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  • Open AccessOpen Access

    ARTICLE

    The Meshless Local Petrov-Galerkin (MLPG) Method for Solving Incompressible Navier-Stokes Equations

    H. Lin, S.N. Atluri1
    CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.2, pp. 117-142, 2001, DOI:10.3970/cmes.2001.002.117
    Abstract The truly Meshless Local Petrov-Galerkin (MLPG) method is extended to solve the incompressible Navier-Stokes equations. The local weak form is modified in a very careful way so as to ovecome the so-called Babus~ka-Brezzi conditions. In addition, The upwinding scheme as developed in Lin and Atluri (2000a) and Lin and Atluri (2000b) is used to stabilize the convection operator in the streamline direction. Numerical results for benchmark problems show that the MLPG method is very promising to solve the convection dominated fluid mechanics problems. More >

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    1966

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    1474

  • Open AccessOpen Access

    ARTICLE

    Molecular Dynamics Simulation of Crack Propagation in Polycrystalline Material

    K. Nishimura1, N. Miyazaki2
    CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.2, pp. 143-154, 2001, DOI:10.3970/cmes.2001.002.143
    Abstract In this paper, we present a classical molecular dynamics algorithm and its implementation on Cray C90 and Fujitsu VPP700. The characters of this algorithm consist in a grid based on the block division of the atomic system and a neighbor list based on the use of a short range potential. The computer program is used for large scale simulations on a Cray C90 and a 32-node VPP700, and measurements of computational performance are reported. Then, we examine the interaction between a crack propagating and a tilt grain boundary under uniaxial tension using this computer program.… More >

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    2048

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    1365

  • Open AccessOpen Access

    ARTICLE

    Three-dimensional Numerical Simulation of Unsteady Marangoni Convection in the CZ Method using GSMAC-FEM

    Haruhiko Kohno, Takahiko Tanahashi1
    CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.2, pp. 155-170, 2001, DOI:10.3970/cmes.2001.002.155
    Abstract Three-dimensional (3D) unsteady numerical simulations are carried out by means of the finite element method (FEM) with the generalized simplified marker and cell (GSMAC) method in silicon melt with a non-deformable free surface with Prandtl number Pr = 1.8534 × 10-2, Marangoni number Ma = 0.0 - 6.2067 × 102, Grashof number Gr = 7.1104 × 106, and the aspect ratio As = 1.0 in the Czochralski (CZ) method. The flow state becomes unstable earlier by increasing the absolute value of the thermal coefficient of surface tension in the range of σT =0.0 - 1.5 × 10-5N/mK. Although… More >

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    1644

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    1321

  • Open AccessOpen Access

    ARTICLE

    Coupling of BEM/FEM for Time Domain Structural-Acoustic Interaction Problems

    S.T. Lie1, Guoyou Yu, Z. Zhao2
    CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.2, pp. 171-182, 2001, DOI:10.3970/cmes.2001.002.171
    Abstract The BEM/FEM coupling procedure is applied to 2-D time domain structural-acoustic interaction problems. The acoustic domain for fluid or air is modeled by BEM scheme that is suitable for both finite and infinite domains, while the structure is modeled by FEM scheme. The input impact, which can be either plane waves or non-plane waves, can either be forces acting directly on the structural-acoustic system or be explosion sources. The far field or near field explosion sources which are difficult to be simulated by finite element modeling, can be simulated exactly by boundary element modeling as More >

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    1585

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    1260

  • Open AccessOpen Access

    ARTICLE

    A Naturally Parallelizable Computational Method for Inhomogeneous Parabolic Problems

    M.Ganesh1, D. Sheen2
    CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.2, pp. 183-194, 2001, DOI:10.3970/cmes.2001.002.183
    Abstract A parallel numerical algorithm is introduced and analyzed for solving inhomogeneous initial-boundary value parabolic problems. The scheme is based on the method recently introduced in Sheen, Sloan, and Thomée (2000) for homogeneous problems. We give a method based on a suitable choice of multiple parameters. Our scheme allows one to compute solutions in a wide range of time. Instead of using a standard time-marching method, which is not easily parallelizable, we take the Laplace transform in time of the parabolic problems. The resulting elliptic problems can be solved in parallel. Solutions are then computed by More >

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    1510

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    1166

  • Open AccessOpen Access

    ARTICLE

    On Finite Element Analysis of Fluid Flows Fully Coupled with Structural Interactions

    S. Rugonyi, K. J. Bathe1
    CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.2, pp. 195-212, 2001, DOI:10.3970/cmes.2001.002.195
    Abstract The solution of fluid flows, modeled using the Navier-Stokes or Euler equations, fully coupled with structures/solids is considered. Simultaneous and partitioned solution procedures, used in the solution of the coupled equations, are briefly discussed, and advantages and disadvantages of their use are mentioned. In addition, a simplified stability analysis of the interface equations is presented, and unconditional stability for certain choices of time integration schemes is shown. Furthermore, the long-term dynamic stability of fluid-structure interaction systems is assessed by the use of Lyapunov characteristic exponents, which allow differentiating between a chaotic and a regular system More >

