C.W. Chen¹, C.M. Fan¹, D.L. Young^1,2, K. Murugesan¹, C.C Tsai³

CMES-Computer Modeling in Engineering & Sciences, Vol.8, No.1, pp. 29-44, 2005, DOI:10.3970/cmes.2005.008.029

Abstract We use a meshless numerical method to analyze the eigenanalysis of thin circular membranes with degenerate boundary conditions, composed by different orientations and structures of stringers. The membrane eigenproblem is studied by solving the two-dimensional Helmholtz equation utilizing the method of fundamental solutions and domain decomposition technique as well. The method of singular value decomposition is adopted to obtain eigenvalues and eigenvectors of the resulting system of global linear equation. The proposed novel numerical scheme was first validated by three circular membranes which are structured with a single edge stringer, two opposite edge stringers and… More >

Alexandre S. Botta¹, Wilson S. Venturini²

CMES-Computer Modeling in Engineering & Sciences, Vol.8, No.1, pp. 15-28, 2005, DOI:10.3970/cmes.2005.008.015

Abstract In this work a regularized boundary-finite element combination is proposed to analyse 2D elastostatic solids reinforced by fibres. The boundary element is adopted to model the matrix behaviour, while finite elements model the embedded fibres. The debonding effects caused by the adherence loss between the two materials are also considered. A three-degree polynomial is adopted to approach the displacement field along the fibre elements, while linear approximations are used to represent the bonding forces between fibres and the matrix. The non-linear debonding model is governed by a loading function written in terms of the contact More >

C. K. Au¹

CMES-Computer Modeling in Engineering & Sciences, Vol.8, No.1, pp. 1-14, 2005, DOI:10.3970/cmes.2005.008.001

Abstract Solving the Eikonal equation is popular due to its potential applications in various areas. Numerical method is the most common approach to solve the equation. This paper presents a geometric approach to solve the equation. Each point in a two dimensional domain with a given velocity field is characterized by the least time from the source. The path of least time is obtained by the Euler equations characterizing the extrema of the variation problem. A geometric representation of the space time function for the source is constructed. The solution to the eikonal equation is obtained More >

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 >

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 >

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 >

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 >

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 >

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 >

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 >