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  • Open Access

    ARTICLE

    A Modified Trefftz Method for Two-Dimensional Laplace Equation Considering the Domain's Characteristic Length

    Chein-Shan Liu1

    CMES-Computer Modeling in Engineering & Sciences, Vol.21, No.1, pp. 53-66, 2007, DOI:10.3970/cmes.2007.021.053

    Abstract A newly modified Trefftz method is developed to solve the exterior and interior Dirichlet problems for two-dimensional Laplace equation, which takes the characteristic length of problem domain into account. After introducing a circular artificial boundary which is uniquely determined by the physical problem domain, we can derive a Dirichlet to Dirichlet mapping equation, which is an exact boundary condition. By truncating the Fourier series expansion one can match the physical boundary condition as accurate as one desired. Then, we use the collocation method and the Galerkin method to derive linear equations system to determine the Fourier coefficients. Here, the factor… More >

  • Open Access

    ARTICLE

    A Systematic Approach for the Development of Weakly–Singular BIEs

    Z. D. Han, S. N. Atluri1

    CMES-Computer Modeling in Engineering & Sciences, Vol.21, No.1, pp. 41-52, 2007, DOI:10.3970/cmes.2007.021.041

    Abstract Straight-forward systematic derivations of the weakly singular boundary integral equations (BIEs) are presented, following the simple and directly-derived approach by Okada, Rajiyah, and Atluri (1989b) and Han and Atluri (2002). A set of weak-forms and their algebraic combinations have been used to avoid the hyper-singularities, by directly applying the "intrinsic properties'' of the fundamental solutions. The systematic decomposition of the kernel functions of BIEs is presented for regularizing the BIEs. The present approach is general, and is applied to developing weakly-singular BIEs for solids and acoustics successfully. More >

  • Open Access

    ARTICLE

    An Unconditionally Time-Stable Level Set Method and Its Application to Shape and Topology Optimization

    S.Y. Wang1,2, K.M. Lim2,3, B.C. Khoo2,3, M.Y. Wang4

    CMES-Computer Modeling in Engineering & Sciences, Vol.21, No.1, pp. 1-40, 2007, DOI:10.3970/cmes.2007.021.001

    Abstract The level set method is a numerical technique for simulating moving interfaces. In this paper, an unconditionally BIBO (Bounded-Input-Bounded-Output) time-stable consistent meshfree level set method is proposed and applied as a more effective approach to simultaneous shape and topology optimization. In the present level set method, the meshfree infinitely smooth inverse multiquadric Radial Basis Functions (RBFs) are employed to discretize the implicit level set function. A high level of smoothness of the level set function and accuracy of the solution to the Hamilton-Jacobi partial differential equation (PDE) can be achieved. The resulting dynamic system of coupled Ordinary Differential Equations (ODEs)… More >

  • Open Access

    ARTICLE

    Recent Evolution of the Simulation Tools for Computer Aided Design of Electron-optical Systems for Powerful Gyrotrons

    S. Sabchevski1, I. Zhelyazkov2, M. Thumm3, S. Illy4, B. Piosczyk5, T.-M. Tran6,7, J. Gr. Pagonakis8

    CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.3, pp. 203-220, 2007, DOI:10.3970/cmes.2007.020.203

    Abstract Computer aided design of powerful gyrotrons for electron cyclotron resonance heating and current drive of fusion plasmas requires adequate physical models and efficient software packages for analysis, comparison and optimization of their electron-optical systems through numerical experiments. In this paper, we present and discuss the current status of the simulation tools available to the researchers involved in the development of multi-megawatt gyrotrons for the ITER project, review some of their recent upgrades and formulate directions for further modifications and improvements. Illustrative examples used represent results from recent numerical investigations of real constructions. Some physical problems that are outside of the… More >

  • Open Access

    ARTICLE

    An Elastic-Plastic Constitutive Equation Taking Account of Particle Size and Its Application to A Homogenized Finite Element Analysis of A Composite Material

    Shuji Takashima1, Michihiko Nakagaki2, Noriyuki Miyazaki1

    CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.3, pp. 193-202, 2007, DOI:10.3970/cmes.2007.020.193

    Abstract Composite materials have complicated microstructures. These microstructures affect the macroscopic deformation of composite materials. In the present study, we focus on the effect of particle size in a particle-dispersed composite material on the mechanical strength of the material. For this purpose, we derived a macroscopic elastic-plastic constitutive equation using a modified version of the Eshelby's equivalent inclusion method combined with the gradient plasticity. We incorporated this macroscopic elastic-plastic constitutive equation into a finite element program and performed a homogenized finite element analysis of a particle-dispersed composite material in which both the macroscopic and microscopic behaviors of the composite material were… More >

