M.G. Armentano¹, C. Padra², R. Rodríguez³, M. Scheble²

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.4, pp. 359-382, 2012, DOI:10.3970/cmes.2012.084.359

Abstract In this paper we propose an hp finite element method to solve a two-dimensional fluid-structure vibration problem. This problem arises from the computation of the vibration modes of a bundle of parallel tubes immersed in an incompressible fluid. We use a residual-type a posteriori error indicator to guide an hp adaptive algorithm. Since the tubes are allowed to be different, the weak formulation is a non-standard generalized eigenvalue problem. This feature is inherited by the algebraic system obtained by the discretization process. We introduce an algebraic technique to solve this particular spectral problem. We report several numerical tests which allow… More >

Ali Shokri¹, Mehdi Dehghan¹

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.4, pp. 333-358, 2012, DOI:10.3970/cmes.2012.084.333

Abstract The Ginzburg-Landau equation has been used as a mathematical model for various pattern formation systems in mechanics, physics and chemistry. In this paper, we study the complex Ginzburg-Landau equation in two spatial dimensions with periodical boundary conditions. The method numerically approximates the solution by collocation method based on radial basis functions (RBFs). To improve the numerical results we use a predictor-corrector scheme. The results of numerical experiments are presented, and are compared with analytical solutions to confirm the accuracy and efficiency of the presented method. More >

Min Ki Kim¹, Seung Jo Kim²

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.4, pp. 297-332, 2012, DOI:10.3970/cmes.2012.084.297

Abstract Hybrid parallelization of multifrontal solution method and its parallel performances in a multicore distributed parallel computing architecture are represented in this paper. To utilize a state-of-the-art multicore computing architecture, parallelization of the multifrontal method for a symmetric multiprocessor machine is required. Multifrontal method is easier to parallelize than other direct solution methods because the solution procedure implies that the elimination of unknowns can be executed simultaneously. This paper focuses on the multithreaded parallelism and mixing distributed algorithm and multithreaded algorithm together in a unified software. To implement the hybrid parallelized algorithm in a distributed shared memory environment, two innovative ideas… More >

Shuncai Li^1,2,3, Shichuang Zhuo⁴, Qiang Zhang⁵

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.3, pp. 283-296, 2012, DOI:10.3970/cmes.2012.084.283

Abstract Based on the complex functions theory in elastic mechanics, the bending deflection formula expressed by the complex Fourier series is derived for the infinite plate with a circular opening at first, then the boundary conditions of the circular opening are expanded in Fourier Series, and the unknown coefficients of the Fourier series are determined by comparing coefficients method. By means of the convolution of the complex Fourier series and some basic formulas in the generalized functions theory, the natural boundary integral formula or the analytical deflection formulas expressed by the boundary displacement or loads are developed for the infinite plates… More >

Ryuta Imai¹, Masatoshi Nakagawa²

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.3, pp. 253-282, 2012, DOI:10.3970/cmes.2012.084.253

Abstract In order to evaluate seismic response of fast breeder reactors, finite element analysis for core vibration with contact/impact is performed so far. However a full model analysis of whole core vibration requires huge calculation times and memory sizes. In this research, we propose an acceleration method of reducing the number of degrees of freedom to be solved until converged for nonlinear contact problems. Furthermore we show a sufficient condition for the algorithm to work well and discuss its efficiency and a generalization of the algorithm. In particular we carry out the full model analysis to show that our method can… More >

Yu Wang¹, Zhen Luo^1,2, Nong Zhang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.3, pp. 229-252, 2012, DOI:10.3970/cmes.2012.084.229

Abstract This paper proposes an alternative topology optimization method for the optimal design of continuum structures, which involves a multilevel nodal density-based approximant based on the concept of conventional SIMP (solid isotropic material with penalization) model. First, in terms of the original set of nodal densities, the Shepard function method is applied to generate a non-local nodal density field with enriched smoothness over the design domain. The new nodal density field possesses non-negative and range-bounded properties to ensure a physically meaningful approximation of topology optimization design. Second, the density variables at the nodes of finite elements are used to interpolate elemental… More >

Bing Li^1,2, Hongbo Dong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.3, pp. 205-228, 2012, DOI:10.3970/cmes.2012.084.205

Abstract Different from single crack identification method, the number of cracks should be firstly identified, and then the location and depth of each crack can be predicted for multiple cracks identification technology. This paper presents a multiple crack identification algorithm for rotor using wavelet finite element method. Firstly, the changes in natural frequency of a structure with various crack locations and depths are accurately obtained by means of wavelet finite element method; and then the damage coefficient method is used to determine the number and region of cracks. Finally, by finding the points of intersection of three frequency contour lines in… More >

T.-T. Hoang-Trieu¹, N. Mai-Duy¹, T. Tran-Cong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.2, pp. 171-204, 2012, DOI:10.3970/cmes.2012.084.171

Abstract In this paper, new compact local stencils based on integrated radial basis functions (IRBFs) for solving fourth-order ordinary differential equations (ODEs) and partial differential equations (PDEs) are presented. Five types of compact stencils - 3-node and 5-node for 1D problems and 5×5-node, 13-node and 3×3 -node for 2D problems - are implemented. In the case of 3-node stencil and 3×3-node stencil, nodal values of the first derivative(s) of the field variable are treated as additional unknowns (i.e. 2 unknowns per node for 3-node stencil and 3 unknowns per node for 3×3-node stencil). The integration constants arising from the construction of… More >

Wei-Chung Tien¹, Yue-Tzu Yang¹, Cha’o-Kuang Chen^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.2, pp. 155-170, 2012, DOI:10.3970/cmes.2012.084.155

Abstract In this paper, the homotopy analysis method is applied to analyze the heat transfer of the oscillating base temperature processes occurring in a convective rectangular fin with variable thermal conductivity. This method is a powerful and easy-to-use tool for non-linear problems and it provides us with a simple way to adjust and control the convergence region of solution series. Without the need of iteration, the obtained solution is in the form of an infinite power series and the results indicated that the series has high accuracy by comparing it with those generated by the complex combination method. More >

J. D. Hales¹, S. R. Novascone¹, R. L. Williamson¹, D. R. Gaston¹, M. R. Tonks¹

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.2, pp. 123-154, 2012, DOI:10.3970/cmes.2012.084.123

Abstract The equations governing solid mechanics are often solved via Newton's method. This approach can be problematic if the Jacobian determination, storage, or solution cost is high. These challenges are magnified for multiphysics applications. The Jacobian-free Newton-Krylov (JFNK) method avoids many of these difficulties through a finite difference approximation. A parallel, nonlinear solid mechanics and multiphysics application named BISON has been created that leverages JFNK. We overview JFNK, outline the capabilities of BISON, and demonstrate the effectiveness of JFNK for solid mechanics and multiphysics applications using a series of demonstration problems. We show that JFNK has distinct advantages in many cases. More >