Método dos elementos finitos generalizados aplicado a problemas de fratura elástica em 3D

Abstract

The Generalized Finite Element Method (GFEM) was consolidated in the scientic eld as a very useful tool in the resolution of complex structural models using an eective approximate approach to represent the propagation of cracks and other micro-defects. This is a non-conventional formulation of the Finite Element Method (FEM), in that there is an expansion of the solution space from the use of enrichment functions associated with the nodes. The enrichment functions can be singular functions derived from analytic deductions, polynomial functions, or even functions resulting from other solution processes, such as the Global-Local strategy. The INSANE (INteractive Structural ANalysis Environment) is a computational platform of the Department of Structural Engineering (DEES) of the Federal University of Minas Gerais (UFMG) and aims to analyze structures of engineering interest. In its current version, it is able to solve problems through several analysis models of any dimension using GFEM. This work proposes the expansion of the system to consider the possibility of using dierent enrichment functions in three-dimensional models, such as functions that contain singularities and those obtained under the GlobalLocal technique approach. Numerical examples from the Linear Elastic Fracture Mechanics are presented to validate the proposed implementation