Open Access

ARTICLE

A MLPG4 (LBIE) Formulation in Elastostatics

V. Vavourakis, D. Polyzos¹

1 Department of Mechanical Engineering and Aeronautics, University of Patras, Patras (Greece) Institute of Chemical Engineering and High Temperature Process ICEHT-FORTH, Rio (Greece)

Computers, Materials & Continua 2007, 5(3), 185-196. https://doi.org/10.3970/cmc.2007.005.185

Abstract

Very recently, Vavourakis, Sellountos and Polyzos (2006) ({CMES: Computer Modeling in Engineering {\&} Sciences, vol. 13, pp. 171--184}) presented a comparison study on the accuracy provided by five different elastostatic Meshless Local Petrov-Galerkin (MLPG) type formulations, which are based on Local Boundary Integral Equation (LBIE) considerations. One of the main conclusions addressed in this paper is that the use of derivatives of the Moving Least Squares (MLS) shape functions decreases the solution accuracy of any MLPG(LBIE) formulation. In the present work a new, free of MLS-derivatives and non-singular MLPG(LBIE) method for solving elastic problems is demonstrated. This is accomplished by treating displacements and stresses as independent variables through the corresponding local integral equations and considering nodal points located only internally and externally and not on the global boundary of the analyzed elastic structure. The MLS approximation scheme for the interpolation of both displacements and stresses is exploited. The essential displacement and traction boundary conditions are easily satisfied via the corresponding displacement and stress local integral equations. Representative numerical examples that demonstrate the achieved accuracy of the proposed MLPG(LBIE) method are provided.

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Keywords

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