical example with hysteretic damping
  • 6.3. Numerical example with viscoelastic damping described by internal variables
• 7. Conclusions on the use of reduction methods
• 8. References