Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.21, No.1, pp. 53-66, 2007, DOI:10.3970/cmes.2007.021.053

Abstract A newly modified Trefftz method is developed to solve the exterior and interior Dirichlet problems for two-dimensional Laplace equation, which takes the characteristic length of problem domain into account. After introducing a circular artificial boundary which is uniquely determined by the physical problem domain, we can derive a Dirichlet to Dirichlet mapping equation, which is an exact boundary condition. By truncating the Fourier series expansion one can match the physical boundary condition as accurate as one desired. Then, we use the collocation method and the Galerkin method to derive linear equations system to determine the More >

Z. D. Han, S. N. Atluri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.21, No.1, pp. 41-52, 2007, DOI:10.3970/cmes.2007.021.041

Abstract Straight-forward systematic derivations of the weakly singular boundary integral equations (BIEs) are presented, following the simple and directly-derived approach by Okada, Rajiyah, and Atluri (1989b) and Han and Atluri (2002). A set of weak-forms and their algebraic combinations have been used to avoid the hyper-singularities, by directly applying the "intrinsic properties'' of the fundamental solutions. The systematic decomposition of the kernel functions of BIEs is presented for regularizing the BIEs. The present approach is general, and is applied to developing weakly-singular BIEs for solids and acoustics successfully. More >

W.H. Chen¹, H.C. Cheng², Y.C. Hsu³

CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.2, pp. 123-146, 2007, DOI:10.3970/cmes.2007.020.123

Abstract The evaluation of the fundamental mechanical properties of single/multi-walled carbon nanotubes(S/MWCNTs) is of great importance for their industrial applications. The present work is thus devoted to the determination of various mechanical properties of S/MWCNTs using molecular dynamics (MD) simulations. The study first focuses on the exploration of the effect of the weak inlayer van der Waals (vdW) atomistic interactions on the mechanical properties of S/MWCNTs. Secondly, in addition to the zig-zag and armchair types of CNTs, the hybrid type of MWCNTs that comprise a zig-zag outer tube and an inner armchair tube is also analyzed.… More >

Leevan Ling¹, Tomoya Takeuchi²

CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.2, pp. 99-110, 2007, DOI:10.3970/cmes.2007.020.099

Abstract We aim to identify the unknown source locations in a two-dimensional heat equation from scattered measurements. In [Inverse Problems, 22(4):1289--1305, 2006], we proposed a numerical procedure that identifies the unknown source locations of 2D heat equation solely based on three measurement points. Due to the nonlinearity and complexity of the problem, the quality of the resulting estimations is often poor especially when the number of unknown is large. In this paper, we purpose a linear refinement scheme that takes the outputs of the existing nonlinear algorithm as initial guesses and iteratively improves on the accuracy More >

A. Arockiarajan¹, A. Menzel²

CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.1, pp. 55-72, 2007, DOI:10.3970/cmes.2007.020.055

Abstract To study rate-dependent properties of piezoelectric materials a micro-mechanically motivated model is applied in this work. The developed framework is embedded into a coupled three-dimensional finite element setting, whereby each element is assumed to represent one grain and, moreover, possesses a random initialisation of the underlying polarisation direction. Furthermore, an energy-based criterion is used for the initiation of the onset of domain switching and the subsequent propagation of domain wall motion during the switching process is modelled via a linear kinetics theory. The interaction between individual grains is thereby incorporated by means of a probabilistic More >

N. Osawa¹, K. Hashimoto¹, J. Sawamura¹, J. Kikuchi², Y. Deguchi², T. Yamaura²

CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.1, pp. 43-54, 2007, DOI:10.3970/cmes.2007.020.043

Abstract A new hypothesis regarding heat transmission during line heating is proposed. It states that the distribution of the temperature of the gas adjacent to the plate, T_G, and the overall local heat transfer coefficient, α, depend only on the distance from the torch. An identification technique for T_G and α is developed. The validity of the employed hypothesis and the proposed technique is demonstrated by comparing the measured and identified T_G during a spot heating test. The plate temperature calculated by direct heat conduction analysis closely approximates the one measured for the spot and line heating tests, More >

S. Chen^1,2, Y. Liu^1,3, B.C. Khoo⁴, X.J. Fan⁵, J.T. Fan⁶

CMES-Computer Modeling in Engineering & Sciences, Vol.19, No.3, pp. 181-196, 2007, DOI:10.3970/cmes.2007.019.181

Abstract The mesoscopic simulation for fluids flow in a square microchannel is investigated using dissipative particle dynamics. The velocity distribution for single fluid in a square channel is compared with the solutions of CFD solver, which is found to be in good agreement with each other. The no-slip boundary condition could be well held for the repulsive coefficient ranged from 9.68 to 18.0. For the same range of repulsive coefficient, various wettabilities could be obtained by changing the repulsive coefficient for binary immiscible fluids, in which the immiscible fluids are achieved by increasing the repulsive force… More >

A. Arockiarajan¹, A. Menzel²

CMES-Computer Modeling in Engineering & Sciences, Vol.19, No.2, pp. 163-178, 2007, DOI:10.3970/cmes.2007.019.163

Abstract To study rate-dependent properties of piezoelectric materials a micro-mechanically motivated model is applied in this work. The developed framework is embedded into a coupled three-dimensional finite element setting, whereby each element is assumed to represent one grain and, moreover, possesses a random initialisation of the underlying polarisation direction. Furthermore, an energy-based criterion is used for the initiation of the onset of domain switching and the subsequent propagation of domain wall motion during the switching process is modelled via a linear kinetics theory. The interaction between individual grains is thereby incorporated by means of a probabilistic More >

Y.F. Nie¹, S. Chang¹, X.K. Fan¹

CMES-Computer Modeling in Engineering & Sciences, Vol.19, No.2, pp. 135-144, 2007, DOI:10.3970/cmes.2007.019.135

Abstract A new parallel mechanism for Node-based Seamless Finite Element Method was proposed in this paper, which possessed the following three prominent points: realizing the workload balance for the parallel processes naturally, achieving synchronization of all the schedules under complex parallel environment, and filling up the gap between pre-processing and main processing. To support the scheme, three specific solutions of the parallel mechanism were proposed in this paper, all of which achieved the highly efficient parallel seamless connection between the FEM mesh generation process and structure analysis process. Two of the three schemes, i.e. dynamic scheme More >

T.C. Theodosiou¹, D.A. Saravanos²

CMES-Computer Modeling in Engineering & Sciences, Vol.19, No.2, pp. 121-134, 2007, DOI:10.3970/cmes.2007.019.121

Abstract In this paper a new method is introduced for carbon nanotube modeling combining features of Molecular Mechanics and Finite Element Analysis. Repetitive atomic cells are treated as finite elements, whose internal energy is determined by the semi-empirical Brenner molecular potential model; internal forces and linearized stiffness matrices are formulated analytically in order to gain in speed and accuracy, and the resultant discrete system is formulated and solved using the Newton-Raphson method. The presented method is validated through comparisons to numerical and experimental results provided by other researchers. The bending and shearing of CNTs is also More >