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  • Open Access

    ABSTRACT

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

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

    The International Conference on Computational & Experimental Engineering and Sciences, Vol.5, No.2, pp. 99-120, 2008, DOI: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 More >

  • Open Access

    ARTICLE

    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

    CMC-Computers, Materials & Continua, Vol.7, No.1, pp. 43-58, 2008, DOI:10.3970/cmc.2008.007.043

    Abstract 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 More >

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