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    BEST PAPER 2021

    Numerical Solution of Nonlinear Schrodinger Equations by Collocation Method Using Radial Basis Functions

    Sirajul Haq1,2, Siraj-Ul-Islam3, Marjan Uddin1,4 CMES-Computer Modeling in Engineering & Sciences, Vol.44, No.2, pp. 115-136, 2009, DOI:10.3970/cmes.2009.044.115
    Abstract A mesh free method for the numerical solution of the nonlinear Schrodinger (NLS) and coupled nonlinear Schrodinger (CNLS) equation is implemented. The presented method uses a set of scattered nodes within the problem domain as well as on the boundaries of the domain along with approximating functions known as radial basis functions (RBFs). The set of scattered nodes do not form a mesh, means that no information of relationship between the nodes is needed. Error norms L2, L are used to estimate accuracy of the method. Stability analysis of the method is given to demonstrate its practical applicability. More >

  • Research Article

    BEST PAPER 2021

    Investigation of Inherent Deformation in Fillet Welded Thin Plate T-joints Based on Interactive Substructure and Inverse Analysis Method

    Rui Wang1, Jianxun Zhang1, Hisashi Serizawa2, Hidekazu Murakawa2 CMES-Computer Modeling in Engineering & Sciences, Vol.44, No.1, pp. 97-114, 2009, DOI:10.3970/cmes.2009.044.097
    Abstract In this paper, the inherent deformation of fillet welded thin plate T-joints is studied. The prediction procedure of inherent deformation consists of three parts: part one, a three dimensional (3D) thermo-elastic-plastic analysis using an in house finite element (FE) code of interactive substructure method (ISM) is utilized to obtain the welding distortions; part two, corresponding experiments are carried out to verify the computational results of ISM; part three, using the verified computational results, the inverse analysis is utilized to evaluate the welding inherent deformation. Based on the results in this study, an inherent deformations database of fillet welded thin plate… More >

  • Research Article

    BEST PAPER 2021

    Solution of Incompressible Turbulent Flow by a Mesh-Free Method

    R. Vertnik1, B. Šarler2 CMES-Computer Modeling in Engineering & Sciences, Vol.44, No.1, pp. 65-96, 2009, DOI:10.3970/cmes.2009.044.065
    Abstract The application of the mesh-free Local Radial Basis Function Collocation Method (LRBFCM) in solution of incompressible turbulent flow is explored in this paper. The turbulent flow equations are described by the low - Re number k-emodel with Jones and Launder [Jones and Launder (1971)] closure coefficients. The involved velocity, pressure, turbulent kinetic energy and dissipation fields are represented on overlapping 5-noded sub-domains through collocation by using multiquadrics Radial Basis Functions (RBF). The involved first and second derivatives of the fields are calculated from the respective derivatives of the RBF's. The velocity, turbulent kinetic energy and dissipation equations are solved through… More >

  • Research Article

    BEST PAPER 2021

    A Simplified Analysis of the Tire-Tread Contact Problem using Displacement Potential Based Finite-Difference Technique

    S Reaz Ahmed1, S K Deb Nath1 CMES-Computer Modeling in Engineering & Sciences, Vol.44, No.1, pp. 35-64, 2009, DOI:10.3970/cmes.2009.044.035
    Abstract The paper presents a simplified analysis of stresses and deformations at critical sections of a tire-tread. Displacement potential formulation is used in conjunction with the finite-difference method to model the present contact problem. The solution of the problem is obtained for two limiting cases of the contact boundary - one allows the lateral slippage and the other conforms to the no-slip condition along the lateral direction. The influential effects of tire material and tread aspect-ratio are discussed. The reliability and accuracy of the solution is also discussed in light of comparison made with the usual computational approach. More >

  • Research Article

    BEST PAPER 2021

    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 with the Radial Point Interpolators.… More >

