Emprego de formulações não-convencionais de elementos finitos na análise linear bidimensional de sólidos com múltiplas fissuras

Abstract

ARGOLO, H. S. D. de (2010). Use of non-conventional formulations of finite element method in the analysis of linear two-dimensional solids with multiple cracks. M.Sc. Dissertation, Escola de Engenharia de Sao Carlos, Universidade de Sao Paulo, Sao Carlos. This paper treats with the use of non-conventional finite element formulations to obtain the stress intensity factor of multiple cracks located in a two-dimensional domain. The formulation of the multiple cracks problem is based on an overlapping approach suggested by the Splitting Method. Accordingly, the solution of the problem can be achieved by dividing the problem in three steps, combined so that the resulting stress flux is zero on the cracks face. The use of the Finite Element Method (FEM) in its conventional formulation requires a mesh refinement in this kind of problem, then increasing the computational cost. Aiming to reduce this cost, two non-conventional formulations are used independently to solve the local problem: the Hybrid-Trefftz stress formulation and the Generalized Finite Elements Method (GFEM). The Hybrid-Trefftz formulation is applied with selective enrichment using prefinement in the displacements field on the element boundaries. The GFEM employs polynomial functions and analytical solutions of the fracture mechanics as enrichment functions. Examples of numerical simulations are presented in order to show that nonconventional formulations and the Splitting Method can provide accurate results with coarse mesh, thus reducing the computational cost.