Integração numérica por decomposição de elementos no contexto do método dos elementos finitos generalizados

Abstract

The current work presents the employment of alternative numerical integration strategies over the conventional ones to be applied in the Generalized Finite Element Method context, specifically in two-dimensional Fracture Mechanics models. It is suggested to utilize the subdivision of elements and mapping of the integration points in mesh elements containing discontinuities or singularities, therefore representing the displacements and stress fields more precisely. It is aimed to validate the implemented strategies by analysing the strain energy and stiffness computed in a range of examples, comparing them to conventional Gauss quadrature situations. The cited strategies are also applied in cases modelled by the Stable Generalized Finite Element Method (GFEM), the global-local methodology (GFEMgl) and the Physically Non-Linear Analysis. It is achieved good results and reduced processing times due to the decrease in the number of integration points, which are allocated taking into account problems particularities. Computational implementations were performed as part of the expansion of INSANE (INteractive Structural ANalysis Environment), an open-source software project developed by the Structural Department of the Federal University of Minas Gerais.