A MLPG4 (LBIE) Formulation in Elastostatics

Abstract

Very recently, Vavourakis, Selloun- tos and Polyzos (2006) (CMES: Computer Mod- eling 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 Bound- ary Integral Equation (LBIE) considerations. One of the main conclusions addressed in this pa- per is that the use of derivatives of the Moving Least Squares (MLS) shape functions decreases the solution accuracy of any MLPG(LBIE) for- mulation. In the present work a new, free of MLS-derivatives and non-singular MLPG(LBIE) method for solving elastic problems is demon- strated. This is accomplished by treating dis- placements and stresses as independent variables through the corresponding local integral equa- tions 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 bound- ary conditions are easily satisfied via the corre- sponding displacement and stress local integral equations. Representative numerical examples that demonstrate the achieved accuracy of the pro- posed MLPG(LBIE) method are provided. Keyword: MLPG4, LBIE, MLS, hypersingu- lar, elastostatics