K.G. Vinod¹, S. Gopalakrishnan¹, R. Ganguli¹

CMES-Computer Modeling in Engineering & Sciences, Vol.16, No.3, pp. 197-208, 2006, DOI:10.3970/cmes.2006.016.197

Abstract A spectral finite element formulation for a rotating beam subjected to small duration impact is presented in this paper. The spatial variation in centrifugal force is modeled in an average sense. Spectrum and dispersion plots are obtained as a function of rotating speed. It is shown that the flexural wave tends to behave non-dispersively at very high rotation speeds. The numerical results are simulated for two rotating waveguides of different dimensions. The results show that there is a steep increase in responses with the response peaks and the reflected signals almost vanishing at higher rotating speeds. The solution obtained in… More >

A. Sellier¹, L. Pasol²

CMES-Computer Modeling in Engineering & Sciences, Vol.16, No.3, pp. 187-196, 2006, DOI:10.3970/cmes.2006.016.187

Abstract This paper examines the slow viscous settling migration of a solid particle immersed in a viscous fluid film confined by {two plane and parallel solid wall and free surface}. The approach rests on the use of suitable boundary-integral equations on the surface of the particle and the analytical calculation of a new Green tensor that complies with all the boundary conditions satisfied by the liquid flow on the plane boundaries. The numerical implementation resorts to standard boundary elements on the particle's surface and provides at a reasonable cpu time cost the motion of the particle and, if necessary, the velocity… More >

N. Mai-Duy^1,2, T. Tran-Cong², R.I. Tanner³

CMES-Computer Modeling in Engineering & Sciences, Vol.16, No.3, pp. 177-186, 2006, DOI:10.3970/cmes.2006.016.177

Abstract This paper presents a new high-order time-kernel boundary-integral-equation method (BIEM) for numerically solving transient problems governed by the Burgers equation. Instead of using high-order Lagrange polynomials such as quadratic and quartic interpolation functions, the proposed method employs integrated radial-basis-function networks (IRBFNs) to represent the unknown functions in boundary and volume integrals. Numerical implementations of ordinary and double integrals involving time in the presence of IRBFNs are discussed in detail. The proposed method is verified through the solution of diffusion and convection-diffusion problems. A comparison of the present results and those obtained by low-order BIEMs and other methods is also given. More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.16, No.3, pp. 157-176, 2006, DOI:10.3970/cmes.2006.016.157

Abstract To characterize largely deformed spin-free reference configuration of materials, we have to construct an orthogonal transformation tensor Q relative to the fixed frame, such that the tensorial equation Q^˙ = WQ holds for a given spin history W. This paper addresses some interesting issues about this equation. The Euler's angles representation, and the (modified) Rodrigues parameters representation of the rotation group SO(3) unavoidably suffer certain singularity, and at the same time the governing equations are nonlinear three-dimensional ODEs. A decomposition Q = FQ₁ is first derived here, which is amenable to a simpler treatment of Q₁ than Q, and… More >

Y. J. Guo¹, J. A. Nairn²

CMES-Computer Modeling in Engineering & Sciences, Vol.16, No.3, pp. 141-156, 2006, DOI:10.3970/cmes.2006.016.141

Abstract This paper describes algorithms for three-dimensional dynamic stress and fracture analysis using the material point method (MPM). By allowing dual velocity fields at background grid nodes, the method provides exact numerical implementation of explicit cracks in a predominantly meshless method. Crack contact schemes were included for automatically preventing crack surfaces from interpenetration. Crack-tip parameters, dynamic$J$-integral vector and mode I, II, and III stress intensity factors, were calculated from the dynamic stress solution. Comparisons to finite difference method (FDM), finite element method (FEM), and boundary element method (BEM), as well as to static theories showed that MPM can efficiently and accurately… More >

J. X. Zhou¹, T. Koziara¹, T. G. Davies¹

CMES-Computer Modeling in Engineering & Sciences, Vol.16, No.2, pp. 131-140, 2006, DOI:10.3970/cmes.2006.016.131

Abstract The classical BEM approach for elastodynamics can produce poor results when high gradients are generated by impulses. High gradient areas evolve over time and their locations are unknown a priori, so they usually can not be captured by uniform meshes. In this paper, we propose a novel method which interpolates both spatial and temporal domains. A direct space-time discretization scheme is used to capture the wave fronts accurately and to forestall generation of spurious oscillations there. Some numerical examples are given to demonstrate the power and scope of the method. More >

Timon Rabczuk¹, Pedro Areias²

CMES-Computer Modeling in Engineering & Sciences, Vol.16, No.2, pp. 115-130, 2006, DOI:10.3970/cmes.2006.016.115

Abstract This paper proposes a meshfree method for arbitrary evolving cracks in thin shells. The approach is an improvement of the method proposed by Rabczuk T., Areias P.M.A., Belytschko T. (A meshfree thin shell for large deformation, finite strain and arbitrary evolving cracks, International Journal for Numerical Methods in Engineering). In the above cited paper, a shell was developed based on an intrinsic basis of third order completeness. Third order completeness was necessary to remove membrane locking. This resulted in the use of very large domains of influence that made the method computationally expensive. If the crack was modelled by a… More >

C.C. Tsai¹, Y.C. Lin², D.L. Young^2,3, S.N. Atluri⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.16, No.2, pp. 103-114, 2006, DOI:10.3970/cmes.2006.016.103

Abstract In the applications of the method of fundamental solutions, locations of sources are treated either as variables or a priori known constants. In which, the former results in a nonlinear optimization problem and the other has to face the problem of locating sources. Theoretically, farther sources results in worse conditioning and better accuracy. In this paper, a practical procedure is provided to locate the sources for various time-independent operators, including Laplacian, Helmholtz operator, modified Helmholtz operator, and biharmonic operator. Wherein, the procedure is developed through systematic numerical experiments for relations among the accuracy, condition number, and source positions in different… More >

Shiwei Zhou¹, Michael Yu Wang²

CMES-Computer Modeling in Engineering & Sciences, Vol.16, No.2, pp. 83-102, 2006, DOI:10.3970/cmes.2006.016.083

Abstract This paper describes a self-mass-conservative Cahn-Hilliard (C-H) model with elastic strain energy (mean compliance) for the optimization of multi-material structure topology. The total free energy of the generalized C-H system can be represented as a Lyapunov functional so that the elastic strain energy, as a part of the total free energy, decreases gradually to attain optimal material distribution. The interface energy relating to phase gradient in the total free energy plays an important role in regularizing the original ill-posed problem by restricting the structure's boundaries. On the other hand, interface coalescence and break-up due to phase separation and grain coarsening… More >

G.A. Gravvanis¹, K.M. Giannoutakis¹

CMES-Computer Modeling in Engineering & Sciences, Vol.16, No.2, pp. 69-82, 2006, DOI:10.3970/cmes.2006.016.069

Abstract A new class of normalized explicit optimized approximate inverse finite element matrix techniques, based on normalized finite element approximate factorization procedures, for solving sparse linear systems resulting from the finite element discretization of partial differential equations in three space variables are introduced. A new parallel normalized explicit preconditioned conjugate gradient square method in conjunction with normalized approximate inverse finite element matrix techniques for solving efficiently sparse finite element linear systems on distributed memory systems is also presented along with theoretical estimates on speedups and efficiency. The performance on a distributed memory machine, using Message Passing Interface (MPI) communication library, is… More >