Structural uncertainty modeling for nonlinear geometric response using nonintrusive reduced order models

• Published in: Probabilistic engineering mechanics 2020-04, Vol.60 (103033), p.103033-9, Article 103033
• Main Authors: Wang, X.Q., Mignolet, Marc P., Soize, Christian
• Format: Article
• Language: English
• Subjects: Engineering Sciences; Finite element analysis; Finite element method; Mapping; Mathematical models; Mathematics; Matrix methods; Maximum entropy; Maximum entropy method; Mechanics; Model forms; Modelling; Nonlinear geometric structural response; Nonlinear response; Probability; Reduced order modeling; Reduced order models; Software; Statistics; Stiffness coefficients; Structural mechanics; Thermics; Uncertain structure; Uncertainty; Uncertainty analysis; Uncertainty modeling; Vibrations
• ISSN: 0266-8920; 1878-4275
• DOI: 10.1016/j.probengmech.2020.103033

The focus of the present investigation is on the introduction of uncertainty directly in reduced order models of the nonlinear geometric response of structures following maximum entropy concepts. While the approach was formulated and preliminary validated in an earlier paper, its broad application to a variety of structures based on their finite element models from commercial software was impeded by two key challenges. The first of these involves an indeterminacy in the mapping of the nonlinear stiffness coefficients identified from the finite element model to those of the reduced order model form that is suitable for the uncertainty analysis. The second challenge is that a key matrix in the uncertainty modeling was expected to be positive definite but was numerically observed not to be. This latter issue is shown here to be rooted in differences in nonlinear finite element modeling between the commercial software and the theoretical developments. Both of these challenges are successfully resolved and applications examples are presented that confirm the broad applicability of the methodology.