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  • Open Access


    Eshelby Stress Tensor T: a Variety of Conservation Laws for T in Finite Deformation Anisotropic Hyperelastic Solid & Defect Mechanics, and the MLPG-Eshelby Method in Computational Finite Deformation Solid Mechanics-Part I

    Z. D. Han1, S. N. Atluri2,3

    CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.1, pp. 1-34, 2014, DOI:10.3970/cmes.2014.097.001

    Abstract The concept of a stress tensor [for instance, the Cauchy stress σ, Cauchy (1789-1857); the first Piola-Kirchhoff stress P, Piola (1794-1850), and Kirchhoff (1824-1889); and the second Piola-Kirchhoff stress, S] plays a central role in Newtonian continuum mechanics, through a physical approach based on the conservation laws for linear and angular momenta. The pioneering work of Noether (1882-1935), and the extraordinarily seminal work of Eshelby (1916- 1981), lead to the concept of an “energy-momentum tensor” [Eshelby (1951)]. An alternate form of the “energy-momentum tensor” was also given by Eshelby (1975) by taking the two-point deformation gradient tensor as an independent… More >

  • Open Access


    MLPG6 for the Solution of Incompressible Flow Equations

    V. C. Loukopoulos1, G. C. Bourantas2

    CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.6, pp. 531-558, 2012, DOI:10.3970/cmes.2012.088.531

    Abstract Meshless Local Petrov-Galerkin (MLPG) approach is used for the solution of the Navier-Stokes and energy equations. More specific as a special case we apply the MLPG6 approach. In the MLPG6 method, the test function is chosen to be the same as the trial function (Galerkin method). The MLPG local weak form is written over a local sub-domain which is completely independent from the trial or test functions. The sizes of nodal trial and test function domains, as well as the size of the local sub-domain over which the local weak-form is considered, can be arbitrary. This may lead to either… More >

  • Open Access


    Optimal Shape of Fibers in Transmission Problem

    P.P. Prochazka1, M.J. Valek1

    CMES-Computer Modeling in Engineering & Sciences, Vol.87, No.3, pp. 207-224, 2012, DOI:10.3970/cmes.2012.087.207

    Abstract In classical theories of homogenization and localization of composites the effect of shape of inclusions is not taken into account. This is probably done because of very small fibers in classical composites based on epoxy matrix. Applying more precise theoretical and numerical tools appears that the classical theories desire corrections in this direction. Today many types of materials their fiber are much bigger and with various material properties are used and behave as typical composites. They enable producers to create the fiber cross-sections and model them in various shapes, so that it is meaningful to carry out the optimization. In… More >

  • Open Access


    Prediction of High-frequency Vibro-acoustic Coupling in Anechoic Chamber Using Energy Finite Element Method and Energy Boundary Element Method

    Miaoxia Xie1, Yueming Li1, Hualing Chen1,2

    CMES-Computer Modeling in Engineering & Sciences, Vol.85, No.1, pp. 65-78, 2012, DOI:10.3970/cmes.2012.085.065

    Abstract Energy finite element method(EFEM) is a promising method to solve high-frequency vibro-acoustic problem. Energy boundary element method (EBEM) is an effective way to compute high-frequency sound radiation in the unbounded medium. Vibro-acoustic coupling of cavity structure in anechoic chamber includes both the interior acoustic field and unbounded exterior acoustic field. In order to predict this kind of high-frequency vibro-acoustic coupling problem in anechoic chamber, an approach combined EFEM and EBEM is developed in this paper. As a numerical example, the approach is applied to solve the high-frequency vibro-acoustic coupling response of a cubic cavity structure excited by a point sound… More >

  • Open Access


    Turbulentlike Quantitative Analysis on Energy Dissipation in Vibrated Granular Media

    Zhi Yuan Cui1, Jiu Hui Wu1, Di Chen Li1

    CMES-Computer Modeling in Engineering & Sciences, Vol.71, No.2, pp. 149-156, 2011, DOI:10.3970/cmes.2011.071.149

    Abstract A quantitative rule of the vibrated granular media's energy dissipation is obtained by adopting the turbulence theory in this letter. Our results show that, similar to the power spectrum in fully developed fluid turbulence as described in Kolmogorov's theory, the power spectrum of vibrated granular media also exhibits a k - 5 / 3 (k is the wave number) power which characterizes the local isotropic flow. What's more, the mean energy dissipation rate in vibrated granular media rises with the increase of particle size and volume ratio. The theoretical results in this letter can be verified by the previous experimental… More >

  • Open Access


    Application of Energy Finite Element Method to High-frequency Structural-acoustic Coupling of an Aircraft Cabin with Truncated Conical Shape

