CMES-Vol. 41, No. 1, 2009

Open Access

ARTICLE

The Fourth-Order Group Preserving Methods for the Integrations of Ordinary Differential Equations
Hung-Chang Lee¹, Chein-Shan Liu²
CMES-Computer Modeling in Engineering & Sciences, Vol.41, No.1, pp. 1-26, 2009, DOI:10.3970/cmes.2009.041.001
Abstract The group-preserving schemes developed by Liu (2001) for integrating ordinary differential equations system were adopted the Cayley transform and Padé approximants to formulate the Lie group from its Lie algebra. However, the accuracy of those schemes is not better than second-order. In order to increase the accuracy by employing the group-preserving schemes on ordinary differential equations, according to an efficient technique developed by Runge and Kutta to raise the order of accuracy from the Euler method, we combine the Runge-Kutta method on the group-preserving schemes to obtain the higher-order numerical methods of group-preserving type. They More >

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Isoparametric FEM vs. BEM for Elastic Functionally Graded Materials
V. Minutolo¹, E. Ruocco¹, S. Ciaramella¹
CMES-Computer Modeling in Engineering & Sciences, Vol.41, No.1, pp. 27-48, 2009, DOI:10.3970/cmes.2009.041.027
Abstract A Field Boundary Element Method (FBEM) for Functionally Graded Materials (FGM) is presented and compared with Isoparametric Finite Element Method. The presented formulation, using the Kelvin's fundamental solution, is able to analyse structures although no fundamental solution is actually known. Isoparametric FGM Finite Element Method is a well established tool for FGM structural analysis. The comparison shows that both FBEM and FEM give accurate results. In the paper, the solution of some examples for 2D plates are reported both using FEM and FBEM. Some comparisons with analytical results are discussed and accuracy of the solutions More >

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Estimation and Validation of Elastic Modulus of Carbon Nanotubes Using Nano-Scale Tensile and Vibrational Analysis
C. J. Wu¹, C. Y. Chou¹, C. N. Han¹, K. N. Chiang²
CMES-Computer Modeling in Engineering & Sciences, Vol.41, No.1, pp. 49-68, 2009, DOI:10.3970/cmes.2009.041.049
Abstract In this paper, the atomistic-continuum mechanics method (ACM) is applied for carbon nanotube modeling. The atomistic-continuum mechanics is based on the transformation of chemical bonds between atoms in molecular mechanics into appropriate elements in finite element method and continuum mechanics. Spring elements are treated as chemical bonds between carbon atoms in carbon nanotube, whose force-displacement function is determined by the Reactive Empirical Bond Order (REBO) potential model. The advantages and unique feature of ACM method is same analytical model can be used for both tensile and vibration analyses, and most importantly, there are no prior More >

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Effects of the local structure on a cracked periodically distributed composite
M. Patrício¹, R. Mattheij¹, G. de With²
CMES-Computer Modeling in Engineering & Sciences, Vol.41, No.1, pp. 69-94, 2009, DOI:10.3970/cmes.2009.041.069
Abstract In this paper the effect of the local structure of a highly heterogeneous composite material on the parameters that characterise crack propagation is analysed. The evaluation of stress intensity factors is discussed. A hybrid approach based on domain decomposition and homogenisation methods is employed to obtain accurate solutions with reduced computational complexity. More >

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