Home / Journals / CMES / Vol.2, No.4, 2001
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  • Open Access

    ARTICLE

    A Pure Contour Formulation for the Meshless Local Boundary Integral Equation Method in Thermoelasticity

    J. Sladek1, V. Sladek1, S.N. Atluri2
    CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.4, pp. 423-434, 2001, DOI:10.3970/cmes.2001.002.423
    Abstract A new meshless method for solving stationary thermoelastic boundary value problems is proposed in the present paper. The moving least square (MLS) method is used for the approximation of physical quantities in the local boundary integral equations (LBIE). In stationary thermoelasticity, the temperature and displacement fields are uncoupled. In the first step, the temperature field, described by the Laplace equation, is analysed by the LBIE. Then, the mechanical quantities are obtained from the solution of the LBIEs, which are reduced to elastostatic ones with redefined body forces due to thermal loading. The domain integrals with temperature gradients are transformed to… More >

  • Open Access

    ARTICLE

    Steady Heat Conduction Analysis in Orthotropic Bodies by Triple-reciprocity BEM

    Y. Ochiai
    CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.4, pp. 435-446, 2001, DOI:10.3970/cmes.2001.002.435
    Abstract The boundary element method (BEM) is useful in solving the steady heat conduction problem of orthotropic bodies without heat generation. However, for cases with arbitrary heat generation, a number of internal cells are necessary. In this paper, it is shown that the problem of steady heat conduction in orthotropic bodies with heat generation can be solved without internal cells by the triple-reciprocity BEM. In this method, the distribution of heat generation is interpolated using integral equations. In order to solve the problem, the values of heat generation at internal points and on the boundary are used. Furthermore, a new interpolation… More >

  • Open Access

    ARTICLE

    On the Equivalence Between Least-Squares and Kernel Approximations in Meshless Methods

    Xiaozhong Jin1, Gang Li2, N. R. Aluru3
    CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.4, pp. 447-462, 2001, DOI:10.3970/cmes.2001.002.447
    Abstract Meshless methods using least-squares approximations and kernel approximations are based on non-shifted and shifted polynomial basis, respectively. We show that, mathematically, the shifted and non-shifted polynomial basis give rise to identical interpolation functions when the nodal volumes are set to unity in kernel approximations. This result indicates that mathematically the least-squares and kernel approximations are equivalent. However, for large point distributions or for higher-order polynomial basis the numerical errors with a non-shifted approach grow quickly compared to a shifted approach, resulting in violation of consistency conditions. Hence, a shifted polynomial basis is better suited from a numerical implementation point of… More >

  • Open Access

    ARTICLE

    A Meshless Local Petrov-Galerkin (MLPG) Formulation for Static and Free Vibration Analyses of Thin Plates

    Y. T. Gu, G. R. Liu1
    CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.4, pp. 463-476, 2001, DOI:10.3970/cmes.2001.002.463
    Abstract A meshless method for the analysis of Kirchhoff plates based on the Meshless Local Petrov-Galerkin (MLPG) concept is presented. A MLPG formulation is developed for static and free vibration analyses of thin plates. Local weak form is derived using the weighted residual method in local supported domains from the 4th order partial differential equation of Kirchhoff plates. The integration of the local weak form is performed in a regular-shaped local domain. The Moving Least Squares (MLS) approximation is used to constructed shape functions. The satisfaction of the high continuity requirements is easily met by MLS interpolant, which is based on… More >

  • Open Access

    ARTICLE

    2.5D Green's Functions for Elastodynamic Problems in Layered Acoustic and Elastic Formations

    António Tadeu, Julieta António1
    CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.4, pp. 477-496, 2001, DOI:10.3970/cmes.2001.002.477
    Abstract This paper presents analytical solutions, together with explicit expressions, for the steady state response of homogeneous three-dimensional layered acoustic and elastic formations subjected to a spatially sinusoidal harmonic line load. These formulas are theoretically interesting in themselves and they are also useful as benchmark solutions for numerical applications. In particular, they are very important in formulating three-dimensional elastodynamic problems in layered fluid and solid formations using integral transform methods and/or boundary elements, avoiding the discretization of the solid-fluid interfaces. The proposed Green's functions will allow the solution to be obtained for high frequencies, for which the conventional boundary elements' solution… More >

  • Open Access

    ARTICLE

    Element Free Galerkin Method for Three-dimensional Structural Analysis

    Wen-Hwa Chen1, Xhu-Ming Guo2
    CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.4, pp. 497-508, 2001, DOI:10.3970/cmes.2001.002.497
    Abstract An Element Free Galerkin Method is developed for the analysis of three-dimensional structures. A highly accurate and reliable relation between the number of the quadrature orders nQ and nodes in a three-dimensional cell nc, nQ3nc + 3, is established to accomplish the required integral calculation in the cell. Based on the theory of topology, the generation of nodes in the solution procedure consists of three sequential steps, say, defining the geometric boundary, arranging inside of the body, and improving numerical accuracy. In addition, by selecting the Dirac Delta function as the weighting function, a three-dimensional scattering sub-domain is… More >

  • Open Access

    ARTICLE

    An Improved Contact Algorithm for the Material Point Method and Application to Stress Propagation in Granular Material

    S.G. Bardenhagen1, J.E. Guilkey2, K.M. Roessig3, J.U. Brackbill4, W.M. Witzel5, J.C.Foster6
    CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.4, pp. 509-522, 2001, DOI:10.3970/cmes.2001.002.509
    Abstract Contact between deformable bodies is a difficult problem in the analysis of engineering systems. A new approach to contact has been implemented using the Material Point Method for solid mechanics, Bardenhagen, Brackbill, and Sulsky (2000a). Here two improvements to the algorithm are described. The first is to include the normal traction in the contact logic to more appropriately determine the free separation criterion. The second is to provide numerical stability by scaling the contact impulse when computational grid information is suspect, a condition which can be expected to occur occasionally as material bodies move through the computational grid. The modifications… More >

  • Open Access

    ARTICLE

    Optimization of a Low Reynolds Number Airfoil with Flexible Membrane

    Ori Levin, Wei Shyy1
    CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.4, pp. 523-536, 2001, DOI:10.3970/cmes.2001.002.523
    Abstract Typical low Reynolds number airfoils suffer from reduced lift-to-drag ratio and are prone to flow separation. In order to improve the aerodynamic performance of such airfoils in an unsteady freestream, the concept of passive control is investigated. In this study, a membrane with varying thickness distribution and mechanical properties is attached on the upper surface of a modified Clark-Y airfoil and is free to move upwards and downwards in response to the pressure difference across it. The response surface method is employed to investigate the individual and collective effects of the membrane's prestress, elastic modulus, and thickness distribution on aerodynamic… More >

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