Yi W. Wan¹, Huan J. Keh²

CMES-Computer Modeling in Engineering & Sciences, Vol.53, No.1, pp. 73-94, 2009, DOI:10.3970/cmes.2009.053.073

Abstract The problem of the rotation of a rigid particle of revolution about its axis in a viscous fluid is studied theoretically in the steady limit of low Reynolds number. The fluid is allowed to slip at the surface of the particle. A singularity method based on the principle of distribution of a set of spherical singularities along the axis of revolution within a prolate particle or on the fundamental plane within an oblate particle is used to find the general solution for the fluid velocity field that satisfies the boundary condition at infinity. The slip condition on the surface of… More >

Ching Kong Chao^1,2, Chin Kun Chen¹, Fu Mo Chen³

CMES-Computer Modeling in Engineering & Sciences, Vol.47, No.3, pp. 283-298, 2009, DOI:10.3970/cmes.2009.047.283

Abstract Analytical exact solutions of a fundamental heat conduction problem for a three-phase elliptical composite under a remote uniform heat flow are provided in this paper. The steady-state temperature and heat flux fields in each phase of an elliptical composite are analyzed in detail. Investigations on the present heat conduction problem are tedious due to the presence of material inhomogeneities and geometric discontinuities. Based on the technique of conformal mapping and the method of analytical continuation in conjunction with the alternating technique, the general expressions of the temperature and heat flux are derived explicitly in a closed form. Some numerical results… More >

Chia-Cheng Tsai¹

CMES-Computer Modeling in Engineering & Sciences, Vol.45, No.3, pp. 249-272, 2009, DOI:10.3970/cmes.2009.045.249

Abstract Analytical particular solutions of Chebyshev polynomials are obtained for problems of Reissner plates under arbitrary loadings, which are governed by three coupled second-ordered partial differential equation (PDEs). Our solutions can be written explicitly in terms of monomials. By using these formulas, we can obtain the approximate particular solution when the arbitrary loadings have been represented by a truncated series of Chebyshev polynomials. In the derivations of particular solutions, the three coupled second-ordered PDE are first transformed into a single six-ordered PDE through the Hörmander operator decomposition technique. Then the particular solutions of this six-ordered PDE can be found in the… More >

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 >

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 + ... + a_nxⁿ 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 >

A. Brancati¹, M. H. Aliabadi¹, I. Benedetti^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.43, No.2, pp. 149-172, 2009, DOI:10.3970/cmes.2009.043.149

Abstract In this paper a new Rapid Acoustic Boundary Element Method (RABEM) is presented using a Hierarchical GMRES solver for 3D acoustic problems. The Adaptive Cross Approximation is used to generate both the system matrix and the right hand side vector. The ACA is also used to evaluate the potential and the particle velocity values at selected internal points. Two different GMRES solution strategies (without preconditioner and with a block diagonal preconditioner) are developed and tested for low and high frequency problems. Implementation of different boundary conditions (i.e. Dirichlet, Neumann and mixed Robin) is also described. The applications presented include the… More >

E. Brusa¹, E. Franceschinis², S. Morsut²

CMES-Computer Modeling in Engineering & Sciences, Vol.42, No.2, pp. 75-106, 2009, DOI:10.3970/cmes.2009.042.075

Abstract Electrodes motion and positioning are critical issues of the Electric Arc Furnace (EAF) operation in steelmaking process. During the melting process electrode is exposed to some impulsive and harmonic forces, superimposing to the structure's static loading. Unfortunately, structural vibration may interact with the electric arc regulation, because of the dynamic resonance. Instability in the furnace power supplying and dangerous electrode breakage may occur as a consequence of those dynamic effects. In this paper the dynamic behaviour of a real EAF structure is discussed and some numerical models are proposed. Available experimental data, collected by a monitoring system on a real… More >

Rencheng Song^1,2, Wen Chen^2,3

CMES-Computer Modeling in Engineering & Sciences, Vol.42, No.1, pp. 59-70, 2009, DOI:10.3970/cmes.2009.042.059

Abstract The regularized meshless method (RMM) is a novel boundary-type meshless method but by now has mainly been tested successfully to the regular domain problems in reports. This note makes a further investigation on its solution of irregular domain problems. We find that the method fails to produce satisfactory results for some benchmark problems. The reason is due to the inaccurate calculation of the diagonal elements of the numerical discretization matrix in the original RMM, which have strong effect on the resulting solution accuracy. To overcome this severe drawback, this study introduces the weighted diagonal element approach. Our numerical experiments demonstrate… More >

D. L. Young^1,3, K. H. Chen², T. Y. Liu³, L. H. Shen³, C. S. Wu³

CMES-Computer Modeling in Engineering & Sciences, Vol.40, No.3, pp. 225-270, 2009, DOI:10.3970/cmes.2009.040.225

Abstract In this article, a hypersingular meshless method (HMM) is extended to solve 3D potential problems for arbitrary domains after a 2D model was successfully developed (Young et al. 2005a). The solutions are represented by a distribution of the double layer potentials instead of the single layer potentials as generally used in the conventional method of fundamental solutions (MFS). By using the desingularization technique to regularize the singularity and hypersingularity of the double layer potentials, the source points can be located exactly on the real boundary to avoid the sensitivity of locating fictitious boundary for putting the singularity outside the computational… More >

X.Y. Cui^1,2, G. R. Liu^2,3, G. Y. Li^1,4, G. Zheng¹

CMES-Computer Modeling in Engineering & Sciences, Vol.38, No.3, pp. 217-230, 2008, DOI:10.3970/cmes.2008.038.217

Abstract In this paper, a gradient smoothed formulation is proposed to deal with a fourth-order differential equation of Bernoulli-Euler beam problems for static and dynamic analysis. Through the smoothing operation, the C¹ continuity requirement for fourth-order boundary value and initial value problems can be easily relaxed, and C⁰ interpolating function can be employed to solve C¹ problems. In present thin beam problems, linear shape functions are employed to approximate the displacement field, and smoothing domains are further formed for computing the smoothed curvature and bending moment field. Numerical examples indicate that very accurate results can be yielded when a reasonable number… More >