CMES-Vol. 6 No. 2, 2004

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Fast Multipole Boundary Element Analysis of Corrosion Problems
S.Aoki¹, K.Amaya², M.Urago³, A.Nakayama⁴
CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.2, pp. 123-132, 2004, DOI:10.3970/cmes.2004.006.123
Abstract The Fast Multipole Boundary Element Method(FMBEM) which is suitable for a large scale computation is applied to corrosion analysis. Many techniques of the FMBEM on the potential problems can be usefully employed. Additionally, some procedures are developed for corrosion analysis. To cope with the non-linearity due to the polarization curve, the Bi-CGSTAB iterative method which is commonly used in the FMBEM is modified. To solve infinite domain problems, the M₀⁰ which is obtained naturally in the multipole expansion is conveniently used. A pipe element for the FMBEM is developed. A couple of example problems are solved to show the… More >

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Non-Hyper-Singular Boundary Integral Equations for Acoustic Problems, Implemented by the Collocation-Based Boundary Element Method
Z.Y. Qian¹, Z.D. Han¹, P. Ufimtsev¹, S.N. Atluri¹
CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.2, pp. 133-144, 2004, DOI:10.3970/cmes.2004.006.133
Abstract The weak-form of Helmholtz differential equation, in conjunction with vector test-functions (which are gradients of the fundamental solutions to the Helmholtz differential equation in free space) is utilized as the basis in order to directly derive non-hyper-singular boundary integral equations for the velocity potential, as well as its gradients. Thereby, the presently proposed boundary integral equations, for the gradients of the acoustic velocity potential, involve only O(r⁻²) singularities at the surface of a 3-D body. Several basic identities governing the fundamental solution to the Helmholtz differential equation for velocity potential, are also derived for the further desingularization of the strongly… More >

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The Relationship between Contact Pressure, Insert Thickness, and Mild Wear in Total Knee Replacements
Y. Bei¹, B.J. Fregly¹, W.G. Sawyer¹, S.A. Banks^1,2, N.H. Kim¹
CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.2, pp. 145-152, 2004, DOI:10.3970/cmes.2004.006.145
Abstract Mild wear of ultra-high molecular weight polyethylene tibial inserts continues to affect the longevity of total knee replacements (TKRs). Using static finite element and elasticity analyses, previous studies have hypothesized that polyethylene wear can be reduced by using a thicker tibial insert to decrease contact pressures. To date, no study has taken this hypothesis to the next step by performing dynamic analyses under in vivo functional conditions to quantify the relationship between contact pressures, insert thickness, and mild wear. This study utilizes multibody dynamic simulations incorporating elastic contact to perform such analyses. \textit {In vivo} fluoroscopic gait data from two… More >

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Large Scale Parallel Simulation and Visualization of 3D Seismic Wavefield \\ Using the Earth Simulator
T. Furumura¹, L. Chen²
CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.2, pp. 153-168, 2004, DOI:10.3970/cmes.2004.006.153
Abstract Recent developments of the Earth Simulator, a high-performance parallel computer, has made it possible to realize realistic 3D simulations of seismic wave propagations on a regional scale including higher frequencies. Paralleling this development, the deployment of dense networks of strong ground motion instruments in Japan (K-NET and KiK-net) has now made it possible to directly visualize regional seismic wave propagation during large earthquakes. Our group has developed an efficient parallel finite difference method (FDM) code for modeling the seismic wavefield and a 3D visualization technique, both suitable for implementation on the Earth Simulator. Large-scale 3D simulations of seismic wave propagation… More >

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Meshless Local Petrov-Galerkin (MLPG) approaches for solving 3D Problems in elasto-statics
Z. D. Han¹, S. N. Atluri¹
CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.2, pp. 169-188, 2004, DOI:10.3970/cmes.2004.006.169
Abstract Three different truly Meshless Local Petrov-Galerkin (MLPG) methods are developed for solving 3D elasto-static problems. Using the general MLPG concept, these methods are derived through the local weak forms of the equilibrium equations, by using different test functions, namely, the Heaviside function, the Dirac delta function, and the fundamental solutions. The one with the use of the fundamental solutions is based on the local unsymmetric weak form (LUSWF), which is equivalent to the local boundary integral equations (LBIE) of the elasto-statics. Simple formulations are derived for the LBIEs in which only weakly-singular integrals are included for a simple numerical implementation.… More >

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An Integrated Design of Generalized Single Step LMS Time Operators for Nonlinear Structural Dynamics
R.Kanapady¹, K.K.Tamma²
CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.2, pp. 189-208, 2004, DOI:10.3970/cmes.2004.006.189
Abstract An integrated design of generalized single step LMS methods for applications to nonlinear structural dynamics is described. The design of the mathematical framework encompasses all the traditional and new and recent optimal algorithms encompassing LMS methods, and readily permits the different a-form, v-form and d-form representations in a unique mathematical setting. As such, the theoretical developments and implementation aspects are detailed for subsequent applications to nonlinear structural dynamics problems. The developments naturally inherit a consistent treatment of nonlinear internal forces under the present umbrella of predictor multi-corrector generalized single step representations with a wide variety of algorithmic choices as options… More >

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Indirect RBFN Method with Scattered Points for Numerical Solution of PDEs
Nam Mai-Duy¹
CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.2, pp. 209-226, 2004, DOI:10.3970/cmes.2004.006.209
Abstract This paper is concerned with the use of the indirect radial basis function network (RBFN) method in solving partial differential equations (PDEs) with scattered points. Indirect RBFNs (Mai-Duy and Tran-Cong, 2001a), which are based on an integration process, are employed to approximate the solution of PDEs via point collocation mechanism in the set of randomly distributed points. The method is tested with the solution of Poisson's equations and the Navier-Stokes equations (Boussinesq material). Good results are obtained using relatively low numbers of data points. For example, the natural convection flow in a square cavity at Rayleigh number of 1.e6 is… More >

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