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  • Open Access


    A High-Order Time and Space Formulation of the Unsplit Perfectly Matched Layer for the Seismic Wave Equation Using Auxiliary Differential Equations (ADE-PML)

    R. Martin1, D. Komatitsch1,2, S. D. Gedney3, E. Bruthiaux1,4

    CMES-Computer Modeling in Engineering & Sciences, Vol.56, No.1, pp. 17-42, 2010, DOI:10.3970/cmes.2010.056.017

    Abstract Unsplit convolutional perfectly matched layers (CPML) for the velocity and stress formulation of the seismic wave equation are classically computed based on a second-order finite-difference time scheme. However it is often of interest to increase the order of the time-stepping scheme in order to increase the accuracy of the algorithm. This is important for instance in the case of very long simulations. We study how to define and implement a new unsplit non-convolutional PML called the Auxiliary Differential Equation PML (ADE-PML), based on a high-order Runge-Kutta time-stepping scheme and optimized at grazing incidence. We demonstrate that when a second-order time-stepping… More >

  • Open Access


    Size Effects and Mesh Independence in Dynamic Fracture Analysis of Brittle Materials

    Letícia Fleck Fadel Miguel1, Ignacio Iturrioz2, Jorge Daniel Riera3

    CMES-Computer Modeling in Engineering & Sciences, Vol.56, No.1, pp. 1-16, 2010, DOI:10.3970/cmes.2010.056.001

    Abstract Numerical predictions of the failure load of large structures, accounting for size effects, require the adoption of appropriate constitutive relations. These relations depend on the size of the elements and on the correlation lengths of the random fields that describe material properties. The authors proposed earlier expressions for the tensile stress-strain relation of concrete, whose parameters are related to standard properties of the material, such as Young's modulus or specific fracture energy and to size. Simulations conducted for a typical concrete showed that as size increases, the effective stress-strain diagram becomes increasingly linear, with a sudden rupture, while at the… More >

  • Open Access


    Numerical Phenomenology: Virtual Testing of the Hierarchical Structure of a Bundle of Strands

    D.P. Boso1, M. Lefik2

    CMES-Computer Modeling in Engineering & Sciences, Vol.55, No.3, pp. 319-338, 2010, DOI:10.3970/cmes.2010.055.319

    Abstract In this paper we study numerically the mechanical behaviour of wire ropes, particularly the influence of the geometrical configuration on the overall stiffness of the cables. Modelling the behaviour of a cable is a difficult problem, given the complexity of the geometrical layout, contact phenomena occurring among wires and possible yielding of the material. For this reason we pursue a "hierarchical beam approach", to substitute recursively, at each cabling stage, the bundle of wires with an equivalent single strand, having the characteristics computed from the previous level. We consider the first two levels of the bundle hierarchy and investigate the… More >

  • Open Access


    A State Parameter Based Generalized Plasticity Model for Unsaturated Soils

    D. Manzanal1,2, M. Pastor2,3, J.A. Fern,ez Merodo4, P. Mira2,3

    CMES-Computer Modeling in Engineering & Sciences, Vol.55, No.3, pp. 293-318, 2010, DOI:10.3970/cmes.2010.055.293

    Abstract This paper presents an extension of the Generalized Plasticity model proposed by Pastor - Zienkiewicz in 1986. The extension is based on (i) incorporating a state dependant parameter to model the mechanical behaviour of sand under a wide range of relative densities and confining pressures (ii) the definition of the effective stress of Schrefler (1984) modified to obtain unique CSL for different suction and (iii) the work conjugated variable proposed by Houlsby (1997). Several examples are presented for saturated and unsaturated soils. More >

  • Open Access


    A Relocalization Technique for the Multiscale Computation of Delamination in Composite Structures

    O. Allix1, P. Kerfriden1, P. Gosselet1

    CMES-Computer Modeling in Engineering & Sciences, Vol.55, No.3, pp. 271-292, 2010, DOI:10.3970/cmes.2010.055.271

    Abstract We present numerical enhancements of a multiscale domain decomposition strategy based on a LaTIn solver and dedicated to the computation of the debounding in laminated composites. We show that the classical scale separation is irrelevant in the process zones, which results in a drop in the convergence rate of the strategy. We show that performing nonlinear subresolutions in the vicinity of the front of the crack at each prediction stage of the iterative solver permits to restore the effectiveness of the method. More >

