CMES-Vol. 4, No. 6, 2003

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A MLPG (LBIE) method for solving frequency domain elastic problems
E. J. Sellountos¹, D. Polyzos²
CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.6, pp. 619-636, 2003, DOI:10.3970/cmes.2003.004.619
Abstract A new meshless local Petrov-Galerkin (MLPG) method for solving two dimensional frequency domain elastodynamic problems is proposed. Since the method utilizes, in its weak formulation, either the elastostatic or the frequency domain elastodynamic fundamental solution as test function, it is equivalent to the local boundary integral equation (LBIE) method. Nodal points spread over the analyzed domain are considered and the moving least squares (MLS) interpolation scheme for the approximation of the interior and boundary variables is employed. Two integral equations suitable for the integral representation of the displacement fields in the local sub- domains are… More >

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Application of Meshless Local Petrov-Galerkin (MLPG) Method to Elastodynamic Problems in Continuously Nonhomogeneous Solids
Jan Sladek¹, Vladimir Sladek¹, Chuanzeng Zhang²
CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.6, pp. 637-648, 2003, DOI:10.3970/cmes.2003.004.637
Abstract A new computational method for solving transient elastodynamic initial-boundary value problems in continuously non-homogeneous solids, based on the meshless local Petrov-Galerkin (MLPG) method, is proposed in the present paper. The moving least squares (MLS) is used for interpolation and the modified fundamental solution as the test function. The local Petrov-Galerkin method for unsymmetric weak form in such a way is transformed to the local boundary integral equations (LBIE). The analyzed domain is divided into small subdomains, in which a weak solution is assumed to exist. Nodal points are randomly spread in the analyzed domain and More >

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Material Point Method Calculations with Explicit Cracks
J. A. Nairn¹
CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.6, pp. 649-664, 2003, DOI:10.3970/cmes.2003.004.649
Abstract A new algorithm is described which extends the material point method (MPM) to allow explicit cracks within the model material. Conventional MPM enforces velocity and displacement continuity through its background grid. This approach is incompatible with cracks which are displacement and velocity discontinuities. By allowing multiple velocity fields at special nodes near cracks, the new method (called CRAMP) can model cracks. The results provide an ``exact'' MPM analysis for cracks. Comparison to finite element analysis and to experiments show it gets good results for crack problems. The intersection of crack surfaces is prevented by implementing More >

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Truly Meshless Local Petrov-Galerkin (MLPG) Solutions of Traction & Displacement BIEs
Z. D. Han¹, S. N. Atluri¹
CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.6, pp. 665-678, 2003, DOI:10.3970/cmes.2003.004.665
Abstract The numerical implementation of the truly Meshless Local Petrov-Galerkin (MLPG) type weak-forms of the displacement and traction boundary integral equations is presented, for solids undergoing small deformations. In the accompanying part I of this paper, the general MLPG/BIE weak-forms were presented [Atluri, Han and Shen (2003)]. The MLPG weak forms provide the most general basis for the numerical solution of the non-hyper-singular displacement and traction BIEs [given in Han, and Atluri (2003)], which are simply derived by using the gradients of the displacements of the fundamental solutions [Okada, Rajiyah, and Atluri (1989a,b)]. By employing the… More >

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Three-Dimensional Simulation of Turbulent Cavitating Flows in a Hollow-Jet Valve
Jiongyang Wu¹, Inanc Senocak¹, Guoyu Wang², Yulin Wu³, Wei Shyy¹
CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.6, pp. 679-690, 2003, DOI:10.3970/cmes.2003.004.679
Abstract Cavitation appears in a wide variety of fluid machinery, and can often cause negative impacts on performance and structural integrity. A main computational difficulty for cavitation is the large density ratio between liquid and vapor phases, around 1000 for water under normal temperature and pressure conditions. Moreover, cavitating flows are usually turbulent and the interfacial dynamics is complex. The fast time scales associated with turbulent cavitation also poses substantial challenges computationally and experimentally. In the present study, pressure-based algorithms are adopted to simulate three-dimensional turbulent cavitating flows in a hollow-jet valve. The Favre-averaged Navier-Stokes equations… More >

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Numerical Computation of Discrete Differential Operators on Non-Uniform Grids
N. Sukumar¹, J. E. Bolander¹
CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.6, pp. 691-706, 2003, DOI:10.3970/cmes.2003.004.691
Abstract In this paper, we explore the numerical approximation of discrete differential operators on non-uniform grids. The Voronoi cell and the notion of natural neighbors are used to approximate the Laplacian and the gradient operator on irregular grids. The underlying weight measure used in the numerical computations is the {\em Laplace weight function}, which has been previously adopted in meshless Galerkin methods. We develop a difference approximation for the diffusion operator on irregular grids, and present numerical solutions for the Poisson equation. On regular grids, the discrete Laplacian is shown to reduce to the classical finite More >

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Computational Simulation of Localized Damage by Finite Element Remeshing based on Bubble Packing Method
Soon Wan Chung¹, Yoo Jin Choi¹, Seung Jo Kim¹
CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.6, pp. 707-718, 2003, DOI:10.3970/cmes.2003.004.707
Abstract In this paper, an automatic finite element remeshing algorithm based on the bubble packing method is utilized for the purpose of numerical simulations of localized damage, because fine meshes are needed to represent the gradually concentrated damage. The bubble packing method introduces two parameters that easily control the remeshing criterion and the new mesh size. The refined area is determined by \textit {a posteriori} error estimation utilizing the value obtained from Superconvergent Patch Recovery. The isotropic ductile damage theory, founded on continuum damage mechanics, is used for this damage analysis. It was successfully shown in More >

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