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  • Open Access

    ARTICLE

    Adaptive Support Domain Implementation on the Moving Least Squares Approximation for Mfree Methods Applied on Elliptic and Parabolic PDE Problems Using Strong-Form Description

    G. C. Bourantas1, E. D. Skouras2,3,4, G. C. Nikiforidis1

    CMES-Computer Modeling in Engineering & Sciences, Vol.43, No.1, pp. 1-26, 2009, DOI:10.3970/cmes.2009.043.001

    Abstract The extent of application of meshfree methods based on point collocation (PC) techniques with adaptive support domain for strong form Partial Differential Equations (PDE) is investigated. The basis functions are constructed using the Moving Least Square (MLS) approximation. The weak-form description of PDEs is used in most MLS methods to circumvent problems related to the increased level of resolution necessary near natural (Neumann) boundary conditions (BCs), dislocations, or regions of steep gradients. Alternatively, one can adopt Radial Basis Function (RBF) approximation on the strong-form of PDEs using meshless PC methods, due to the delta function… More >

  • Open Access

    ARTICLE

    A Mesh-Free DRK-Based Collocation Method for the Coupled Analysis of Functionally Graded Magneto-Electro-Elastic Shells and Plates

    Chih-Ping Wu1,2, Kuan-Hao Chiu2, Yung-Ming Wang2

    CMES-Computer Modeling in Engineering & Sciences, Vol.35, No.3, pp. 181-214, 2008, DOI:10.3970/cmes.2008.035.181

    Abstract A mesh-free collocation method based on differential reproducing kernel (DRK) approximations is developed for the three-dimensional (3D) analysis of simply-supported, doubly curved functionally graded (FG) magneto-electro-elastic shells under the mechanical load, electric displacement and magnetic flux. The material properties of FG shells are firstly regarded as heterogeneous through the thickness coordinate and then specified to obey an identical power-law distribution of the volume fractions of the constituents. The novelty of the present DRK-based collocation method is that the shape functions of derivatives of reproducing kernel (RK) approximants are determined using a set of differential reproducing… More >

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