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

K.Y. Liu1,2,3, S.Y. Long1,2,4, G.Y. Li1

State Key Laboratory of Advanced Design and Manufacture for Vehicle Body, Hunan University, Changsha, China
College of Mechanics and Aerospace Engineering, Hunan University, Changsha, China
Mid-south Design & Research Institute, Changsha ,China
Corresponding author. Tel.: +86-0731-8822114. E-mail:

Computers, Materials & Continua 2008, 7(1), 43-58.


A meshless local Petrov-Galerkin method (MLPG) [[Atluri and Zhu (1998)] 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 [Rao and Rahman (2003a,b)] 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.


Cite This Article

K. . Liu, S. . Long and G. . Li, "A meshless local petrov-galerkin method for the analysis of cracks in the isotropic functionally graded material," Computers, Materials & Continua, vol. 7, no.1, pp. 43–58, 2008.

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