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  • Open Access


    A Unified Computational Approach to Instability of Periodic Laminated Materials

    M.V. Menshykova1, I.A. Guz, O.V. Menshykov

    CMES-Computer Modeling in Engineering & Sciences, Vol.51, No.3, pp. 239-260, 2009, DOI:10.3970/cmes.2009.051.239

    Abstract The present work is devoted to the investigation of the internal instability in laminated materials. The paper is concerned with the development of a unified computational procedure for numerical realisation of the method as applied to various constitutive equations of the layers, different loading schemes (uniaxial or biaxial loading) and different precritical conditions (large or small precritical deformations). It contains many examples of critical stresses/strains calculations for particular composites as well as analysis of different buckling modes. More >

  • Open Access


    A Cartesian-Grid Discretisation Scheme Based on Local Integrated RBFNs for Two-Dimensional Elliptic Problems

    N. Mai-Duy1, T. Tran-Cong1

    CMES-Computer Modeling in Engineering & Sciences, Vol.51, No.3, pp. 213-238, 2009, DOI:10.3970/cmes.2009.051.213

    Abstract This paper reports a new numerical scheme based on Cartesian grids and local integrated radial-basis-function networks (IRBFNs) for the solution of second-order elliptic differential problems defined on two-dimensional regular and irregular domains. At each grid point, only neighbouring nodes are activated to construct the IRBFN approximations. Local IRBFNs are introduced into two different schemes for discretisation of partial differential equations, namely point collocation and control-volume (CV)/subregion-collocation. Linear (e.g. heat flow) and nonlinear (e.g. lid-driven triangular-cavity fluid flow) problems are considered. Numerical results indicate that the local IRBFN CV scheme outperforms the local IRBFN point-collocation scheme regarding accuracy. Moreover, the former… More >

  • Open Access


    An Efficient Petrov-Galerkin Chebyshev Spectral Method Coupled with the Taylor-series Expansion Method of Moments for Solving the Coherent Structures Effect on Particle Coagulation in the Exhaust Pipe

    Chan T.L.1,2, Xie M.L.1,3, Cheung C.S.1

    CMES-Computer Modeling in Engineering & Sciences, Vol.51, No.3, pp. 191-212, 2009, DOI:10.3970/cmes.2009.051.191

    Abstract An efficient Petrov-Galerkin Chebyshev spectral method coupled with the Taylor-series expansion method of moments (TEMOM) was developed to simulate the effect of coherent structures on particle coagulation in the exhaust pipe. The Petrov-Galerkin Chebyshev spectral method was presented in detail focusing on the analyticity of solenoidal vector field used for the approximation of the flow. It satisfies the pole condition exactly at the origin, and can be used to expand the vector functions efficiently by using the solenoidal condition. This developed TEMOM method has no prior requirement for the particle size distribution (PSD). It is much simpler than the method… More >

  • Open Access


    Multi-Point Shape Optimization of Airfoils at Low Reynolds Numbers

    D.N. Srinath1, Sanjay Mittal1, Veera Manek2

    CMES-Computer Modeling in Engineering & Sciences, Vol.51, No.2, pp. 169-190, 2009, DOI:10.3970/cmes.2009.051.169

    Abstract A continuous adjoint method is formulated and implemented for the multi-point shape optimization of airfoils at low Re. The airfoil shape is parametrized with a non-uniform rational B-Spline (NURBS). Optimization studies are carried out for two different objective functions. The first involves an inverse function on the lift coefficient over a range of Re. The objective is to determine a shape that results in a lift coefficient of 0.4 at three values of Re: 10, 100 and 500. The second objective involves a direct function on the lift coefficient over a range of angles of attack,a. The lift coefficient is… More >

  • Open Access


    An Implementation of the Longman's Integration Method on Graphics Hardware

    E. Mesquita1, J.Labaki 1 and L.O.S.Ferreira1

    CMES-Computer Modeling in Engineering & Sciences, Vol.51, No.2, pp. 143-168, 2009, DOI:10.3970/cmes.2009.051.143

    Abstract There is a growing trend towards solving problems of computational mechanics by parallelization strategies. The traditional approach is to implement the parallelization procedures on CPUs based on the MPI or OpenMP paradigms. Recent efforts have been made to implement computational tasks on general-purpose programmable graphics hardware (GPGPU). The GPU is specially well-suited to address problems that can be formulated in form of data-parallel computations with high arithmetic intensity. This work addresses the implementation of the Longman's integration method on graphics hardware. A serial implementation of Longman's method was rewritten under the SIMD (Single Input Multiple Data) parallel programming paradigm. The… More >

