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  • Open Access

    ARTICLE

    Large Deformation Applications with the Radial Natural Neighbours Interpolators

    L.M.J.S. Dinis1, R.M. Natal Jorge2, J. Belinha3

    CMES-Computer Modeling in Engineering & Sciences, Vol.44, No.1, pp. 1-34, 2009, DOI:10.3970/cmes.2009.044.001

    Abstract The Natural Neighbour Radial Point Interpolation Method (NNRPIM) is extended to the large deformation analysis of non-linear elastic structures. The nodal connectivity in the NNRPIM is enforced using the Natural Neighbour concept. After the Voronoï diagram construction of the unstructured nodal mesh, which discretize the problem domain, small cells are created, the "influence-cells". These cells are in fact influence-domains entirely nodal dependent. The Delaunay triangles are used to create a node-depending background mesh used in the numerical integration of the NNRPIM interpolation functions. The NNRPIM interpolation functions, used in the Galerkin weak form, are constructed… More >

  • Open Access

    ARTICLE

    A Local Meshless Shepard and Least Square Interpolation Method Based on Local Weak Form

    Y.C. Cai1 and H.H. Zhu1

    CMES-Computer Modeling in Engineering & Sciences, Vol.34, No.2, pp. 179-204, 2008, DOI:10.3970/cmes.2008.034.179

    Abstract The popular Shepard PU approximations are easy to construct and have many advantages, but they have several limitations, such as the difficulties in handling essential boundary conditions and the known problem of linear dependence regarding PU-based methods, and they are not the good choice for MLPG method. With the objective of alleviating the drawbacks of Shepared PU approximations, a new meshless PU-based Shepard and Least Square (SLS) interpolation is employed here to develop a new type of MLPG method, which is named as Local Meshless Shepard and Least Square (LMSLS) method. The SLS interpolation possesses… More >

  • Open Access

    ARTICLE

    A Topology Optimization Design for the Continuum Structure Based on the Meshless Numerical Technique

    Zheng Juan1,2,3, Long Shuyao1,2, Xiong Yuanbo1,2, Li Guangyao1

    CMES-Computer Modeling in Engineering & Sciences, Vol.34, No.2, pp. 137-154, 2008, DOI:10.3970/cmes.2008.034.137

    Abstract In this paper, the meshless radial point interpolation method (RPIM) is applied to carry out a topology optimization design for the continuum structure. Considering the relative density of nodes as a design variable, and the minimization of compliance as an objective function, the mathematical formulation of the topology optimization design is developed using the SIMP (solid isotropic microstructures with penalization) interpolation scheme. The topology optimization problem is solved by the optimality criteria method. Numerical examples show that the proposed approach is feasible and efficient for the topology optimization design for the continuum structure, and can More >

  • Open Access

    ARTICLE

    A Meshless Local Natural Neighbour Interpolation Method Applied to Structural Dynamic Analysis

    Y. H. Liu1,2, S. S. Chen1, J. Li1, Z. Z. Cen1

    CMES-Computer Modeling in Engineering & Sciences, Vol.31, No.3, pp. 145-156, 2008, DOI:10.3970/cmes.2008.031.145

    Abstract A novel meshless method for structural dynamic analysis is presented and discussed in this paper. It is called meshless local natural neighbour interpolation (MLNNI) method, which uses a meshless spatial approximation based only on nodes. The MLNNI is derived from the generalized meshless local Petrov-Galerkin (MLPG) method as a special case. Local weak forms are developed using weighted residual method locally from the dynamic partial differential equation. In the construction of trial functions, the natural neighbour interpolation (NNI) is employed to simplify the treatment of the essential boundary conditions. The domain integration is evaluated over More >

  • Open Access

    ARTICLE

    An Analysis for the Elasto-Plastic Fracture Problem by the Meshless Local Petrov-Galerkin Method

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

    CMES-Computer Modeling in Engineering & Sciences, Vol.28, No.3, pp. 203-216, 2008, DOI:10.3970/cmes.2008.028.203

    Abstract A meshless local Petrov-Galerkin method (MLPG) for the analysis of the elasto-plastic fracture problem is presented in this paper. The meshless method uses the moving least squares (MLS) to approximate the field functions. The shape function has not 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 if body force is ignored. It only involves a regular boundary integral. Two numerical examples show that results obtained by the present method have a good agreement More >

  • Open Access

    ARTICLE

    A Novel Form of Reproducing Kernel Interpolation Method with Applications to Nonlinear Mechanics

    Amit Shaw1, D Roy2

    CMES-Computer Modeling in Engineering & Sciences, Vol.19, No.1, pp. 69-98, 2007, DOI:10.3970/cmes.2007.019.069

    Abstract A novel discretization strategy and derivative reproduction based on reproducing kernel (RK) particle approximations of functions are proposed. The proposed scheme is in the form of an RK interpolation that offers significant numerical advantages over a recent version of the strategy by Chen et al. (2003), wherein the authors added a set of primitive functions to the reproducing kernel (enrichment) functions. It was also required that the support size of the primitive function be less than the smallest distance between two successive grid points. Since the primitive function was required to vary from 0 to… More >

  • Open Access

    ARTICLE

    A Comparative Study of Meshless Approximations in Local Integral Equation Method

    Vladimir Sladek1, Jan Sladek1, Chuanzeng Zhang2

    CMC-Computers, Materials & Continua, Vol.4, No.3, pp. 177-188, 2006, DOI:10.3970/cmc.2006.004.177

    Abstract This paper concerns the stability, convergence of accuracy and cost efficiency of four various formulations for solution of boundary value problems in non-homogeneous elastic solids with functionally graded Young's modulus. The meshless point interpolation method is employed with using various basis functions. The interaction among the elastic continuum constituents is considered in the discretized formulation either by collocation of the governing equations or by integral satisfaction of the force equilibrium on local sub-domains. The exact benchmark solutions are used in numerical tests. More >

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