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International Journal for Multiscale Computational Engineering
IF: 1.016 5-Year IF: 1.194 SJR: 0.554 SNIP: 0.68 CiteScore™: 1.18

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.2019028866
pages 239-260

HIGHER ORDER MULTIPOINT MESHLESS FINITE DIFFERENCE METHOD FOR TWO-SCALE ANALYSIS OF HETEROGENEOUS MATERIALS

Irena Jaworska
Institute for Computational Civil Engineering, Cracow University of Technology, Warszawska 24, 31-155 Cracow, Poland

ABSTRACT

This article is an introduction to the numerical homogenization of the heterogeneous material with periodic structure by the new Multipoint solution approach−a higher order extension of the Meshless Finite Difference Method (MFDM). The recently developed Multipoint method follows the original Collatz higher order concept and the essential idea of the MFDM−the moving weighted least squares approximation, using the arbitrarily irregular cloud of nodes as well as various formulations of boundary value problems. The method improves the former procedure without the necessity of providing additional unknowns to both the mesh and the MFD operator. The Multipoint meshless method, like the MFDM, may be used at the macro and the micro levels in the two-scale analysis of heterogeneous materials based on the single Representative Volume Element (RVE). The analysis of the convergence of the effective material parameters for the set of meshes was conducted and compared with the FEM. The error analysis at the micro and macro level confirm the high quality of the Multipoint solution, which may also be used as the improved reference solution instead of the true analytical one for the a posteriori error estimation.

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