Métodos sem malha e método dos elementos finitos generalizados em análise não-linear de estruturas / Meshless Methods and Generalized Finite Element Method in Structural Nonlinear Analysis

AUTOR(ES)

Felício Bruzzi Barros

DATA DE PUBLICAÇÃO

2002

RESUMO

The Generalized Finite Element Method, GFEM, shares several features with the so called meshless methods. The approximation functions used in the GFEM are associated with nodal points like in meshless methods. In addition, the enrichment of the approximation spaces can be done in the same fashion as in the meshless hp-Cloud method. On the other hand, the partition of unity used in the GFEM is provided by Lagrangian finite element shape functions. Therefore, this method can also be understood as a variation of the Finite Element Method. Indeed, both interpretations of the GFEM are valid and give unique insights into the method. The meshless character of the GFEM justified the investigation of meshless methods in this work. Among them, the Element Free Galerkin Method and the hp-Cloud Method are described aiming to introduce key concepts of the GFEM formulation. Following that, several linear problems are solved using these three methods. Such linear analysis demonstrates several features of the GFEM and its suitability to simulate propagating discontinuities. Next, damage models employed to model the nonlinear behavior of concrete structures are discussed and numerical analysis using the hp-Cloud Method and the GFEM are presented. The results motivate the implementation of a p-adaptive procedure tailored to the GFEM. The technique adopted is the Equilibrated Element Residual Method. The estimator is modified to take into account nonlinear peculiarities of the problems considered. The hypotheses assumed in the definition of the error measure are sometimes violated. Nonetheless, it is shown that the proposed error indicator is effective for the class of p-adaptive nonlinear analysis investigated. Finally, several suggestions are enumerated considering future applications of the GFEM, specially for the simulation of damage and crack propagation

ASSUNTO(S)

mecânica do dano métodos sem malha adaptatividade método dos elementos finitos damage mechanics análise nãolinear finite element method estimador de erro adaptivity error estimator meshless method nonlinear analysis

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