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  • Open Access


    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


    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


    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 >

  • Open Access


    An Accurate Refinement Scheme for Inverse Heat Source Location Identifications

    Leevan Ling1, Tomoya Takeuchi2

    CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.2, pp. 99-110, 2007, DOI:10.3970/cmes.2007.020.099

    Abstract We aim to identify the unknown source locations in a two-dimensional heat equation from scattered measurements. In [Inverse Problems, 22(4):1289--1305, 2006], we proposed a numerical procedure that identifies the unknown source locations of 2D heat equation solely based on three measurement points. Due to the nonlinearity and complexity of the problem, the quality of the resulting estimations is often poor especially when the number of unknown is large. In this paper, we purpose a linear refinement scheme that takes the outputs of the existing nonlinear algorithm as initial guesses and iteratively improves on the accuracy of the estimations; the convergence… More >

  • Open Access


    An Investigation of Wave Propagation with High Wave Numbers via the Regularized LBIEM

    H.B. Chen1, D.J. Fu1, P.Q. Zhang1

    CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.2, pp. 85-98, 2007, DOI:10.3970/cmes.2007.020.085

    Abstract Researches today show that, both approximation and dispersion errors are encountered by classical Galerkin FEM solutions for Helmholtz equation governing the harmonic wave propagation, which leads to numerical inaccuracies especially for high wave number cases. In this paper, Local Boundary Integral Equation Method (LBIEM) is firstly implemented to solve the boundary value problem of Helmholtz equation. Then the regularized LBIE is proposed to overcome the singularities of the boundary integrals in the LBIEM. Owing to the advantages of the Moving Least Square Approximation (MLSA), the frequency-dependent basis functions modified by the harmonic wave propagation solutions are easily adopted instead of… More >

  • Open Access


    Viscous Incompressible Flows by the Velocity-Vorticity Navier-Stokes Equations

    Alfredo Nicolás1, Blanca Bermúdez2

    CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.2, pp. 73-84, 2007, DOI:10.3970/cmes.2007.020.073

    Abstract 2D viscous incompressible flows are presented from the unsteady Navier-Stokes equations in its velocity-vorticity formulation. The results are obtained using a simple numerical procedure based on a fixed point iterative process to solve the nonlinear elliptic system that results once a second order time discretization is performed. Flows on the un-regularized unit driven cavity problem are reported up to Reynolds numbers Re=4000 to compare them with those reported by other authors, mainly solving the steady problem, and supposed to be correct. Moreover, results are reported for Re = 1000, 4000, 5000, and 10000 to see how their flows look like… More >

  • Open Access


    On the Modelling of Rate-Dependent Domain Switching in Piezoelectric Materials under Superimposed Stresses

    A. Arockiarajan1, A. Menzel2

    CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.1, pp. 55-72, 2007, DOI:10.3970/cmes.2007.020.055

    Abstract To study rate-dependent properties of piezoelectric materials a micro-mechanically motivated model is applied in this work. The developed framework is embedded into a coupled three-dimensional finite element setting, whereby each element is assumed to represent one grain and, moreover, possesses a random initialisation of the underlying polarisation direction. Furthermore, an energy-based criterion is used for the initiation of the onset of domain switching and the subsequent propagation of domain wall motion during the switching process is modelled via a linear kinetics theory. The interaction between individual grains is thereby incorporated by means of a probabilistic approach -- a purely phenomenologically… More >

  • Open Access


    Development of Heat Input Estimation Technique for Simulation of Shell Forming by Line-Heating

    N. Osawa1, K. Hashimoto1, J. Sawamura1, J. Kikuchi2, Y. Deguchi2, T. Yamaura2

    CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.1, pp. 43-54, 2007, DOI:10.3970/cmes.2007.020.043

    Abstract A new hypothesis regarding heat transmission during line heating is proposed. It states that the distribution of the temperature of the gas adjacent to the plate, TG, and the overall local heat transfer coefficient, α, depend only on the distance from the torch. An identification technique for TG and α is developed. The validity of the employed hypothesis and the proposed technique is demonstrated by comparing the measured and identified TG during a spot heating test. The plate temperature calculated by direct heat conduction analysis closely approximates the one measured for the spot and line heating tests, when TG and… More >

  • Open Access


    A Posteriori Error Estimation and Adaptive Node Refinement for Fast Moving Least Square Reproducing Kernel (FMLSRK) Method

    Chany Lee1, Chang-Hwan Im2, Hyun-Kyo Jung3, Hong-Kyu Kim4, Do Wan Kim5

    CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.1, pp. 35-42, 2007, DOI:10.3970/cmes.2007.020.035

    Abstract In the present study, a residual-based a posteriori error estimation for a kind of meshless method, called fast moving least square reproducing kernel (FMLSRK) method is proposed. The proposed error estimation technique does not require any integration cells in evaluating error norm but recovers the exact solutions in a virtual area defined by a dilation parameter of FMLSRK and node density. The proposed technique was tested on typical electrostatic problems with gird or random node sets and the simulation results show that the proposed error estimation technique can be applied to adaptive node refinement process for more efficient meshless analysis… More >

  • Open Access


    The Trefftz Boundary Method in Viscoelasticity

    Berardi Sensale Cozzano1, Berardi Sensale Rodríguez2

    CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.1, pp. 21-34, 2007, DOI:10.3970/cmes.2007.020.021

    Abstract In this paper, the Trefftz method is applied to solve linear viscoelasticity problems in the time domain, using Trefftz elastic series and considering the viscoelastic components in each time domain as fictitious body forces. The direct application of the Trefftz method to elastic problems is typically constrained to those cases in which the Navier equation is homogeneous. In the presence of body forces, the method of the particular solution or the method of the generalized particular solution should be used, depending on whether the body forces are constant or not inside the considered domain. Many viscoelasticity problems with or without… More >

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