Open Access

ABSTRACT

A Meshless Local Petrov-Galerkin Method for the Analysis of Cracks in the Isotropic Functionally Graded Material

K. Y. Liu^1,2, S. Y. Long^1,2,3, G. Y. Li¹

1 State Key Laboratory of Advanced Design and Manufacture for Vehicle Body
2 College of Mechanics and Aerospace Engineering, Hunan University, Changsha 410082, China
3 Corresponding author. Tel.: +86-0731-8822114. E-mail address: sylong@hnu.cn

The International Conference on Computational & Experimental Engineering and Sciences 2008, 5(2), 99-120. https://doi.org/10.3970/icces.2008.005.099

Abstract

A meshless local Petrov-Galerkin method (MLPG)^[1] for the analysis of cracks in isotropic functionally graded materials is presented. The meshless method uses the moving least squares (MLS) to approximate the field unknowns. The shape function has not the Kronecker Delta properties for the trial-function-interpolation, and a direct interpolation method is adopted to impose essential boundary conditions. The MLPG method does not involve any domain and singular integrals to generate the global effective stiffness matrix if body force is ignored; it only involves a regular boundary integral. The material properties are smooth functions of spatial coordinates and two interaction integrals^[2,3] are used for the fracture analysis. Two numerical examples including both mode-I and mixed-mode problems are presented to calculated the stress intensity factors (SIFs) by the proposed method. Example problems in functionally graded materials are presented and compared with available reference solutions. A good agreement obtained show that the proposed method possesses no numerical difficulties.

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Keywords

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