Ruben Avila¹, Zhidong Han², Satya N. Atluri³

CMES-Computer Modeling in Engineering & Sciences, Vol.71, No.4, pp. 363-396, 2011, DOI:10.3970/cmes.2011.071.363

Abstract The two dimensional steady state Stokes equations are solved by using a novel MLPG-Mixed Finite Volume method, that is based on the independent meshless interpolations of the deviatoric velocity strain tensor, the volumetric velocity strain tensor, the velocity vector and the pressure. The pressure field directly obtained from this method does not suffer from the malady of checker-board patterns. Numerical simulations of the flow field, and trajectories of passive fluid elements in a new complex Stokes flow are also presented. The new flow geometry consists of three coaxial cylinders two of smaller diameter, that steadily rotate independently, inside a third… More >

Jianxin Zhu¹, Zheqi Shen¹

CMES-Computer Modeling in Engineering & Sciences, Vol.71, No.4, pp. 347-362, 2011, DOI:10.3970/cmes.2011.071.347

Abstract It is known that the perfectly matched layer (PML) is a powerful tool to truncate the unbounded domain. Recently, the PML technique has been introduced in the computation of nonlinear Schrödinger equations (NSE), in which the nonlinearity is separated by some efficient time-splitting methods. A major task in the study of PML is that the original equation is modified by a factor c which varies fast inside the layer. And a large number of grid points are needed to capture the profile of c in the discretization. In this paper, the possibility is discussed for using some nonuniform finite difference… More >

Seyed Mahmoud Hosseini¹, Farzad Shahabian²,Jan Sladek³, Vladimir Sladek³

CMES-Computer Modeling in Engineering & Sciences, Vol.71, No.1, pp. 39-66, 2011, DOI:10.3970/cmes.2011.071.039

Abstract The thermo-elastic wave propagation based on Green-Naghdi (GN) coupled thermo-elasticity (without energy dissipation) is studied in a functionally graded thick hollow cylinder considering uncertainty in constitutive mechanical properties under thermal shock loading. The meshless local Petrov-Galerkin method accompanied with Monte-Carlo simulation is developed to solve the stochastic boundary value problem. In the presented method, the mechanical properties of FGM are considered to be as random variables with Gaussian distribution and mean values equal to deterministic values reported in previous works, which are generated using Monte-Carlo simulation with various coefficients of variations (COVs). The time evolution for transient problems is treated… More >

S. Abbasbandy^1,2, V. Sladek³, A. Shirzadi¹, J. Sladek³

CMES-Computer Modeling in Engineering & Sciences, Vol.71, No.1, pp. 15-38, 2011, DOI:10.3970/cmes.2011.071.015

Abstract This paper deals with the development of a new method for solution of initial-boundary value problems governed by a couple of nonlinear diffusion equations occurring in the theory of self-organization in non-equilibrium systems. The time dependence is treated by linear interpolation using the finite difference method and the semi-discrete partial differential equations are considered in a weak sense by using the local integral equation method with approximating 2-d spatial variations of the field variables by the Moving Least Squares. The evaluation techniques are discussed and the applicability of the presented method is demonstrated on two illustrative examples with exact solutions… More >

J. Sladek¹, V. Sladek¹, Ch. Zhang², M. Wünsche²

CMES-Computer Modeling in Engineering & Sciences, Vol.68, No.2, pp. 185-220, 2010, DOI:10.3970/cmes.2010.068.185

Abstract A meshless method based on the local Petrov-Galerkin approach is proposed to solve initial-boundary value crack problems of piezoelectric solids with nonlinear electrical boundary conditions on crack faces. Homogeneous and continuously varying material properties of the piezoelectric solid are considered. Stationary governing equations for electrical fields and the elastodynamic equations with an inertial term for mechanical 2-D fields are considered. Nodal points are spread on the analyzed domain, and each node is surrounded by a small circle for simplicity. The spatial variation of displacements and electric potential are approximated by the Moving Least-Squares (MLS) scheme. After performing the spatial integrations,… More >

