J. P. Agnantiaris¹, D. Polyzos^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.1, pp. 197-212, 2003, DOI:10.3970/cmes.2003.004.197

Abstract A Boundary Element Method (BEM), for the three-dimensional solution of both non-axisymmetric and axisymmetric coupled acoustic-elastic problems in the frequency domain, is presented. The present BEM makes use of the Burton and Miller integral equation for infinite acoustic spaces, while elastic structures are dealt with the standard boundary integral equation of elastodynamics. The axisymmetric formulation involves the use of the fast Fourier transform algorithm. Highly accurate numerical algorithms are used for the evaluation of singular integrals, while nearly singular integrals are treated, also with high accuracy, through the use of practical numerical techniques, for both More >

Z.Tang, S. Shen, S.N. Atluri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.1, pp. 177-196, 2003, DOI:10.3970/cmes.2003.004.177

Abstract A meshless numerical implementation is reported of the 2-D Fleck-Hutchinson phenomenological strain-gradient theory, which fits within the framework of the Toupin-Mindlin theories and deals with first-order strain gradients and the associated work-conjugate higher-order stresses. From a mathematical point of view, the two-dimensional Toupin-Mindlin strain gradient theory is a generalization of the Poisson-Kirchhoff plate theories, involving, in addition to the fourth-order derivatives of the displacements, also a second-order derivative. In the conventional displacement-based approaches in FEM, the interpolation of displacement requires C$^{1}$ --continuity (in order to ensure convergence of the finite element procedure for 4$^{th}$ order… More >

L. F. Qian^1,3, R. C. Batra², L. M. Chen³

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.1, pp. 161-176, 2003, DOI:10.3970/cmes.2003.004.161

Abstract We use two meshless local Petrov-Galerkin formulations, namely, the MLPG1 and the MLPG5, to analyze infinitesimal deformations of a homogeneous and isotropic thick elastic plate with a higher-order shear and normal deformable plate theory. It is found that the two MLPG formulations give results very close to those obtained by other researchers and also by the three-dimensional analysis of the problem by the finite element method. More >

I. S. Raju¹, D. R. Phillips²

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.1, pp. 141-160, 2003, DOI:10.3970/cmes.2003.004.141

Abstract An accurate and yet simple Meshless Local Petrov-Galerkin (MLPG) formulation for analyzing beam problems is presented. In the formulation, simple weight functions are chosen as test functions as in the conventional MLPG method. Linear test functions are also chosen, leading to a variation of the MLPG method that is computationally efficient compared to the conventional implementation. The MLPG method is evaluated by applying the formulation to a variety of patch tests, thin beam problems, and problems with load discontinuities. The formulation successfully reproduces exact solutions to machine accuracy when higher order power and spline functions More >

T. Nishioka¹, F. Stan¹

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.1, pp. 119-140, 2003, DOI:10.3970/cmes.2003.004.119

Abstract In this paper we investigate the essentially unexplored area of three-dimensional dynamic fracture mechanics. The general objective sought by this investigation is the understanding of three-dimensional dynamic crack propagation and arrest, and, specifically, the effect that the specimen thickness has on the dynamic fracture mechanism. In particular, in the context of the present paper, it is intended to provide a summary of the achievements on the issue of three-dimensional dynamic fracture parameters. Furthermore, the behavior of the three-dimensional field near the crack front is investigated. The issue that will be addressed is the extent of More >

R.Kanapady¹, K.K.Tamma²

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.1, pp. 103-118, 2003, DOI:10.3970/cmes.2003.004.103

Abstract Of general interest here is the time dimension aspect wherein discretized operators in time may be continuous or discontinuous; and of particular interest and focus here is the design of time discretized operators in the context of discontinuous state-phase for computational dynamics applications. Based on a generalized bi-discontinuous time weighted residual formulation, the design leading to a new unified set of hierarchical energy conserving and energy dissipating time discretized operators are developed for the first time that are fundamentally useful for time adaptive computations for dynamic problems. Unlike time discontinuous Galerkin approaches, the design is… More >

N. Mai-Duy, T. Tran-Cong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.1, pp. 85-102, 2003, DOI:10.3970/cmes.2003.004.085

Abstract This paper reports a mesh-free Indirect Radial Basis Function Network method (IRBFN) using Thin Plate Splines (TPSs) for numerical solution of Differential Equations (DEs) in rectangular and curvilinear coordinates. The adjustable parameters required by the method are the number of centres, their positions and possibly the order of the TPS. The first and second order TPSs which are widely applied in numerical schemes for numerical solution of DEs are employed in this study. The advantage of the TPS over the multiquadric basis function is that the former, with a given order, does not contain the… More >

Rosario M. A. Marretta¹, Giovanni Lombardi², Roberto Antinoro¹

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.1, pp. 73-84, 2003, DOI:10.3970/cmes.2003.004.073

Abstract An approach based on Lighthill's transpiration velocity is explored and proposed for a new design criterion for airfoils in unsteady and viscous flows. This criterion confines its methodologies to the close proximity of the laminar and turbulent boundary layer and it shows good efficiency in predicting and calculating the wake evolution regions in a wide range of operating unsteady parameters. Also, the criterion is capable of predicting low Mach number, attached flow-fields as accurately as the full Navier-Stokes solutions when the massive flow separation is avoided. The agreement of the present results with those empirically More >

E. Ferretti¹

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.1, pp. 51-72, 2003, DOI:10.3970/cmes.2003.004.051

Abstract A numerical code for modeling crack propagation using the cell method is proposed. The Mohr-Coulomb criterion is used to compute the direction of crack propagation, and the new crack geometry is realized by an intra-element propagation technique. Automatic remeshing is then activated. Applications in Mode I and Mixed Mode are presented to illustrate the robustness of the implementation. More >

A. Aimi¹, M. Diligenti¹, F. Lunardini¹, A. Salvadori²

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.1, pp. 31-50, 2003, DOI:10.3970/cmes.2003.004.031

Abstract This paper is devoted to the study of a new application of the Panel Clustering Method [Hackbusch and Sauter (1993); Hackbusch and Nowak (1989)]. By considering a classical 3D Neumann screen problem in its boundary integral formulation discretized with the Galerkin BEM, which requires the evaluation of double integrals with hypersingular kernel, we recall and use some recent results of analytical evaluation of the inner hypersingular integrals. Then we apply the Panel Clustering Method (PCM) for the evaluation of the outer integral. For this approach error estimate is shown. Numerical examples and comparisons with classical More >