J. Sladek¹, P. Stanak¹, Z-D. Han², V. Sladek¹, S.N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.92, No.5, pp. 423-475, 2013, DOI:10.3970/cmes.2013.092.423

Abstract A review is presented for analysis of problems in engineering & the sciences, with the use of the meshless local Petrov-Galerkin (MLPG) method. The success of the meshless methods lie in the local nature, as well as higher order continuity, of the trial function approximations, high adaptivity and a low cost to prepare input data for numerical analyses, since the creation of a finite element mesh is not required. There is a broad variety of meshless methods available today; however the focus is placed on the MLPG method, in this paper. The MLPG method is a fundamental base for the… More >

S. D. Akbarov^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.92, No.4, pp. 387-421, 2013, DOI:10.3970/cmes.2013.092.387

Abstract Flexural wave dispersion in finitely pre-stretched (or pre-compressed) solid and hollow, circular cylinders is investigated with the use of the threedimensional linearized theory of elastic waves in initially stressed bodies. It is assumed that the initial strains in the cylinders are homogeneous and correspond to the uniaxial tension, or compression, along their central axes. The elasticity relations of the cylinders’ materials are described by the harmonic potential. The analytical solution of the corresponding field equations is presented and, using these solutions, the dispersion equations for the cases under consideration are obtained. The dispersion equations are solved numerically and based on… More >

Shou-Zhong Fu¹, Zhong Wang¹, Jun-Sheng Duan^1,2,3

CMES-Computer Modeling in Engineering & Sciences, Vol.92, No.4, pp. 369-385, 2013, DOI:10.3970/cmes.2013.092.369

Abstract Quadratic integral equations are a class of nonlinear integral equations having many important uses in engineering and sciences. In this work we display an efficient application of the Adomian decomposition method to the quadratic integral equations of Volterra type. The analytical approximate solution obtained can be directly inserted into the original equation to verify the accuracy and estimate the error with a computing software. Four numerical examples demonstrate the efficiency of the method. More >

Lifeng Wang¹, Yunpeng Ma¹, Zhijun Meng¹, Jun Huang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.92, No.4, pp. 353-368, 2013, DOI:10.3970/cmes.2013.092.353

Abstract In this paper, a wavelet operational matrix method based on the second kind Chebyshev wavelet is proposed to solve the fractional integral and differential equations of Bratu-type. The second kind Chebyshev wavelet operational matrix of fractional order integration is derived. A truncated second kind Chebyshev wavelet series together with the wavelet operational matrix is utilized to reduce the fractional integral and differential equations of Bratu-type to a system of nonlinear algebraic equations. The convergence and the error analysis of the method are also given. Two examples are included to verify the validity and applicability of the proposed approach. More >

K. Mramor¹, R. Vertnik^2,3, B. Šarler^1,3,4,5

CMES-Computer Modeling in Engineering & Sciences, Vol.92, No.4, pp. 327-352, 2013, DOI:10.3970/cmes.2013.092.327

Abstract The purpose of the present paper is to extend and explore the application of a novel meshless Local Radial Basis Function Collocation Method (LRBFCM) in solution of a steady, laminar, natural convection flow, influenced by magnetic field. The problem is defined by coupled mass, momentum, energy and induction equations that are solved in two dimensions by using local collocation with multiquadrics radial basis functions on an overlapping five nodded subdomains and explicit time-stepping. The fractional step method is used to couple the pressure and velocity fields. The considered problem is calculated in a square cavity with two insulated horizontal and… More >

Yaochan Zhu¹, Eckart Schnack¹, Al Mahmudur Rahman¹

CMES-Computer Modeling in Engineering & Sciences, Vol.92, No.3, pp. 315-326, 2013, DOI:10.32604/cmes.2013.092.315

Abstract A novel multiphase field model is formulated to simulate the complex microstructure evolution during chemical vapor infiltration (CVI) process, which is widely used technique to produce SiC matrix composites reinforced by SiC fibers in ceramic engineer. The model consists of a set of nonlinear partial differential equations by coupling Ginzburg-Landau type phase field equations with mass/heat balance equations as well as modified Navier-Stokes equations. The microstructure evolution of preferential codeposition of Si, SiC and C under high ratio of H2 to MTS is simulated. The simulation is in good agreement with experiments result. The potential risk of blockage of the… More >

Emrah Yilmaz¹, Hikmet Koyunbakan², Unal Ic³

CMES-Computer Modeling in Engineering & Sciences, Vol.92, No.3, pp. 301-313, 2013, DOI:10.32604/cmes.2013.092.301

Abstract In this study, some results are given about Sturm-Liouville operator having a singularity at zero. For this problem, asymptotic form of nodal data and a reconstruction formula for the potential function are given. In addition, a numerical example is established and illustrated the results in some tables and graphics. More >

J. A. Nairn¹

CMES-Computer Modeling in Engineering & Sciences, Vol.92, No.3, pp. 271-299, 2013, DOI:10.32604/cmes.2013.092.271

Abstract The “multimaterial” version of the material point method (MPM) extrapolates each material to its own velocity field on a background grid. By reconciling momenta on nodes interacting with two or more materials, MPM is able to automatically handle contact without any need for special contact elements. This paper extends multimaterial MPM to automatically handle imperfect interfaces between materials as well. The approach is to evaluate displacement discontinuity on multimaterial nodes and then add internal forces and interfacial energy determined by an imperfect interface traction law. The concept is simple, but implementation required numerous corrections to make the analysis mesh independent,… More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.92, No.3, pp. 241-269, 2013, DOI:10.32604/cmes.2013.092.241

Abstract In order to solve an ill-posed linear problem, we propose an innovative Jacobian type iterative method by presetting a conditioner before the steepest descent direction. The preconditioner is derived from an invariant manifold approach, which includes two parameters α and γ to be determined. When the weighting parameter α is optimized by minimizing a properly defined objective function, the relaxation parameter γ can be derived to accelerate the convergence speed under a switching criterion. When the switch is turned-on, by using the derived value of γ it can pull back the iterative orbit to the fast manifold. It is the… More >

Chein-Shan Liu¹, Satya N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.92, No.2, pp. 213-239, 2013, DOI:10.3970/cmes.2013.092.213

Abstract We show that the problem "real-time numerical differentiation" of a given noisy signal in time, by supplementing a compensated controller in the second-order robust exact differentiator, the tracking differentiator or the continuous hybrid differentiator, can be viewed as a set of differential algebraic equations (DAEs) to enhance a precise tracking of the given noisy signal. Thus, we are able to solve the highly ill-posed problem of numerical differentiation of noisy signal by using the Lie-group differential algebraic differentiators (LGDADs) based on the Lie-group GL(n,R), whose accuracy and tracking performance are better than before. The "index-two" differentiators (ITDs), which do not… More >