  • Research Article

    BEST PAPER 2021

    MLPG_R Method for Numerical Simulation of 2D Breaking Waves

    Q.W. Ma1,2, J.T. Zhou1 CMES-Computer Modeling in Engineering & Sciences, Vol.43, No.3, pp. 277-304, 2009, DOI:10.3970/cmes.2009.043.277
    Abstract Following our previous work, the Meshless Local Petrov-Galerin me -thod based on Rankine source solution (MLPG_R) will be extended in this paper to deal with breaking waves. For this purpose, the governing equation for pressure is improved and a new technique called Mixed Particle Number Density and Auxiliary Function Method (MPAM) is suggested for identifying the free surface particles. Due to complexity of the problem, two dimensional (2D) breaking waves are only concerned here. Various cases are investigated and some numerical results are compared with experimental data available in literature to show the newly developed method is robust. More >

  • Research Article

    BEST PAPER 2021

    A Highly Accurate Technique for Interpolations Using Very High-Order Polynomials, and Its Applications to Some Ill-Posed Linear Problems

    Chein-Shan Liu1, Satya N. Atluri2 CMES-Computer Modeling in Engineering & Sciences, Vol.43, No.3, pp. 253-276, 2009, DOI:10.3970/cmes.2009.043.253
    Abstract Since the works of Newton and Lagrange, interpolation had been a mature technique in the numerical mathematics. Among the many interpolation methods, global or piecewise, the polynomial interpolation p(x) = a0 + a1x + ... + anxn expanded by the monomials is the simplest one, which is easy to handle mathematically. For higher accuracy, one always attempts to use a higher-order polynomial as an interpolant. But, Runge gave a counterexample, demonstrating that the polynomial interpolation problem may be ill-posed. Very high-order polynomial interpolation is very hard to realize by numerical computations. In this paper we propose a new polynomial interpolation… More >

  • Research Article

    BEST PAPER 2021

    Elastic analysis in 3D anisotropic functionally graded solids by the MLPG

    J. Sladek1, V. Sladek1, P. Solek2 CMES-Computer Modeling in Engineering & Sciences, Vol.43, No.3, pp. 223-252, 2009, DOI:10.3970/cmes.2009.043.223
    Abstract A meshless method based on the local Petrov-Galerkin approach is proposed for solution of static and elastodynamic problems in 3-D continuously non-homogeneous anisotropic bodies. Functionally graded materials (FGM) are multi-phase materials with the phase volume fractions varying gradually in space, in a pre-determined profile. The Heaviside step function is used as the test functions in the local weak form resulting into the derived local integral equations (LIEs). For transient elastodynamic problems either the Laplace transform or the time difference techniques are applied. Nodal points are randomly distributed in the 3D analyzed domain and each node is surrounded by a spherical… More >

  • Research Article

    BEST PAPER 2021

    Transient Thermal Response of a Partially Insulated Crack in an Orthotropic Functionally Graded Strip under Convective Heat Supply

    Yueting Zhou1, Xing Li2, Dehao Yu1 CMES-Computer Modeling in Engineering & Sciences, Vol.43, No.3, pp. 191-222, 2009, DOI:10.3970/cmes.2009.043.191
    Abstract The transient response of an orthotropic functionally graded strip with a partially insulated crack under convective heat transfer supply is considered. It is modeled there exists thermal resistant in the heat conduction through the crack region. The mixed boundary value problems of the temperature field and displacement field are reduced to a system of singular integral equations in Laplace domain. The expressions with high order asymptotic terms for the singular integral kernel are considered to improve the accuracy and efficiency. The numerical results present the effect of the material nonhomogeneous parameters, the orthotropic parameters and dimensionless thermal resistant on the… More >

  • Research Article

    BEST PAPER 2021

    Applications of the Fictitious Time Integration Method Using a New Time-Like Function

    Cheng-Yu Ku1,2, Weichung Yeih1,2, Chein-Shan Liu3, Chih-Chang Chi2 CMES-Computer Modeling in Engineering & Sciences, Vol.43, No.2, pp. 173-190, 2009, DOI:10.3970/cmes.2009.043.173
    Abstract In this paper, a new time-like function with the incorporation of the fictitious time integration method (FTIM) is proposed. The new time-like function is modified from the original time-like function in the FTIM by adding a control parameter m, which dramatically improves the performance of the FTIM for solving highly nonlinear boundary value problems (BVPs) and plays as an important controller to assure the convergence of the solution during the time integration process. The requirements and the characteristics of the new time-like function are presented by examining the FTIM through the perspective of the new time-like function in which the… More >

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