    M. X. Xie1, H. L. Chen1, J. H. Wu1, F. G. Sun1

    CMES-Computer Modeling in Engineering & Sciences, Vol.61, No.1, pp. 1-22, 2010, DOI:10.3970/cmes.2010.061.001

    Abstract Energy finite element method (EFEM) is a new method to solve high-frequency structural-acoustic coupling problems, but its use has been limited to solving simple structures such as rods, beams, plates and combined structures. In this paper, the high-frequency structural-acoustic coupling characteristics of an aircraft cabin are simulated by regarding the shell as a number of flat shell elements connected with a certain angle in EFEM. Two tests validated the method employed in this paper. First, the structural response analysis of a cylinder was calculated in two ways: dividing the shell by axis-symmetric shells after deriving the governing equation of axis-symmetric… More >

  • Open Access


    Energy-Conserving Local Time Stepping Based on High-Order Finite Elements for Seismic Wave Propagation Across a Fluid-Solid Interface

    Ronan Madec1, Dimitri Komatitsch1,2, Julien Diaz3

    CMES-Computer Modeling in Engineering & Sciences, Vol.49, No.2, pp. 163-190, 2009, DOI:10.3970/cmes.2009.049.163

    Abstract When studying seismic wave propagation in fluid-solid models based on a numerical technique in the time domain with an explicit time scheme it is often of interest to resort to time substepping because the stability condition in the solid part of the medium can be more stringent than in the fluid. In such a case, one should enforce the conservation of energy along the fluid-solid interface in the time matching algorithm in order to ensure the accuracy and the stability of the time scheme. This is often not done in the available literature and approximate techniques that do not enforce… More >

  • Open Access


    Wave Modes of an Elastic Tube Conveying Blood

    Shueei-Muh Lin1,3, Sen-Yung Lee2, Cheng-Chuan Tsai2, Chien-Wi Chen2,Wen-Rong Wang3, Jenn-Fa Lee3

    CMES-Computer Modeling in Engineering & Sciences, Vol.34, No.1, pp. 33-54, 2008, DOI:10.3970/cmes.2008.034.033

    Abstract The conventional theories for circulation of arteries are emphasized on fluid behavior or some simplified models for experimental utility. In this study, a new mathematical theory is proposed to describe the wave propagation through the elastic tube filled with viscous and incompressible fluid. The radial, longitudinal and flexural vibrations of a tube wall are introduced simultaneously. Meanwhile, the linearlized momentum and continuity equations of tube flow field are expressed in the integral form. Based on these considerations, three wave modes are obtained simultaneously. These wave modes are the flexural, Young and Lamb modes, respectively. The characteristics of these modes are… More >

  • Open Access


    Strain Energy on the Surface of an Anisotropic Half-Space Substrate: Effect of Quantum-Dot Shape and Depth

    E. Pan1,2, Y. Zhang2, P. W. Chung3, M. Denda4

    CMES-Computer Modeling in Engineering & Sciences, Vol.24, No.2&3, pp. 157-168, 2008, DOI:10.3970/cmes.2008.024.157

    Abstract Quantum-dot (QD) semiconductor synthesis is one of the most actively investigated fields in strain energy band engineering. The induced strain fields influence ordering and alignment, and the subsequent surface formations determine the energy bandgap of the device. The effect of the strains on the surface formations is computationally expensive to simulate, thus analytical solutions to the QD-induced strain fields are very appealing and useful. In this paper we present an analytical method for calculating the QD-induced elastic field in anisotropic half-space semiconductor substrates. The QD is assumed to be of any polyhedral shape, and its surface is approximated efficiently by… More >

  • Open Access


    Symmetric Variational Formulation of BIE for Domain Decomposition Problems in Elasticity -- An SGBEM Approach for Nonconforming Discretizations of Curved Interfaces

    R. Vodička1, V. Mantič2, F. París2

    CMES-Computer Modeling in Engineering & Sciences, Vol.17, No.3, pp. 173-204, 2007, DOI:10.3970/cmes.2007.017.173

    Abstract An original approach to solve domain decomposition problems by the symmetric Galerkin boundary element method is developed. The approach, based on a new variational principle for such problems, yields a fully symmetric system of equations. A natural property of the proposed approach is its capability to deal with nonconforming discretizations along straight and curved interfaces, allowing in this way an independent meshing of non-overlapping subdomains to be performed. Weak coupling conditions of equilibrium and compatibility at an interface are obtained from the critical point conditions of the energy functional. Equilibrium is imposed through local traction (Neumann) boundary conditions prescribed on… More >

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