2026-04-17T05:26:53Zhttps://recercat.cat/oai/request

oai:recercat.cat:2117/915022026-01-21T10:27:08Zcom_2072_1033col_2072_452950

urn:hdl:2117/91502 Dimensional hyper-reduction of nonlinear finite element models via empirical cubature Hernández Ortega, Joaquín Alberto Caicedo Silva, Manuel Alejandro Ferrer Ferré, Àlex Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits Multiscale modeling Reduced-order model Hyper-reduction Optimized cubature Finite elements Singular Value Decomposition COMP-DES-MAT Project COMPDESMAT Project Escala multidimensional We present a general framework for the dimensional reduction, in terms of number of degrees of freedom as well as number of integration points (“hyper-reduction”), of nonlinear parameterized finite element (FE) models. The reduction process is divided into two sequential stages. The first stage consists in a common Galerkin projection onto a reduced-order space, as well as in the condensation of boundary conditions and external forces. For the second stage (reduction in number of integration points), we present a novel cubature scheme that efficiently determines optimal points and associated positive weights so that the error in integrating reduced internal forces is minimized. The distinguishing features of the proposed method are: (1) The minimization problem is posed in terms of orthogonal basis vector (obtained via a partitioned Singular Value Decomposition) rather that in terms of snapshots of the integrand. (2) The volume of the domain is exactly integrated. (3) The selection algorithm need not solve in all iterations a nonnegative least-squares problem to force the positiveness of the weights. Furthermore, we show that the proposed method converges to the absolute minimum (zero integration error) when the number of selected points is equal to the number of internal force modes included in the objective function. We illustrate this model reduction methodology by two nonlinear, structural examples (quasi-static bending and resonant vibration of elastoplastic composite plates). In both examples, the number of integration points is reduced three order of magnitudes (with respect to FE analyses) without significantly sacrificing accuracy. Peer Reviewed Postprint (published version) 2017-01 Article http://www.sciencedirect.com/science/article/pii/S004578251631355X info:eu-repo/grantAgreement/EC/FP7/320815/EU/Advanced tools for computational design of engineering materials/COMP-DES-MAT http://creativecommons.org/licenses/by-nc-nd/3.0/es/ Open Access