  • Open Access

    ARTICLE

    Smoothed Molecular Dynamics for Large Step Time Integration

    Yan Liu1, Xiong Zhang1, K. Y. Sze2, Min Wang1

    CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.3, pp. 177-192, 2007, DOI:10.3970/cmes.2007.020.177

    Abstract In molecular simulations, the frequencies of the low-frequency modes are many orders of magnitude lower than those of the high-frequency modes. Compared with the amplitudes of the low-frequency modes, the amplitudes of the high-frequency modes are often negligible and, thus, least interesting. As dictated by the period of the highest frequency mode, the critical time step for stable time integration can be significantly increased by suppressing the negligible high-frequency modes yet the solution remains virtually intact. In this light, a smoothed molecular dynamics (SMD) approach is proposed to eliminate the high-frequency modes from the dynamical system through the use of… More >

  • Open Access

    ARTICLE

    New Integrating Methods for Time-Varying Linear Systems and Lie-Group Computations

    Chein-Shan Liu1

    CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.3, pp. 157-176, 2007, DOI:10.3970/cmes.2007.020.157

    Abstract In many engineering applications the Lie group calculation is very important. With this in mind, the subject of this paper is for an in-depth investigation of time-varying linear systems, and its accompanied Lie group calculations. In terms of system matrix A in Eq. (11) and a one-order lower fundamental solution matrix associated with the sub-state matrix function Ass, we propose two methods to nilpotentlize the time-varying linear systems. As a consequence, we obtain two different calculations of the general linear group. Then, the nilpotent systems are further transformed to a unique new system Ż(t) = B(t)Z(t), which having a… More >

  • Open Access

    ARTICLE

    Two Dimensional Dynamic Green's Functions for Piezoelectric Materials

    Kuang-Chong Wu1, Shyh-Haur Chen2

    CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.3, pp. 147-156, 2007, DOI:10.3970/cmes.2007.020.147

    Abstract A formulation for two-dimensional self-similar anisotropic elastodyamics problems is generalized to piezoelectric materials. In the formulation the general solution of the displacements is expressed in terms of the eigenvalues and eigenvectors of a related eight-dimensional eigenvalue problem. The present formulation can be used to derive analytic solutions directly without the need of performing integral transforms as required in Cagniard-de Hoop method. The method is applied to derive explicit dynamic Green's functions. Some analytic results for hexagonal 6mm materials are also derived. Numerical examples for the quartz are illustrated. More >

  • Open Access

    ARTICLE

    Mechanical Properties of Carbon Nanotubes Using Molecular Dynamics Simulations with the Inlayer van der Waals Interactions

    W.H. Chen1, H.C. Cheng2, Y.C. Hsu3

    CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.2, pp. 123-146, 2007, DOI:10.3970/cmes.2007.020.123

    Abstract The evaluation of the fundamental mechanical properties of single/multi-walled carbon nanotubes(S/MWCNTs) is of great importance for their industrial applications. The present work is thus devoted to the determination of various mechanical properties of S/MWCNTs using molecular dynamics (MD) simulations. The study first focuses on the exploration of the effect of the weak inlayer van der Waals (vdW) atomistic interactions on the mechanical properties of S/MWCNTs. Secondly, in addition to the zig-zag and armchair types of CNTs, the hybrid type of MWCNTs that comprise a zig-zag outer tube and an inner armchair tube is also analyzed. Thirdly, the investigation is extended… More >

  • Open Access

    ARTICLE

    A Highly Accurate Solver for the Mixed-Boundary Potential Problem and Singular Problem in Arbitrary Plane Domain

    Chein-Shan Liu 1

    CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.2, pp. 111-122, 2007, DOI:10.3970/cmes.2007.020.111

    Abstract A highly accurate new solver is developed to deal with interior and exterior mixed-boundary value problems for two-dimensional Laplace equation, including the singular ones. To promote the present study, we introduce a circular artificial boundary which is uniquely determined by the physical problem domain, and derive a Dirichlet to Robin mapping on that artificial circle, which is an exact boundary condition described by the first kind Fredholm integral equation. As a consequence, we obtain a modified Trefftz method equipped with a characteristic length factor, ensuring that the new solver is stable because the condition number can be greatly reduced. Then,… More >

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