L.S. Miers, J.C.F. Telles¹

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.5, pp. 431-440, 2004, DOI:10.3970/cmes.2004.006.431

Abstract Most formulations involving the use of the so-called consistent elastoplastic tangent operator procedure, in boundary element analysis, have been presented taking in consideration only a J₂-type yield criterion, like von Mises. The present paper aims at bringing a general consistency concept to tangent operators obtained without yield criterion particularization, ready to be used in implicit schemes for elastoplastic BEM analysis. The ideas follows much of the second author's physically nonlinear implicit BEM solution procedures introduced in the 80's and is based on a Taylor series expansion of the true effective stress around an equivalent stress corresponding More >

S. Callsen¹, O. von Estorff¹, O. Zaleski²

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.5, pp. 421-430, 2004, DOI:10.3970/cmes.2004.006.421

Abstract In standard boundary element formulations, singular integrals need to be solved as soon as the considered sources coincide with the collocation points at the boundary. Using a desingularized boundary element approach, the sources are distributed on a surface outside the acoustic domain which means that they are never located at the boundary. Consequently, all the resulting kernels are nonsingular which reduces the complexity of the numerical treatment of the boundary integral equations considerably. In the current contribution a desingularized formulation is given for both, the direct and the indirect boundary element method used to solve More >

C. K. Au¹

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.5, pp. 409-420, 2004, DOI:10.3970/cmes.2004.006.409

Abstract Tracking the flow fronts arising from a primary source in a bounded space with obstacles is a problem which often requires intensive computation. As the flow propagates through the obstacles, the flow pattern is complicated. This phenomenon is mainly due to the existence of the secondary sources which can be identified in the flow field by visibility. Comparing the flow fronts propagation and the wave equation reveals that the complexity is caused by the propagation phenomena: reflection, refraction, diffraction and interference. This paper investigates a geometric technique to combine these phenomena for computing flow fronts. More >

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 More >

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 More >

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 More >

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… More >

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… More >

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 More >

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 More >