  • Open Access


    A 3D Frictionless Contact Domain Method for Large Deformation Problems

    S. Hartmann1, R. Weyler2, J. Oliver1, J.C. Cante2, J.A. Hernández1

    CMES-Computer Modeling in Engineering & Sciences, Vol.55, No.3, pp. 211-270, 2010, DOI:10.3970/cmes.2010.055.211

    Abstract This work describes a three-dimensional contact domain method for large deformation frictionless contact problems. Theoretical basis and numerical aspects of this specific contact method are given in [Oliver, Hartmann, Cante, Weyler and Hernández (2009)] and [Hartmann, Oliver, Weyler, Cante and Hernández (2009)] for two-dimensional, large deformation frictional contact problems. In this method, in contrast to many other contact formulations, the necessary contact constraints are formulated on a so-called contact domain, which can be interpreted as a fictive intermediate region connecting the potential contact surfaces of the deformable bodies. This contact domain has the same dimension as the contacting bodies. It… More >

  • Open Access


    Error Reduction in Gauss-Jacobi-Nyström Quadraturefor Fredholm Integral Equations of the Second Kind

    M. A. Kelmanson1 and M. C. Tenwick1

    CMES-Computer Modeling in Engineering & Sciences, Vol.55, No.2, pp. 191-210, 2010, DOI:10.3970/cmes.2010.055.191

    Abstract A method is presented for improving the accuracy of the widely used Gauss-Legendre Nyström method for determining approximate solutions of Fredholm integral equations of the second kind on finite intervals. The authors' recent continuous-kernel approach is generalised in order to accommodate kernels that are either singular or of limited continuous differentiability at a finite number of points within the interval of integration. This is achieved by developing a Gauss-Jacobi Nyström method that moreover includes a mean-value estimate of the truncation error of the Hermite interpolation on which the quadrature rule is based, making it particularly accurate at low orders. A… More >

  • Open Access


    An Investigation of Metal 3D Spheroidal Resonators Using a Body of Revolution Approach

    A. Vukovic1, P. Sewell1, T. M. Benson1

    CMES-Computer Modeling in Engineering & Sciences, Vol.55, No.2, pp. 171-190, 2010, DOI:10.3970/cmes.2010.055.171

    Abstract A fast and accurate method is developed for the analysis of a class of metal three-dimensional resonators with rotational symmetry. The analysis is formulated using the Body of Revolution approach and the Method of Analytical Regularization. This development is motivated by the need for three-dimensional analytical solvers that could enable fast and accurate analysis of photonic resonant structures which support very high Q whispering gallery modes and which are computationally challenging for numerical simulations. The paper outlines the formulation of the method and demonstrates the stability and the source of computation errors of the method. As a practical illustration, the… More >

  • Open Access


    On Adaptive Definition of the Plane Wave Basis for Wave Boundary Elements in Acoustic Scattering: the 2D Case

    J. Trevelyan1and G. Coates1

    CMES-Computer Modeling in Engineering & Sciences, Vol.55, No.2, pp. 147-170, 2010, DOI:10.3970/cmes.2010.055.147

    Abstract The terminology "wave boundary elements" relates to boundary elements enriched in the Partition of Unity sense by a multiple plane wave basis for the analysis of the propagation of short wavelength waves. This paper presents a variant of this approach in which the plane wave basis is selected adaptively according to an error indicator. The error indicator is residual based, and exhibits useful local and global properties. Model improvement in each adaptive iteration is carried out by the addition of new plane waves with no h-refinement. The convergence properties of the scheme are demonstrated. More >

  • Open Access


    A Scalable Meshless Formulation Based on RBF Hermitian Interpolation for 3D Nonlinear Heat Conduction Problems

    David Stevens1, Henry Power1,2

    CMES-Computer Modeling in Engineering & Sciences, Vol.55, No.2, pp. 111-146, 2010, DOI:10.3970/cmes.2010.055.111

    Abstract Problems involving nonlinear time-dependent heat conduction in materials which have temperature-dependent thermal properties are solved with a novel meshless numerical solution technique using multiquadric radial basis functions (RBFs). Unlike traditional RBF collocation methods, the local Hermitian interpolation (LHI) method examined here can be scaled to arbitrarily large problems without numerical ill-conditioning or computational cost issues, due to the presence of small overlapping interpolation systems which grow in number but not in size as the global dataset grows. The flexibility of the full-domain multiquadric collocation method to directly interpolate arbitrary boundary conditions is maintained, via the local interpolations. The Kirchhoff transformation… More >

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