ANALISE DE MEIOS PARCIALMENTE FR ́ AGEIS VIA ABORDAGEM GLOBAL-LOCAL COM METODOS SEM MALHA

Resumo

Meshfree Methods have been used as alternatives to Finite Element Method, due to the fle-
xibility in building conforming approximations. Another attractive feature is the capacity of obtaining

approximate solutions of high regularity. Such characteristics can be successfully used to describe state
variables based on the derivatives of the problem solution and responsible for representing the nonlinear

behavior of structures of quasi-brittle material. On the other hand, the lack of the Kronecker-delta pro-
perty, a more complex computation of the shape functions and numerical integration problems represent

drawbacks that can overburden the computational analysis. In nonlinear analysis, the time processing be-
comes an important issue to be considered. Aiming to conciliate the efficiency of finite element analysis

with the flexibility of meshfree methods, coupling techniques for both methods have been proposed, es-
pecially in cases where the nonlinear phenomenon is confined in a small part of the structure. Here, a new

coupling strategy is proposed based on the Global-local Generalized Finite Element Method (GFEM-gl)

to simulate damage propagation in quasi-brittle media. The global domain of the structure is represen-
ted by a coarse mesh of finite elements. The region of damage propagation defines the local domain,

represented by a set of nodes of the meshfree approach called Element Free Galerkin Method (EFG).
This local discretization is responsible for providing a numerically obtained function used to enrich the

approximate solution of the global problem. Numerical examples in two-dimensional domain are pre-
sented to discuss how the meshfree method can efficiently describe the damage propagation, while the

global behavior of the structure is represented by the enriched finite element solution.