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Search Results (106)
  • Open Access

    ARTICLE

    Force State Maps Using Reproducing Kernel Particle Method and Kriging Based Functional Representations

    Vikas Namdeo1,2, C S Manohar1,3

    CMES-Computer Modeling in Engineering & Sciences, Vol.32, No.3, pp. 123-160, 2008, DOI:10.3970/cmes.2008.032.123

    Abstract The problem of identification of nonlinear system parameters from measured time histories of response under known excitations is considered. Solutions to this problem are obtained by using the force state mapping technique with two alternative functional representation schemes. These schemes are based on the application of reproducing kernel particle method (RKPM) and kriging techniques to fit the force state map. The RKPM has the capability to reproduce exactly polynomials of specified order at any point in a given domain. The kriging based methods represent the function under study as a random field and the parameters describing this field are optimally… More >

  • Open Access

    ARTICLE

    A Numerical Solution of 2D Buckley-Leverett Equation via Gradient Reproducing Kernel Particle Method

    Hossein M. Shodja1,2,3, Alireza Hashemian1,4

    CMES-Computer Modeling in Engineering & Sciences, Vol.32, No.1, pp. 17-34, 2008, DOI:10.3970/cmes.2008.032.017

    Abstract Gradient reproducing kernel particle method (GRKPM) is a meshless technique which incorporates the first gradients of the function into the reproducing equation of RKPM. Therefore, in two-dimensional space GRKPM introduces three types of shape functions rather than one. The robustness of GRKPM's shape functions is established by reconstruction of a third-order polynomial. To enforce the essential boundary conditions (EBCs), GRKPM's shape functions are modified by transformation technique. By utilizing the modified shape functions, the weak form of the nonlinear evolutionary Buckley-Leverett (BL) equation is discretized in space, rendering a system of nonlinear ordinary differential equations (ODEs). Subsequently, Gear's method is… More >

  • Open Access

    ARTICLE

    Derivation of Anti-Plane Dynamic Green's Function for Several Circular Inclusions with Imperfect Interfaces

    Jeng-Tzong Chen1, Jia-Nan Ke

    CMES-Computer Modeling in Engineering & Sciences, Vol.29, No.3, pp. 111-136, 2008, DOI:10.3970/cmes.2008.029.111

    Abstract A null-field integral equation is employed to derive the two-dimensional antiplane dynamic Green's functions for a circular inclusion with an imperfect interface. We employ the linear spring model with vanishing thickness to characterize the imperfect interface. Analytical expressions of displacement and stress fields due to time-harmonic antiplane line forces located either in the unbounded matrix or in the circular inclusion are presented. To fully capture the circular geometries, degenerate- kernel expressions of fundamental solutions in the polar coordinate and Fourier series for boundary densities are adopted. Good agreement is made after comparing with the analytical solution derived by Wang and… More >

  • Open Access

    ARTICLE

    A Differential Reproducing Kernel Particle Method for the Analysis of Multilayered Elastic and Piezoelectric Plates

    Chih-Ping Wu1, Kuan-Hao Chiu, Yun-Ming Wang

    CMES-Computer Modeling in Engineering & Sciences, Vol.27, No.3, pp. 163-186, 2008, DOI:10.3970/cmes.2008.027.163

    Abstract A differential reproducing kernel particle (DRKP) method is proposed and developed for the analysis of simply supported, multilayered elastic and piezoelectric plates by following up the consistent concepts of reproducing kernel particle (RKP) method. Unlike the RKP method in which the shape functions for derivatives of the reproducing kernel (RK) approximants are obtained by directly taking the differentiation with respect to the shape functions of the RK approximants, we construct a set of differential reproducing conditions to determine the shape functions for the derivatives of RK approximants. On the basis of the extended Hellinger-Reissner principle, the Euler-Lagrange equations of three-dimensional… More >

  • Open Access

    ARTICLE

    A NURBS-based Parametric Method Bridging Mesh-free and Finite Element Formulations

    Amit Shaw1, B. Banerjee1, D Roy1,2

    CMES-Computer Modeling in Engineering & Sciences, Vol.26, No.1, pp. 31-60, 2008, DOI:10.3970/cmes.2008.026.031

