CMES-Vol. 20, No. 3, 2007

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 >

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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 A_s^s, 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 >

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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 >

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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 >

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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. Tran^6,7, 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 >

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