Estimadores de erro a posteriori para o Método dos Elementos Finitos Generalizados (MEFG) aplicados à análise de estruturas de concreto

Abstract

This work provides a brief description of the main potentialities of the Generalized Finite Element Method (GFEM), which make it a robust tool for solving a wide range of numerical problems. Next, it is introduced the concept of discretization error and its implications for the numerical analysis. The state of art of a posteriori error estimates is presented along with the necessary formulation to the better understanding of their peculiarities. Some of the currently improvements for the Explicit and Implicit residual estimators, based on the Gradient Recovery, Constitutive Relation Error (CRE) and Goal-Oriented are discussed. Special interest is directed to the implicit error estimators (Equilibrated Element Residual-EERM and Subdomain Residua-SRM). The performance of both estimators (efficiency and robustness) is evaluated by local and global effectiveness indices. These measures, are calculated for GFEM numerical solutions of two-dimensional concrete structures, basing on the analysis of coarse and overkill meshes. Firstly, a problem with linear behavior is analyzed and the investigation procedure of the error measures is validated. In the sequence, the estimators are extended for the nonlinear case and two concrete structures are used to assess the quality of EERM and SRM. The physical nonlinearity is incorporated into the calculations adopting the Mazars damage model and some of the main advances in this research segment are emphasized. Undoubtedly, this is the first time that SRM estimator is formulated and applied in solving problems of this kind.