Harishchandra Thakur¹, K. M. Singh², P. K. Sahoo³

CMES-Computer Modeling in Engineering & Sciences, Vol.68, No.2, pp. 117-150, 2010, DOI:10.3970/cmes.2010.068.117

Abstract MLPG method is a meshfree method which removes the need of meshing of computational domain at any stage of numerical analysis. Current article extends MLPG method to nonlinear heat conduction in irregular domains including the problem of solid-liquid phase change. Moving least square (MLS) scheme is used to interpolate the trial function and a fourth order spline function is used as the test function. Method of direct interpolation is used to enforce essential boundary conditions. Nonlinearities in the problems are handled with an iterative predictor-corrector method. Time integration is performed using θ-method. MLPG method has also been extended to non-homogeneous… More >

Jin Yeon Cho¹, Min Hwan Oh¹

CMES-Computer Modeling in Engineering & Sciences, Vol.66, No.3, pp. 187-214, 2010, DOI:10.3970/cmes.2010.066.187

Abstract In this work, a sample-reusable sequential approximate optimization (SAO) procedure is suggested. The suggested sequential approximate optimization procedure utilizes a newly proposed sample-reusable meta-model along with the trust region algorithm. Domain of design is sequentially updated to search for the optimal solution through the trust region algorithm, and the system response in the updated design region at each sequential stage is approximated by the proposed sample-reusable meta-model. The proposed sample-reusable meta-model is based on the moving least squares(MLS) approximation scheme. Thanks to the merits of moving least squares scheme, the proposed meta-model can fully utilize the previously sampled responses as… More >

P. Bettini¹, M. Midrio², R. Specogna²

CMES-Computer Modeling in Engineering & Sciences, Vol.66, No.2, pp. 117-134, 2010, DOI:10.3970/cmes.2010.066.117

Abstract In this paper we propose a geometric formulation to solve 3D electromagnetic wave problems in unbounded regions in the frequency domain. An absorbing boundary condition (ABC) is introduced to limit the size of the computational domain by means of anisotropic Perfectly Matched Layers (PML) absorbing media in the outer layers of an unstructured mesh. The numerical results of 3D benchmark problems are presented and the effect of the PML parameters and scaling functions on PML effectiveness are discussed. More >

Ahmad Akbari R.¹, Akbar Bagri², Stéphane P. A. Bordas^3,4, Timon Rabczuk⁵

CMES-Computer Modeling in Engineering & Sciences, Vol.65, No.1, pp. 27-74, 2010, DOI:10.3970/cmes.2010.065.027

Abstract This contribution focuses on the simulation of two-dimensional elastic wave propagation in functionally graded solids and structures. Gradient volume fractions of the constituent materials are assumed to obey the power law function of position in only one direction and the effective mechanical properties of the material are determined by the Mori-Tanaka scheme. The investigations are carried out by extending a meshless method known as the Meshless Local Petrov-Galerkin (MLPG) method which is a truly meshless approach to thermo-elastic wave propagation. Simulations are carried out for rectangular domains under transient thermal loading. To investigate the effect of material composition on the… More >

P.H. Wen¹, M.H. Aliabadi²

CMES-Computer Modeling in Engineering & Sciences, Vol.61, No.2, pp. 133-154, 2010, DOI:10.3970/cmes.2010.061.133

Abstract A meshless local Petrov-Galerkin method, for the micro-mechanical material model of woven fabric composite material is presented in this paper. The material models are based on a repeated unit cell approach and two smooth fibre modes. A unit step function is used as the test functions in the local weak-form which leads to local boundary integral equations. The analysed domain is divided into small sub-domains and the radial basis function interpolation without element mesh is adopted. The woven fabric composite elastic moduli evaluated have been shown to be in good agreement with finite element results. More >