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 >

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 >

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 >

Z.Y. Qian¹, Z.D. Han¹, S.N. Atluri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.1, pp. 115-122, 2004, DOI:10.3970/cmes.2004.006.115

Abstract This article has no abstract. More >

N. Mai-Duy¹, T. Tran-Cong²

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.1, pp. 59-76, 2004, DOI:10.3970/cmes.2004.006.059

Abstract This paper presents a new domain decomposition technique based on the use of Boundary Integral Equations (BIEs) for the analysis of viscous flow problems. The domain of interest is divided into a number of non-overlapping subdomains and an iterative procedure is then employed to update the boundary conditions at interfaces. The new feature in the present work is that at each iteration, the relevant two subdomains, together containing a particular interface, are assumed to satisfy the governing BI equations which they do at the end of a convergent iterative process. Hence the boundary conditions on More >

António Tadeu¹, Julieta António and Nuno Simões

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.1, pp. 43-58, 2004, DOI:10.3970/cmes.2004.006.043

Abstract This Analytical Green's functions for the steady-state response of homogeneous three-dimensional unbounded, half-space, slab and layered solid media subjected to a spatially sinusoidal harmonic heat line source are presented. In the literature, this problem is frequently referred to as the two-and-a-half dimensional fundamental solution or 2.5D Green's functions.
The proposed equations are theoretically interesting in themselves and they are also useful as benchmark results for validating numerical applications. They are also of great practical use in the formulation of three dimensional heat transfer problems in layered solid formations using integral transform methods and/or boundary elements.… More >

W. J. Mansur¹, A. I. Abreu¹, J. A. M. Carrer¹

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.1, pp. 31-42, 2004, DOI:10.3970/cmes.2004.006.031

Abstract This work is concerned with the computation of the contribution of initial conditions in two-dimensional (2D) frequency-domain analysis of transient scalar wave propagation problems with the corresponding Boundary Element Method (BEM) formulation. The paper describes how pseudo-forces, represented by generalized functions, can replace the initial conditions, related to the potential and its time derivative. The generation of such pseudo-forces is the subject of a detailed discussion. The formulation presented here carries out Discrete Fourier Transform (Direct: DFT, and Inverse: IDFT) via FFT (Fast Fourier Transform) algorithms. At the end of the paper four examples are More >

J. H. Jackson¹, A. S. Kobayashi², S. N. Atluri³

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.1, pp. 17-30, 2004, DOI:10.3970/cmes.2004.006.017

Abstract The T_ε^*  integral was calculated numerically along an extending, tunneling crack front in an 8 mm thick, aluminum three-point bend (3PB) specimen, using a numerical model driven by experimentally obtained surface displacements. The model provided input to a contour integration for the T_ε^*  integral, via the Equivalent Domain Integral (EDI) method with incremental plasticity. Validity of the analysis was ensured by the agreement of the T_ε^*  integral obtained on the surface (plane stress) and the plane stress values from previous studies. T_ε^*   was observed to decrease from the outer surface of the specimen to More >