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    1795

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    2436

  • Open AccessOpen Access

    ARTICLE

    An Advanced Time-Discontinuous Galerkin Finite Element Method for Structural Dynamics

    Chyou-Chi Chien, Tong-Yue Wu1
    CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.2, pp. 213-226, 2001, DOI:10.3970/cmes.2001.002.213
    Abstract This study presents a novel computational method for implementing the time finite element formulation for the equations of linear structural dynamics. The proposed method adopts the time-discontinuous Galerkin method, in which both the displacement and velocity variables are represented independently by second-order interpolation functions in the time domain. The solution algorithm derived utilizes a predictor/multi-corrector technique that can effectively obtain the solutions for the resulting system of coupled equations. The numerical implementation of the time-discontinuous Galerkin finite element method is verified through several benchmark problems. Numerical results are compared with exact and accepted solutions from More >

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    1718

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    1388

  • Open AccessOpen Access

    ARTICLE

    An Innovative Open Boundary Treatment for Nonlinear Water Waves in a Numerical Wave Tank

    S.-P. Zhu1
    CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.2, pp. 227-236, 2001, DOI:10.3970/cmes.2001.002.227
    Abstract Problems defined on infinite domains must be treated on a finite computational domain. The treatment of the artificially placed boundaries (usually referred to as open boundaries) of such domain truncations can be quite subtle; an over truncation would normally result in large, undesirable reflection of signals back to the computational domain whereas an under truncation would imply an injudicious use of computational resources. In particular, problems occur when strongly nonlinear free surface waves generated in a numerical wave tank are passing through such an open boundary.
    In this paper, some recent numerical test results of… More >

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    1579

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    1247

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    ARTICLE

    A Direct Discrete Formulation of Field Laws: The Cell Method

    Enzo TONTI1
    CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.2, pp. 237-258, 2001, DOI:10.3970/cmes.2001.002.237
    Abstract We present a new numerical method for the solution of field equations. The essence of the method is to directly provide a discrete formulation of field laws, without using and requiring a differential formulation. It is proved that, for linear interpolation, the stiffness matrix so obtained coincides with the one of the Finite Element Method. For quadratic interpolation, however, the present stiffness matrix differs from that of FEM; moreover it is unsymmetric. It is shown that by using a parabolic interpolation, a convergence of the fourth order is obtained. This is greater than the one More >

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    2264

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    1361

  • Open AccessOpen Access

    ARTICLE

    Optimum Design of Adaptive Truss Structures Using the Integrated Force Method

    R. Sedaghati, A. Suleman1, S. Dost, B. Tabarrok2
    CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.2, pp. 259-272, 2001, DOI:10.3970/cmes.2001.002.259
    Abstract A structural analysis and optimization method is developed to find the optimal topology of adaptive determinate truss structures under various impact loading conditions. The objective function is based on the maximization of the structural strength subject to geometric constraints. The dynamic structural analysis is based on the integrated finite element force method and the optimization procedure is based on the Sequential Quadratic Programming (SQP) method. The equilibrium matrix is generated automatically through the finite element analysis and the compatibility matrix is obtained directly using the displacement-deformation relations and the Single Value Decomposition (SVD) technique. By More >

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    2067

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    1251

  • Open AccessOpen Access

    ARTICLE

    Determination of Crack Tip Fields in Linear Elastostatics by the Meshless Local Petrov-Galerkin (MLPG) Method

    H.-K. Ching, R. C. Batra1
    CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.2, pp. 273-290, 2001, DOI:10.3970/cmes.2001.002.273
    Abstract It is shown that the MLPG method augmented with the enriched basis functions and either the visibility criterion or the diffraction criterion successfully predicts the singular stress fields near a crack tip. Results are presented for a single edge-cracked plate and a double edge-cracked plate with plate edges parallel to the crack axis loaded in tension, the single edge-cracked plate with one plate edge parallel to the crack axis clamped and the other loaded by tangential tractions, and for a double edge-notched plate with the side between the notches loaded in compression. For the first More >

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    1492

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    1227

  • Open AccessOpen Access

    ARTICLE

    Modified Potentials as a Tool for Computing Green's Functions in Continuum Mechanics

    Yu.A. Melnikov, M.Yu. Melnikov1
    CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.2, pp. 291-306, 2001, DOI:10.3970/cmes.2001.002.291
    Abstract The use of potential (integral) representations is studied when computing Green's functions for boundary value problems stated for Laplace and biharmonic equations over regions of complex configuration in two dimensions. The emphasis is on the non-traditional potentials, whose observation and source points occupy different sets. Such potentials reduce the original boundary value problems to functional (integral) equations with smooth kernels. Special integral representations are studied, the ones whose kernels are built not of the fundamental solutions of governing differential equations but of the Green's functions for simply shaped regions, which are associated with boundary value More >

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    1488

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    1485

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