CMES-Vol. 21, No. 1, 2007

Open Access

ARTICLE

An Unconditionally Time-Stable Level Set Method and Its Application to Shape and Topology Optimization
S.Y. Wang^1,2, K.M. Lim^2,3, B.C. Khoo^2,3, M.Y. Wang⁴
CMES-Computer Modeling in Engineering & Sciences, Vol.21, No.1, pp. 1-40, 2007, DOI:10.3970/cmes.2007.021.001
Abstract The level set method is a numerical technique for simulating moving interfaces. In this paper, an unconditionally BIBO (Bounded-Input-Bounded-Output) time-stable consistent meshfree level set method is proposed and applied as a more effective approach to simultaneous shape and topology optimization. In the present level set method, the meshfree infinitely smooth inverse multiquadric Radial Basis Functions (RBFs) are employed to discretize the implicit level set function. A high level of smoothness of the level set function and accuracy of the solution to the Hamilton-Jacobi partial differential equation (PDE) can be achieved. The resulting dynamic system of… More >

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ARTICLE

A Systematic Approach for the Development of Weakly–Singular BIEs
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 >

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ARTICLE

A Modified Trefftz Method for Two-Dimensional Laplace Equation Considering the Domain's Characteristic Length
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 >

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Acoustic Scattering from Fluid Bodies of Arbitrary Shape
B. Ch,rasekhar¹, Sadasiva M. Rao²
CMES-Computer Modeling in Engineering & Sciences, Vol.21, No.1, pp. 67-80, 2007, DOI:10.3970/cmes.2007.021.067
Abstract In this work, a simple and robust numerical method to calculate the scattered acoustic fields from fluid bodies of arbitrary shape subjected to a plane wave incidence is presented. Three formulations are investigated in this work$viz.$ the single layer formulation (SLF), the double layer formulation (DLF), and the combined layer formulation (CLF). Although the SLF and the DLF are prone to non-uniqueness at certain discrete frequencies of the incident wave, the CLF is problem-free, eliminates numerical artifacts, and provides a unique solution at all frequencies. Further, all the three formulations are surface formulations which implies More >

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ARTICLE

A Hyperelastic Description of Single Wall Carbon Nanotubes at Moderate Strains and Temperatures
Xianwu Ling¹, S.N. Atluri¹
CMES-Computer Modeling in Engineering & Sciences, Vol.21, No.1, pp. 81-92, 2007, DOI:10.3970/cmes.2007.021.081
Abstract In this work, single wall carbon nanotubes (SWNTs) are shown to obey a hyperelastic constitutive model at moderate strains and temperatures. We consider the finite temperature effect via the local harmonic approach. The equilibrium configurations were obtained by minimizing the Helmholtz free energy of a representative atom in an atom-based cell model. We show that the strain energy can be fitted by two cubic polynomials, which consequently produces for the linear elasticity a linearly increasing tangent modulus below a critical strain and an almost linearly decreasing tangent modulus beyond the critical strain. To avoid the More >

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