Comparison of enriched meshless finite volume and element free Galerkin methods for the analysis of heterogeneous media

Abstract

Meshless methods are considered as powerful numerical methods for computational mechanics, but due to high-order continuity of solution space in the standard meshless methods, they may lead to undesired oscillations in derivative fields in heterogeneous media. Towards an efficient meshless computation in heterogeneous media, the enrichment technique is already used in combination with different methods, such as element free Galerkin (EFG) method. In this work, it is demonstrated that the enriched formulation of the meshless finite volume method (FVM) can be considered as a potential alternative. In contrast to the EFG method, the meshless FVM is based on local weak form and utilizes a Petrov–Galerkin procedure. In this paper, a detailed comparison is made between the enriched formulation of these two methods, and then, their capability to the analysis of 1D and 2D heterogeneous media is investigated. It is demonstrated that enriched EFG method is more accurate for the analysis of 1D heterogeneous problems. However, for the analysis of 2D heterogeneous problems, enriched meshless FVM reveals more accuracy in both displacement and stress fields predictions.