CMES-Vol. 7, No. 3, 2005

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A Dynamical Approach to the Spatio-temporal Features of the Portevin-Le Chatelier Effect
G.Ananthakrishna¹
CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.3, pp. 233-240, 2005, DOI:10.3970/cmes.2005.007.233
Abstract We show that the extended Ananthakrishna's model exhibits all the features of the Portevin - Le Chatelier effect including the three types of bands. The model reproduces the recently observed crossover from a low dimensional chaotic state at low and medium strain rates to a high dimensional power law state of stress drops at high strain rates. The dynamics of crossover is elucidated through a study of the Lyapunov spectrum. More >

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Simulation of a 4^th Order ODE: Illustration of Various Primal & Mixed MLPG Methods
S. N. Atluri¹, Shengping Shen¹
CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.3, pp. 241-268, 2005, DOI:10.3970/cmes.2005.007.241
Abstract Various MLPG methods, with the MLS approximation for the trial function, in the solution of a 4$^{th}$ order ordinary differential equation are illustrated. Both the primal MLPG methods and the mixed MLPG methods are used. All the possible local weak forms for a 4$^{th}$ order ordinary differential equation are presented. In the first kind of mixed MLPG methods, both the displacement and its second derivative are interpolated independently through the MLS interpolation scheme. In the second kind of mixed MLPG methods, the displacement, its first derivative, second derivative and third derivative are interpolated independently through… More >

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A multiscale approach for the micropolar continuum model
Hiroshi Kadowaki¹, Wing Kam Liu²
CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.3, pp. 269-282, 2005, DOI:10.3970/cmes.2005.007.269
Abstract A method to derive governing equations and elastic-plastic constitutive relations for the micropolar continuum model is proposed. Averaging procedures are operated over a surrounding sub-domain for each material point to bridge a discrete microstructure to a macro continuum model. Material parameters are determined by these procedures. The size of the sub-domain represents the material intrinsic length scale, and it is passed into the macroscopic governing equation so that the numerical solution can be regularized for analyses of failure phenomena. An application to a simple granular material model is presented. More >

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Eliminating Slivers in Three-Dimensional Finite Element Models
R.H. Moore¹, S. Saigal²
CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.3, pp. 283-292, 2005, DOI:10.3970/cmes.2005.007.283
Abstract An efficient method for treating slivers and other poorly shaped elements in finite element solutions is presented. A major difficulty for finite element analyses arises from the creation of slivers in automated mesh generation. Sliver shaped elements can degrade the accuracy of a solution and are difficult to remove from a mesh. The proposed method treats slivers by first merging them with neighboring elements to form polyhedra and next subdividing the polyhedra into well-shaped tetrahedral elements. The method does not require the cumbersome and expensive operations of addition or rearrangement of nodes. The validity and More >

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Finite Element Analysis of Carbon Nanotubes with Stone-Wales Defects
L. Nasdala¹, G. Ernst¹, M. Lengnick¹, H. Rothert¹
CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.3, pp. 293-304, 2005, DOI:10.3970/cmes.2005.007.293
Abstract Like any other geometric structure or building, carbon nanotubes may break down due to either material failure or structural failure. In this paper, it is shown that the failure mechanism of carbon nanotubes not only depends on the type and direction of loading but also on the location and number of defects. For the finite element simulations we use a new 4-node finite element without rotational degrees of freedom based on the force field method. For the examples shown here, mainly a single-walled (10,10) armchair nanotube with different Stone-Wales defects, the material parameters are directly… More >

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A Silent Boundary Scheme with the Material Point Method for Dynamic Analyses
Luming Shen¹, Zhen Chen²
CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.3, pp. 305-320, 2005, DOI:10.3970/cmes.2005.007.305
Abstract To simulate the dynamic responses involving different material phases in a finite computational domain without discretizing the whole problem domain, a silent boundary scheme is proposed within the framework of the material point method (MPM) that is an extension from Computational Fluid Dynamics to Computational Solid Dynamics. Because the MPM does not employ fixed mesh connectivity, a robust spatial discretization procedure in the moving domain of influence could be designed by applying viscous damping forces along the computational boundary. To establish a simple interface between the discretization procedures with and without fixed mesh connectivity, a More >

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Two-Dimensional BEM Thermoelastic Analysis of Anisotropic Media with Concentrated Heat Sources
Y.C. Shiah¹, T.L. Guao¹, C.L. Tan²
CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.3, pp. 321-338, 2005, DOI:10.3970/cmes.2005.007.321
Abstract It is well known in elastic stress analysis using the boundary element method (BEM) that an additional volume integral appears in the basic form of the boundary integral equation if thermal effects are considered. In order to restore this general numerical tool as a truly boundary solution technique, it is perhaps most desirable to transform this volume integral exactly into boundary ones. For general 2D anisotropic thermo-elastostatics without heat sources, this was only achieved very recently. The presence of concentrated heat sources in the domain, however, leads to singularities at these points that pose additional More >

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