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  • Open Access

    ARTICLE

    Geometrically Nonlinear Analysis of Reissner-Mindlin Plate by Meshless Computation

    P. H. Wen1, Y. C. Hon2

    CMES-Computer Modeling in Engineering & Sciences, Vol.21, No.3, pp. 177-192, 2007, DOI:10.3970/cmes.2007.021.177

    Abstract In this paper, we perform a geometrically nonlinear analysis of Reissner-Mindlin plate by using a meshless collocation method. The use of the smooth radial basis functions (RBFs) gives an advantage to evaluate higher order derivatives of the solution at no cost on extra-interpolation. The computational cost is low and requires neither the connectivity of mesh in the domain/boundary nor integrations of fundamental/particular solutions. The coupled nonlinear terms in the equilibrium equations for both the plane stress and plate bending problems are treated as body forces. Two load increment schemes are developed to solve the nonlinear differential equations. Numerical verifications are… More >

  • Open Access

    ARTICLE

    Acoustic Scattering in Prolate Spheroidal Geometry via Vekua Tranformation -- Theory and Numerical Results

    L.N. Gergidis, D. Kourounis, S. Mavratzas, A. Charalambopoulos1

    CMES-Computer Modeling in Engineering & Sciences, Vol.21, No.2, pp. 157-176, 2007, DOI:10.3970/cmes.2007.021.157

    Abstract A new complete set of scattering eigensolutions of Helmholtz equation in spheroidal geometry is constructed in this paper. It is based on the extension to exterior boundary value problems of the well known Vekua transformation pair, which connects the kernels of Laplace and Helmholtz operators. The derivation of this set is purely analytic. It avoids the implication of the spheroidal wave functions along with their accompanying numerical deficiencies. Using this novel set of eigensolutions, we solve the acoustic scattering problem from a soft acoustic spheroidal scatterer, by expanding the scattered field in terms of it. Two approaches concerning the determination… More >

  • Open Access

    ARTICLE

    Wind Set-down Relaxation

    Baran Aydın1,2, Utku Kânoğlu3

    CMES-Computer Modeling in Engineering & Sciences, Vol.21, No.2, pp. 149-156, 2007, DOI:10.3970/cmes.2007.021.149

    Abstract We developed analytical solutions to the wind set-down and the wind set-down relaxation problems. The response of the ocean to the wind blowing over a long-narrow and linearly sloping shallow basin is referred to as wind set-down. The shoreline exhibits oscillatory behavior when the wind calms down and the resulting problem is referred to as wind set-down relaxation. We use an existing hodograph-type transformation that was introduced to solve the nonlinear shallow-water wave equations analytically for long wave propagation and obtain an explicit-transform analytical solution for wind set-down. For the wind set-down relaxation, the nonlinear shallow-water wave equations are solved… More >

  • Open Access

    ARTICLE

    Genetic Programming Metamodel for Rotating Beams

    Anuj Pratap Singh, V. Mani, Ranjan Ganguli1

    CMES-Computer Modeling in Engineering & Sciences, Vol.21, No.2, pp. 133-148, 2007, DOI:10.3970/cmes.2007.021.133

    Abstract This paper investigates the use of Genetic Programming (GP) to create an approximate model for the non-linear relationship between flexural stiffness, length, mass per unit length and rotation speed associated with rotating beams and their natural frequencies. GP, a relatively new form of artificial intelligence, is derived from the Darwinian concept of evolution and genetics and it creates computer programs to solve problems by manipulating their tree structures. GP predicts the size and structural complexity of the empirical model by minimizing the mean square error at the specified points of input-output relationship dataset. This dataset is generated using a finite… More >

  • Open Access

    ARTICLE

    Slow Viscous Migration of a Conducting Solid Particle under the Action of Uniform Ambient Electric and Magnetic Fields

    A. Sellier1

    CMES-Computer Modeling in Engineering & Sciences, Vol.21, No.2, pp. 105-132, 2007, DOI:10.3970/cmes.2007.021.105

    Abstract We examine the low-Reynolds-number migration of a conducting and arbitrarily-shaped solid particle freely immersed in a metal liquid of different conductivity when subject to uniform ambient electric and magnetic fields. The boundary formulation established elsewhere for an insulating particle is extended and the incurred particle's rigid-body motion is then obtained by determinating a very few surface quantities on the particle's surface. The behavior of either oblate or prolate conducting spheroids is analytically investigated and the poposed procedure for the challenging case of other non-trivial geometries is implemented and benchmarked against those solutions. The numerical implementation makes it possible to obtain… More >

  • Open Access

    ARTICLE

    A New Local Contact Search Method Using a Multi-Layer Neural Network

    Atsuya Oishi1, Shinobu Yoshimura2

    CMES-Computer Modeling in Engineering & Sciences, Vol.21, No.2, pp. 93-104, 2007, DOI:10.3970/cmes.2007.021.093

    Abstract This paper describes a new local contact search method using a multi-layer neural network and its application to smoothed contact surface consisting of Gregory patches. A contact search process consists of two phases: a global search phase for finding the nearest node-segment pair and a local search phase for finding an exact local coordinate of the contact point within the segment. In the present method, the multi-layer neural network is utilized in the latter phase. The fundamental formulation of the proposed local contact search method is described in detail, and it is applied to smoothed contact surfaces consisting of Gregory… More >

  • Open Access

    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 strain dependent tangent modulus, we… More >

  • Open Access

    ARTICLE

    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 that only the scatterer surface… More >

  • Open Access

    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 Fourier coefficients. Here, the factor… More >

  • Open Access

    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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