2014•Advanced materials researchRequires access

Application of the Meshless Local Petrov-Galerkin Method for Subsoil Settlement Analysis

Juraj Mužík, Dana Sitányiová

Abstract

The paper deals with use of the meshless method for soil stress-deformation analysis. There are many formulations of the meshless methods. The article presents the Meshless Local Petrov-Galerkin method (MLPG) local weak formulation of the equilibrium equations. The main difference between meshless methods and the conventional finite element method (FEM) is that meshless shape functions are constructed using randomly scattered set of points without any relation between points. The shape function construction is the crucial part of the meshless numerical analysis in the construction of shape functions. The article presents the radial point interpolation method (RPIM) for the shape functions construction.

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Key concepts: Regularized meshless method, Petrov–Galerkin method, Meshfree methods, Mathematics, Finite element method, Singular boundary method, Interpolation (computer graphics), Galerkin method