    Abstract A generalization of a NURBS based parametric mesh-free method (NPMM), recently proposed by Shaw and Roy (2008), is considered. A key feature of this parametric formulation is a geometric map that provides a local bijection between the physical domain and a rectangular parametric domain. This enables constructions of shape functions and their derivatives over the parametric domain whilst satisfying polynomial reproduction and interpolation properties over the (non-rectangular) physical domain. Hence the NPMM enables higher-dimensional B-spline based functional approximations over non-rectangular domains even as the NURBS basis functions are constructed via the usual tensor products of their one-dimensional counterparts. Nevertheless the… More >

  • Open Access

    ARTICLE

    A Posteriori Error Estimation and Adaptive Node Refinement for Fast Moving Least Square Reproducing Kernel (FMLSRK) Method

    Chany Lee1, Chang-Hwan Im2, Hyun-Kyo Jung3, Hong-Kyu Kim4, Do Wan Kim5

    CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.1, pp. 35-42, 2007, DOI:10.3970/cmes.2007.020.035

    Abstract In the present study, a residual-based a posteriori error estimation for a kind of meshless method, called fast moving least square reproducing kernel (FMLSRK) method is proposed. The proposed error estimation technique does not require any integration cells in evaluating error norm but recovers the exact solutions in a virtual area defined by a dilation parameter of FMLSRK and node density. The proposed technique was tested on typical electrostatic problems with gird or random node sets and the simulation results show that the proposed error estimation technique can be applied to adaptive node refinement process for more efficient meshless analysis… More >

  • Open Access

    ARTICLE

    A MRIEM for Solving the Laplace Equation in the Doubly-Connected Domain

    Chein-Shan Liu1

    CMES-Computer Modeling in Engineering & Sciences, Vol.19, No.2, pp. 145-162, 2007, DOI:10.3970/cmes.2007.019.145

    Abstract A new method is developed to solve the Dirichlet problems for the two-dimensional Laplace equation in the doubly-connected domains, namely the meshless regularized integral equations method (MRIEM), which consists of three portions: Fourier series expansion, the Fredholm integral equations, and linear equations to determine the unknown boundary conditions onartificial circles. The boundary integral equations on artificial circles are singular-free and the kernels are degenerate. When boundary-type methods are inefficient to treat the problems with complicated domains, the new method can be applicable for such problems. The new method by using the Fourier series and the Fourier coefficients can be adopted… 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 1 within half of this… More >

  • Open Access

    ARTICLE

    On the Equivalence Between Least-Squares and Kernel Approximations in Meshless Methods

    Xiaozhong Jin1, Gang Li2, N. R. Aluru3

    CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.4, pp. 447-462, 2001, DOI:10.3970/cmes.2001.002.447

    Abstract Meshless methods using least-squares approximations and kernel approximations are based on non-shifted and shifted polynomial basis, respectively. We show that, mathematically, the shifted and non-shifted polynomial basis give rise to identical interpolation functions when the nodal volumes are set to unity in kernel approximations. This result indicates that mathematically the least-squares and kernel approximations are equivalent. However, for large point distributions or for higher-order polynomial basis the numerical errors with a non-shifted approach grow quickly compared to a shifted approach, resulting in violation of consistency conditions. Hence, a shifted polynomial basis is better suited from a numerical implementation point of… More >

  • Open Access

    ARTICLE

    Construction of Green's function using null-field integral approach for Laplace problems with circular boundaries

    Jeng-Tzong Chen1,2, Jia-Nan Ke1, Huan-Zhen Liao1

    CMC-Computers, Materials & Continua, Vol.9, No.2, pp. 93-110, 2009, DOI:10.3970/cmc.2009.009.093

    Abstract A null-field approach is employed to derive the Green's function for boundary value problems stated for the Laplace equation with circular boundaries. The kernel function and boundary density are expanded by using the degenerate kernel and Fourier series, respectively. Series-form Green's function for interior and exterior problems of circular boundary are derived and plotted in a good agreement with the closed-form solution. The Poisson integral formula is extended to an annular case from a circle. Not only an eccentric ring but also a half-plane problem with an aperture are demonstrated to see the validity of the present approach. Besides, a… More >

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