Yaoming Zhang¹, Yan Gu¹, Jeng-Tzong Chen²

CMES-Computer Modeling in Engineering & Sciences, Vol.50, No.1, pp. 1-20, 2009, DOI:10.3970/cmes.2009.050.001

Abstract There exist nearly singular integrals for thin walled structures in the boundary element method (BEM). In this paper, an efficient analytical method is developed to deal with the nearly singular integrals in the boundary integral equations (BIEs) for 2-D thin walled structures. The developed method is possible for problems defined in high-order geometry elements when the nearly singular integrals need to be calculated. For the analysis of nearly singular integrals with high-order geometry elements, much fewer boundary elements can be used to achieve higher accuracy. More importantly, computational models of thin walled structures or thin shapes in structures demand a… More >

M.V. Menshykova¹, O.V. Menshykov, I.A. Guz

CMES-Computer Modeling in Engineering & Sciences, Vol.48, No.2, pp. 107-120, 2009, DOI:10.3970/cmes.2009.048.107

Abstract The study is devoted to the problem for a linear crack located between two dissimilar elastic half-spaces under normally incident time-harmonic plane shear wave. The system of boundary integral equations for displacements and tractions is derived from the dynamic Somigliana identity. The distributions of the displacements and tractions at the bonding interface and the surface of the crack are analysed. The dynamic stress intensity factors (the opening and the transverse shear modes) are computed as functions of the frequency of the incident wave for different material properties. More >

Chih-Chang Chi¹, Weichung Yeih^1,2, Chein-Shan Liu³

CMES-Computer Modeling in Engineering & Sciences, Vol.47, No.2, pp. 167-190, 2009, DOI:10.3970/cmes.2009.047.167

Abstract In this study, a novel method for solving the Cauchy problem of Laplace equation is developed. Through the fictitious time integration method (FTIM), the finding of the root of the resulting linear equations can be transformed into for finding the fixed point of a system of first order ordinary differential equations, in which a fictitious time variable is introduced. In such a sense, the inverse of ill-posed leading matrix is not necessary for the FTIM. This method uses the residual of each equation to control the evolution of unknowns in the fictitious time, and it is different from the conventional… More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.47, No.1, pp. 1-22, 2009, DOI:10.3970/cmes.2009.047.001

Abstract In this paper an analytical method for approximating the solution of backward heat conduction problem is presented. The Fourier series expansion technique is used to formulate a first-kind Fredholm integral equation for the temperature field u(x,t) at any time t < T, when the data are specified at a final time T. Then we consider a direct regularization, instead of the Tikhonov regularization, by adding the term αu(x,t) to obtain a second-kind Fredholm integral equation. The termwise separable property of kernel function allows us by transforming it to a two-point boundary value problem, and thus a closed-form solution is derived.… More >

Y.M. Zhang¹, Y. Gu¹, J.T. Chen²

CMES-Computer Modeling in Engineering & Sciences, Vol.45, No.3, pp. 227-248, 2009, DOI:10.3970/cmes.2009.045.227

Abstract The accurate evaluation of nearly singular integrals is one of the major concerned problems in the boundary element method (BEM). Although the current methods have achieved great progress, it is often possible only for problems defined in the simplest geometrical domains when the nearly singular integrals need to be calculated. However, engineering processes occur mostly in complex geometrical domains, and always, involve nonlinearities of the unknown variables and its derivatives. Therefore, effective methods of dealing with nearly singular integrals for such practical problems are necessary and need to be further investigated. In this paper, a general strategy based on a… More >

Moe M. S. Cheung¹, Zhenyuan Shen², Ben Y.B. Chan³

CMES-Computer Modeling in Engineering & Sciences, Vol.45, No.2, pp. 155-178, 2009, DOI:10.3970/cmes.2009.045.155

Abstract In view of the urgent need for an efficient and accurate structural analysis method in bridge design practice, this paper introduces a total integrated analytical solution for multi-span, continuous slab-on-girder and box girder bridges, by modeling the bridge deck and the piers together, using the finite strip method (FSM). FSM has been well accredited for its efficiency in the structural analysis of bridges, reducing the time required for data input and analysis without affecting the degree of accuracy. By using a continuously differentiable smooth series in the longitudinal direction, a complex 3D problem is reduced to a 2D problem using… More >

Xiaolin Li¹, Jialin Zhu²

CMES-Computer Modeling in Engineering & Sciences, Vol.45, No.1, pp. 1-30, 2009, DOI:10.3970/cmes.2009.045.001

Abstract In this paper, a Galerkin boundary node method (GBNM) is developed for boundary-only analysis of 2D problems in linear elasticity. The GBNM combines the variational form of a boundary integral formulation for the elastic equations with the moving least-squares approximations for generating the trial and test functions. Unlike the boundary node method, the main idea here is to use the Galerkin scheme for numerical analysis, thus boundary conditions in the GBNM can be satisfied easily and directly in the weak formulation of the boundary integral equation. Another advantage with the Galerkin scheme is that the GBNM can keep the symmetry… More >

D. Ho-Minh¹, N. Mai-Duy¹, T. Tran-Cong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.44, No.3, pp. 219-248, 2009, DOI:10.3970/cmes.2009.044.219

Abstract This paper reports a new discretisation technique for the streamfunc -tion-vorticity-temperature (ψ−ω−T) formulation governing natural convection defined in 2D enclosured domains. The proposed technique combines strengths of three schemes, i.e. smooth discretisations (Galerkin formulation), powerful high-order approximations (one-dimensional integrated radial-basis-function networks) and pressure-free low-order system (ψ−ω−T formulation). In addition, a new effective way of deriving computational boundary conditions for the vorticity is proposed. Two benchmark test problems, namely free convection in a square slot and a concentric annulus, are considered, where a convergent solution for the former is achieved up to the Rayleigh number of 10⁸. 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 >

Cheng-Yu Ku^1,2, Weichung Yeih^1,2, 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 >