r4.03.05 Parametric and non-parametric probabilistic models in dynamics

Summary:

This document describes two probabilistic approaches, one parametric and the other non-parametric, in order to take into account model and modeling uncertainties for dynamic systems in structural mechanics. The non-parametric approach is specific to the resolution on a modal basis of linear systems (transient or harmonic) and to the resolution on a modal basis of systems with localized nonlinearities (in transient). The parametric approach is a priory universal, but it is more particularly presented in the case where it is combined with the non-parametric approach.

• 1. Generalities
• 2. Dynamic system modeling
  • 2.1. Average finite element model
  • 2.2. Average reduced matrix model
• 3. Probabilistic model
  • 3.1. Introduction of the probabilistic model in the dynamic problem
  • 3.2. Probabilistic model for dynamic system matrices (non-parametric uncertainties)
  • 3.3. Probabilistic model for real variables (parametric uncertainties)
  • 3.4. Construction of the stochastic response and associated statistics
• 4. Implemented in Code_Aster
  • 4.1. Study of the stochastic convergence of the numerical model
  • 4.2. Choice of dispersion parameters
  • 4.3. Main steps
  • 4.4. Numerical efficiency of the non-parametric approach
• 5. Verification
• 6. Bibliography
• 7. Description of document versions