  • Open Access


    Vibration Analysis of Arbitrarily Shaped Membranes

    S.Yu. Reutskiy1

    CMES-Computer Modeling in Engineering & Sciences, Vol.51, No.2, pp. 115-142, 2009, DOI:10.3970/cmes.2009.051.115

    Abstract In this paper a new numerical technique for problems of free vibrations of arbitrary shaped non-homogeneous membranes:∇2w + k2q(x)w = 0, x∈ Ω⊂R2, B[w] = 0, x∈∂Ω is presented. Homogeneous membranes of a complex form are considered as a particular case. The method is based on mathematically modeling of physical response of a system to excitation over a range of frequencies. The response amplitudes are then used to determine the resonant frequencies. Applying the method, one gets a sequence of boundary value problems (BVPs) depending on the spectral parameter k. The eigenvalues are sought as positions of the maxima of… More >

  • Open Access


    The Coupling Method of Natural Boundary Element and Mixed Finite Element for Stationary Navier-Stokes Equation in Unbounded Domains

    Dongjie Liu1, Dehao Yu2

    CMES-Computer Modeling in Engineering & Sciences, Vol.37, No.3, pp. 305-330, 2008, DOI:10.3970/cmes.2008.037.305

    Abstract The coupling method of natural boundary element and mixed finite element is applied to analyze the stationary Navier-Stokes equation in 2-D unbounded domains. After an artificial smooth boundary is introduced, the original nonlinear problem is reduced into an equivalent problem defined in bounded computational domain. The well-posedness of the reduced problem is proved. The finite element approximation of this problem is given, and numerical example is provided to show the feasibility and efficiency of the method. More >

  • Open Access


    A Variational Formulation of a Stabilized Unsplit Convolutional Perfectly Matched Layer for The Isotropic or Anisotropic Seismic Wave Equation

    R. Martin1, D. Komatitsch1,2, S. D. Gedney3

    CMES-Computer Modeling in Engineering & Sciences, Vol.37, No.3, pp. 274-304, 2008, DOI:10.3970/cmes.2008.037.274

    Abstract In the context of the numerical simulation of seismic wave propagation, the perfectly matched layer (PML) absorbing boundary condition has proven to be efficient to absorb surface waves as well as body waves with non grazing incidence. But unfortunately the classical discrete PML generates spurious modes traveling and growing along the absorbing layers in the case of waves impinging the boundary at grazing incidence. This is significant in the case of thin mesh slices, or in the case of sources located close to the absorbing boundaries or receivers located at large offset. In previous work we derived an unsplit convolutional… More >

  • Open Access


    Scattering of flexural wave in thin plate with multiple holes by using the null-field integral equation approach

    Wei-Ming Lee1, Jeng-Tzong Chen2,3

    CMES-Computer Modeling in Engineering & Sciences, Vol.37, No.3, pp. 243-273, 2008, DOI:10.3970/cmes.2008.037.243

    Abstract In this paper, a semi-analytical approach is proposed to solve the scattering problem of flexural waves and to determine dynamic moment concentration factors (DMCFs) in an infinite thin plate with multiple circular holes. The null-field integral formulation is employed in conjunction with degenerate kernels, tensor transformation and Fourier series. In the proposed direct formulation, all dynamic kernels of plate are expanded into degenerate forms and further the rotated degenerate kernels have been derived for the general exterior problem. By uniformly collocating points on the real boundary, a linear algebraic system is constructed. The results of dynamic moment concentration factors for… More >

  • Open Access


    Stable MFS Solution to Singular Direct and Inverse Problems Associated with the Laplace Equation Subjected to Noisy Data

    LiviuMarin 1

    CMES-Computer Modeling in Engineering & Sciences, Vol.37, No.3, pp. 203-242, 2008, DOI:10.3970/cmes.2008.037.203

    Abstract In this paper, a meshless method for the stable solution of direct and inverse problems associated with the two-dimensional Laplace equation in the presence of boundary singularities and noisy boundary data is proposed. The governing equation and boundary conditions are discretized by the method of fundamental solutions (MFS), whilst the existence of the boundary singularity is taken into account by subtracting from the original MFS solution the corresponding singular solutions, as given by the asymptotic expansion of the solution near the singular point. However, even in the case when the boundary singularity is accounted for, the numerical solutions obtained by… More >

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