R.H. Moore¹, S. Saigal²

CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.3, pp. 283-292, 2005, DOI:10.3970/cmes.2005.007.283

Abstract An efficient method for treating slivers and other poorly shaped elements in finite element solutions is presented. A major difficulty for finite element analyses arises from the creation of slivers in automated mesh generation. Sliver shaped elements can degrade the accuracy of a solution and are difficult to remove from a mesh. The proposed method treats slivers by first merging them with neighboring elements to form polyhedra and next subdividing the polyhedra into well-shaped tetrahedral elements. The method does not require the cumbersome and expensive operations of addition or rearrangement of nodes. The validity and More >

Hiroshi Kadowaki¹, Wing Kam Liu²

CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.3, pp. 269-282, 2005, DOI:10.3970/cmes.2005.007.269

Abstract A method to derive governing equations and elastic-plastic constitutive relations for the micropolar continuum model is proposed. Averaging procedures are operated over a surrounding sub-domain for each material point to bridge a discrete microstructure to a macro continuum model. Material parameters are determined by these procedures. The size of the sub-domain represents the material intrinsic length scale, and it is passed into the macroscopic governing equation so that the numerical solution can be regularized for analyses of failure phenomena. An application to a simple granular material model is presented. More >

S. N. Atluri¹, Shengping Shen¹

CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.3, pp. 241-268, 2005, DOI:10.3970/cmes.2005.007.241

Abstract Various MLPG methods, with the MLS approximation for the trial function, in the solution of a 4$^{th}$ order ordinary differential equation are illustrated. Both the primal MLPG methods and the mixed MLPG methods are used. All the possible local weak forms for a 4$^{th}$ order ordinary differential equation are presented. In the first kind of mixed MLPG methods, both the displacement and its second derivative are interpolated independently through the MLS interpolation scheme. In the second kind of mixed MLPG methods, the displacement, its first derivative, second derivative and third derivative are interpolated independently through… More >

G.Ananthakrishna¹

CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.3, pp. 233-240, 2005, DOI:10.3970/cmes.2005.007.233

Abstract We show that the extended Ananthakrishna's model exhibits all the features of the Portevin - Le Chatelier effect including the three types of bands. The model reproduces the recently observed crossover from a low dimensional chaotic state at low and medium strain rates to a high dimensional power law state of stress drops at high strain rates. The dynamics of crossover is elucidated through a study of the Lyapunov spectrum. More >

D.L. Young^1,2, J.W. Ruan²

CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.2, pp. 223-232, 2005, DOI:10.3970/cmes.2005.007.223

Abstract The applications of the method of fundamental solutions (MFS) for modeling the scattering of time-harmonic electromagnetic fields, which are governed by vector Helmholtz equations with coupled boundary conditions, are described. Various perfectly electric conductors are considered as the scatterers to investigate the accuracy of the numerical performance of the proposed procedure by comparing with the available analytical solutions. It is also the intention of this study to reveal the characteristics of the algorithms by comparisons with other numerical methods. The model is first validated to the exact solutions of the electromagnetic wave propagation problems for More >

A.I.Tolstykh, D.A. Shirobokov¹

CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.2, pp. 207-222, 2005, DOI:10.3970/cmes.2005.007.207

Abstract A way of using RBF as the basis for PDE's solvers is presented, its essence being constructing approximate formulas for derivatives discretizations based on RBF interpolants with local supports similar to stencils in finite difference methods. Numerical results for different types of elasticity equations showing reasonable accuracy and good$h$-convergence properties of the technique are presented. Applications of the technique to problems with non-self-adjoint operators (like those for the Navier-Stokes equations) are also considered. More >

C. Shu^1,2, H. Ding², K.S. Yeo²

CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.2, pp. 195-206, 2005, DOI:10.3970/cmes.2005.007.195

Abstract Local radial basis function-based differential quadrature (RBF-DQ) method was recently proposed by us. The method is a natural mesh-free approach. It can be regarded as a combination of the conventional differential quadrature (DQ) method with the radial basis functions (RBFs) by means of taking the RBFs as the trial functions in the DQ scheme. With the computed weighting coefficients, the method works in a very similar fashion as conventional finite difference schemes. In this paper, we mainly concentrate on the applications of the method to incompressible flows in the steady and unsteady regions. The multiquadric More >

B. Šarler¹

CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.2, pp. 185-194, 2005, DOI:10.3970/cmes.2005.007.185

Abstract This paper explores the application of the mesh-free radial basis function collocation method for solution of heat transfer and fluid flow problems. The solution procedure is represented for a Poisson reformulated general transport equation in terms of a-symmetric, symmetric and modified (double consideration of the boundary nodes) collocation approaches. In continuation, specifics of a primitive variable solution procedure for the coupled mass, momentum, and energy transport representing the natural convection in an incompressible Newtonian Bussinesq fluid are elaborated. A comparison of different collocation strategies is performed based on the two dimensional De Vahl Davis steady More >

B. Pluymers¹, W. Desmet¹, D. Vandepitte¹, P. Sas¹

CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.2, pp. 173-184, 2005, DOI:10.3970/cmes.2005.007.173

Abstract Conventional element based methods for modelling structural-acoustic radiation problems are limited to low-frequency applications. Recently, a novel prediction technique has been developed based on the indirect Trefftz approach. This new wave based method is computationally more efficient than the element based methods and, as a consequence, can tackle problems also at higher frequencies. This paper discusses the basic principles of the new method and illustrates its performance for the two-dimensional radiation analysis of a bass-reflex loudspeaker. More >

L. Mai-Cao¹, T. Tran-Cong²

CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.2, pp. 149-172, 2005, DOI:10.3970/cmes.2005.007.149

Abstract The Indirect Radial Basis Function Network (IRBFN) method has been reported to be a highly accurate tool for approximating multivariate functions and solving elliptic partial differential equations (PDEs). The present method is a truly meshless method as defined in [\citet *{Atluri_Shen_02a}]. A recent development of the method for solving transient problems is presented in this paper. Two numerical schemes combining the IRBFN method with different time integration techniques based on either fully or semi-discrete framework are proposed. The two schemes are implemented making use of Hardy's multiquadrics (MQ) and Duchon's thin plate splines (TPS). Some More >