A computational framework for a two-scale generalized/extended finite element method

Abstract

This paper presents a computational framework to generate numeric enrichment functions for two-dimensional problems dealing with single/multiple local phenomenon. The two-scale generalized/extended finite element method (G/XFEM) approach used here is based on the solution decomposition, having a global and local scale components. This strategy allows the use of a coarse mesh even when the problem produces complex local phenomena. For this purpose, local problems can be defined where these local phenomena are observed and are solved separately using fine meshes. The results of the local problems are used to enrich the global one improving the approximate solution. The implementation of the two-scale G/XFEM formulation follows the object-oriented approach presented by the authors in a previous work, where it is possible to combine different kinds of elements and analysis models with the partition of unity enrichment scheme. Beside the extension of the G/XFEM implementation to enclose the global-local strategy, the imposition of different boundary conditions is also generalized. This generalization is very important since the global-local approach relies on the boundary information transferring process between the two scales of the analysis. The flexibility for the numerical analysis of the proposed framework is illustrated by several examples. Different analysis models, element formulations and enrichment functions are employed and the accuracy, robustness and computational efficiency are demonstrated.

The New Approach to Analysis of Thin Isotropic Symmetrical Plates

“…The extended finite element method (G/XFEM) [3,[49][50][51][52][53][54][55] is generalization of classical finite element method and it was especially developed for modeling structural problems with discontinuities. According to that generalized global approximation of the deflection of the plate is presented as [51]:…”

Analysis of a main fatigue crack interaction with multiple micro-cracks/voids in a compact tension specimen repaired by stop-hole technique

“…The XFEM was introduced to overcome FEM issues with the discontinuity problems. [48][49][50][51][52] This is a partition of unity-based method that uses enrichment functions to represent phenomena of the problem and also to guarantee inter-element continuity. 53 The enrichment function allows the insertion of a crack inside the elements.…”

Imposition of Dirichlet Boundary Conditions in Element Free Galerkin Method through an Object-Oriented Implementation

“…The processor is the numerical core of the system, responsible for obtaining the results of the analysis. There are different computational methods available for the processor, such as FEM, Fonseca and Pitangueira (2007), Generalized/Extended FEM, Alves et al (2013), Malekan and Barros (2016), Malekan et al (2016aMalekan et al ( , 2016bMalekan et al ( , 2017, and Boundary element method, Anacleto et al (2013), Peixoto et al (2016).…”