Generalized Finite Element Method in linear and nonlinear structural dynamic analyses

Abstract

PurposeThe purpose of this study is to evaluate the accuracy and numerical stability of the Generalized Finite Element Method (GFEM) for solving structural dynamic problems.Design/methodology/approachThe GFEM is a numerical method based on the Partition of Unity (PU) concept. The method can be understood as an extension of the conventional Finite Element Method (FEM) for which the local approximation provided by the shape functions can be improved by means of enrichment functions. Polynomial enrichment functions are hereby used combined with an implicit time-stepping integration technique for improving the dynamical response of the models. Both consistent and lumped mass matrices techniques are tested. The method accuracy and stability are investigated through linear and nonlinear elastic problems.FindingsThe results indicate that the adopted strategies can provide stable and accurate responses for GFEM in dynamic analyses. Furthermore, the mass lumping technique provided remarkable reductions of the system of equation condition number, therefore leading to more stable numerical models.Originality/valueThe evaluated features of GFEM models for implicit time-stepping integration schemes represent new information of great deal of interest regarding linear and nonlinear dynamic analyses using such a method.