CMES-Vol. 13, No. 2, 2006

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ARTICLE

Treatment of Sharp Edges & Corners in the Acoustic Boundary Element Method under Neumann Boundary Condition
Zai You Yan¹
CMES-Computer Modeling in Engineering & Sciences, Vol.13, No.2, pp. 81-90, 2006, DOI:10.3970/cmes.2006.013.081
Abstract Boundary element method in acoustics for Neumann boundary condition problems including sharp edges & corners is investigated. In previous acoustic boundary element method, acoustic pressure and normal velocity are the two variables at sharp edges & corners. However, the normal velocity at sharp edges & corners is discontinuous due to the indefinite normal vector. To avoid the indefinite normal vector and the discontinuous normal velocity at sharp edges & corners, normal vector of elemental node is defined and applied in the numerical implementation. Then the normal velocity is transformed to velocity which is unique even at sharp edges & corners.… More >

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Meshfree Solution of Q-tensor Equations of Nematostatics Using the MLPG Method
Radek Pecher¹, Steve Elston, Peter Raynes
CMES-Computer Modeling in Engineering & Sciences, Vol.13, No.2, pp. 91-102, 2006, DOI:10.3970/cmes.2006.013.091
Abstract Meshfree techniques for solving partial differential equations in physics and engineering are a powerful new alternative to the traditional mesh-based techniques, such as the finite difference method or the finite element method. The elimination of the domain mesh enables, among other benefits, more efficient solutions of nonlinear and multi-scale problems. One particular example of these kinds of problems is a Q-tensor based model of nematic liquid crystals involving topological defects.
This paper presents the first application of the meshless local Petrov-Galerkin method to solving the Q-tensor equations of nematostatics. The theoretical part introduces the Landau -- de Gennes free-energy… More >

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Meshless Local Petrov-Galerkin (MLPG) Method for Shear Deformable Shells Analysis
J. Sladek¹, V. Sladek¹, P. H. Wen², M.H. Aliabadi³
CMES-Computer Modeling in Engineering & Sciences, Vol.13, No.2, pp. 103-118, 2006, DOI:10.3970/cmes.2006.013.103
Abstract A meshless local Petrov-Galerkin (MLPG) method is applied to solve bending problems of shear deformable shallow shells described by the Reissner theory. Both static and dynamic loads are considered. For transient elastodynamic case the Laplace-transform is used to eliminate the time dependence of the field variables. A weak formulation with a unit test function transforms the set of governing equations into local integral equations on local subdomains in the mean surface of the shell. Nodal points are randomly spread on that surface and each node is surrounded by a circular subdomain to which local integral equations are applied. The meshless… More >

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Structural Shape and Topology Optimization Using an Implicit Free Boundary Parametrization Method
S.Y. Wang^1,2, M.Y. Wang³
CMES-Computer Modeling in Engineering & Sciences, Vol.13, No.2, pp. 119-148, 2006, DOI:10.3970/cmes.2006.013.119
Abstract In this paper, an implicit free boundary parametrization method is presented as an effective approach for simultaneous shape and topology optimization of structures. The moving free boundary of a structure is embedded as a zero level set of a higher dimensional implicit level set function. The radial basis functions (RBFs) are introduced to parametrize the implicit function with a high level of accuracy and smoothness. The motion of the free boundary is thus governed by a mathematically more convenient ordinary differential equation (ODE). Eigenvalue stability can be guaranteed due to the use of inverse multiquadric RBF splines. To perform both… More >

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The Lie-Group Shooting Method for Nonlinear Two-Point Boundary Value Problems Exhibiting Multiple Solutions
Chein-Shan Liu¹
CMES-Computer Modeling in Engineering & Sciences, Vol.13, No.2, pp. 149-164, 2006, DOI:10.3970/cmes.2006.013.149
Abstract The present paper provides a Lie-group shooting method for the numerical solutions of second order nonlinear boundary value problems exhibiting multiple solutions. It aims to find all solutions as easy as possible. The boundary conditions considered are classified into four types, namely the Dirichlet, the first Robin, the second Robin and the Neumann. The two Robin type problems are transformed into a canonical one by using the technique of symmetric extension of the governing equations. The Lie-group shooting method is very effective to search unknown initial condition through a weighting factor r ∈ (0,1) Furthermore, the closed-form solutions are derived… More >

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