ON SOME ASPECTS OF THE MESHLESS FDM APPLICATION FOR THE HETEROGENEOUS MATERIALS

Abstract

The most commonly used engineering tool for numerical analysis of a variety of the heterogeneous materials is the finite element method. However, this paper focuses on the alternative approach based upon the meshless finite difference method (MFDM). The purpose of the work is to present some key features, as well as the selected results of the MFDM application for the heterogeneous material. The MFDM solution approach and its higher order extensions, e.g., the multipoint meshless method, may be used at both the macro and the micro levels in a two-scale analysis. At the macro level the heterogeneous material with inclusions spaced periodically was assumed. The values of effective material constants were determined by calculation at the micro level for a single representative volume element (RVE). The paper focuses on the numerical analysis, particularly on the examination of the influence of some factors, e.g., stencil configuration on solution quality based on the MFDM.