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• A Simple Collocation Scheme for Obtaining the Periodic Solutions of the Duffing Equation, and its Equivalence to the High Dimensional Harmonic Balance Method: Subharmonic Oscillations
• Hong-Hua Dai^1,2, Matt Schnoor², Satya N. Atluri²
• CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.5, pp. 459-498, 2012, DOI:10.3970/cmes.2012.084.459
• Abstract In this study, the harmonic and 1/3 subharmonic oscillations of a single degree of freedom Duffing oscillator with large nonlinearity and large damping are investigated by using a simple point collocation method applied in the time domain over a period of the periodic solution. The relationship between the proposed collocation method and the high dimensional harmonic balance method (HDHB), proposed earlier by Thomas, Dowell, and Hall (2002), is explored. We demonstrate that the HDHB is not a kind of "harmonic balance method" but essentially a cumbersome version of the collocation method. In using the collocation method, the collocation-resulting nonlinear algebraic…
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• Mode-III Stress Intensity Factors of a Three-Phase Composite with an Eccentric Circular Inclusion
• C.K. Chao¹, A. Wikarta¹
• CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.5, pp. 439-458, 2012, DOI:10.3970/cmes.2012.084.439
• Abstract An analytical solution to a three-phase composite with an eccentric circular inclusion under a remote uniform shear load is given in this work. Mode-III stress intensity factors for an arbitrarily oriented crack embedded in an infinite matrix or a core inclusion are provided in this paper. Based on the method of analytical continuation in conjunction with the alternating technique, the solution for a screw dislocation located either in the core inclusion or in the infinite matrix is first derived in a series form. The integral equations with logarithmic singular kernels for a line crack are established by using the screw…
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• Numerical Solutions of the Symmetric Regularized Long Wave Equation Using Radial Basis Functions
• Ayşe Gül Kaplan¹, Yılmaz Dereli
• CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.5, pp. 423-438, 2012, DOI:10.3970/cmes.2012.084.423
• Abstract In this study, the nonlinear symmetric regularized long wave equation was solved numerically by using radial basis functions collocation method. The single solitary wave solution, the interaction of two positive solitary waves and the clash of two solitary waves were studied. Numerical results and simulations of the wave motions were presented. Validity and accuracy of the method was tested by compared with results in the literature.
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• On Determination of a Finite Jacobi Matrix from Two Spectra
• Gusein Sh. Guseinov¹
• CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.5, pp. 405-422, 2012, DOI:10.3970/cmes.2012.084.405
• Abstract In this work we study the inverse spectral problem for two spectra of finite order real Jacobi matrices (tri-diagonal matrices). The problem is to reconstruct the matrix using two sets of eigenvalues, one for the original Jacobi matrix and one for the matrix obtained by replacing the first diagonal element of the Jacobi matrix by some another number. The uniqueness and existence results for solution of the inverse problem are established and an explicit procedure of reconstruction of the matrix from the two spectra is given.
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• A Globally Optimal Iterative Algorithm to Solve an Ill-Posed Linear System
• Chein-Shan Liu¹
• CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.4, pp. 383-404, 2012, DOI:10.3970/cmes.2012.084.383
• Abstract An iterative algorithm based on the critical descent vector is proposed to solve an ill-posed linear system: Bx = b. We define a future cone in the Minkowski space as an invariant manifold, wherein the discrete dynamics evolves. A critical value α_c in the critical descent vector u = α_cr + B^Tr is derived, which renders the largest convergence rate as to be the globally optimal iterative algorithm (GOIA) among all the numerically iterative algorithms with the descent vector having the form u = αr + B^Tr to solve the ill-posed linear problems. Some numerical examples are used to reveal…
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• An hp Adaptive Strategy to Compute the Vibration Modes of a Fluid-Solid Coupled System
• 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…
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• A Meshless Method Using Radial Basis Functions for the Numerical Solution of Two-Dimensional Complex Ginzburg-Landau Equation
• 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.
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• Hybrid Parallelism of Multifrontal Linear Solution Algorithm with Out Of Core Capability for Finite Element Analysis
• 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…
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• Natural Boundary Element Method for Bending Problem of Infinite Plate with a Circular Opening under the Boundary Loads
• 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…
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• A Reduction Algorithm of Contact Problems for Core Seismic Analysis of Fast Breeder Reactors
• 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…
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