CMES-Vol. 16, No. 3, 2006

Open Access

ARTICLE

Three-Dimensional Dynamic Fracture Analysis Using the Material Point Method
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 More >

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The Computations of Large Rotation Through an Index Two Nilpotent Equation
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 >

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A New High-order Time-kernel BIEM for the Burgers Equation
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 More >

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Sedimentation of a Solid Particle Immersed in a Fluid Film
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 More >

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Wave Propogation Characteristics of Rotating Uniform Euler-Bernoulli Beams
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 More >

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