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  • Open Access

    ARTICLE

    Hypersingular BEM for Piezoelectric Solids: Formulation and Applications for Fracture Mechanics

    J.A. Sanz, M. Solis, J. Dominguez1

    CMES-Computer Modeling in Engineering & Sciences, Vol.17, No.3, pp. 215-230, 2007, DOI:10.3970/cmes.2007.017.215

    Abstract A general mixed boundary element formulation for three-dimensional piezoelectric fracture mechanics problems is presented in this paper. The numerical procedure is based on the extended displacement and traction integral equations for external and crack boundaries, respectively. Integrals with strongly singular and hypersingular kernels appearing in the formulation are analytically transformed into weakly singular and regular integrals. Quadratic boundary elements and quarter-point boundary elements are implemented in a direct way in a computer code. Electric and stress intensity factors are directly computed from nodal values at quarter-point elements. Crack problems in 3D piezoelectric bounded and unbounded solids are solved. The obtained… More >

  • Open Access

    ARTICLE

    Contact Problem for the Flat Elliptical Crack under Normally Incident Shear Wave

    A.N. Guz1, O.V. Menshykov1,2, V.V. Zozulya3, I.A. Guz2

    CMES-Computer Modeling in Engineering & Sciences, Vol.17, No.3, pp. 205-214, 2007, DOI:10.3970/cmes.2007.017.205

    Abstract The contact interaction of opposite faces of an elliptical crack is studied for the case of a normal time-harmonic shear wave loading. The distribution of stress intensity factors (shear modes II and III) as functions of the wave number and the friction coefficient is investigated. The results are compared with those obtained for an elliptical crack without allowance for the contact interaction. More >

  • Open Access

    ARTICLE

    Symmetric Variational Formulation of BIE for Domain Decomposition Problems in Elasticity -- An SGBEM Approach for Nonconforming Discretizations of Curved Interfaces

    R. Vodička1, V. Mantič2, F. París2

    CMES-Computer Modeling in Engineering & Sciences, Vol.17, No.3, pp. 173-204, 2007, DOI:10.3970/cmes.2007.017.173

    Abstract An original approach to solve domain decomposition problems by the symmetric Galerkin boundary element method is developed. The approach, based on a new variational principle for such problems, yields a fully symmetric system of equations. A natural property of the proposed approach is its capability to deal with nonconforming discretizations along straight and curved interfaces, allowing in this way an independent meshing of non-overlapping subdomains to be performed. Weak coupling conditions of equilibrium and compatibility at an interface are obtained from the critical point conditions of the energy functional. Equilibrium is imposed through local traction (Neumann) boundary conditions prescribed on… More >

  • Open Access

    ARTICLE

    Spectral Element Approach for Inverse Models of 3D Layered Pavement

    Chun-Ying. Wu1, R. Al-Khoury2, C. Kasbergen2, Xue-Yan. Liu2, A. Scarpas2

    CMES-Computer Modeling in Engineering & Sciences, Vol.17, No.3, pp. 163-172, 2007, DOI:10.3970/cmes.2007.017.163

    Abstract 3D spectral element method in the article is presented to predict the pavement layer modules using field measurement of Falling Weight Deflectometer (FWD). To improve the computational efficiency of the layer-condition assessment, one type of spectral element is proposed to develop the dynamic analysis of 3D multi-layered system subjected to an impulsive load. Each layer in structure is simulated as two-noded layer spectral element or one-noded spectral element in frequency domain. In order to identify the parameters of layered structures, a nonlinear optimization method called Powell hybrid algorithm is employed. The optimization procedure is performed in frequency domain and aims… More >

  • Open Access

    ARTICLE

    A General Partial Discretization Methodology for Interlaminar Stress Computation in Composite Laminates

    Tarun Kant1, Sandeep S. Pendhari2, Yogesh M. Desai3

    CMES-Computer Modeling in Engineering & Sciences, Vol.17, No.2, pp. 135-162, 2007, DOI:10.3970/cmes.2007.017.135

    Abstract A two-point boundary value problem (BVP) is formed in the present work governed by a set of first-order coupled ordinary differential equations (ODEs) in terms of displacements and the transverse stresses through the thickness of laminate (in domain -h/2 < z < h/2) by introducing partial discretization methodology only in the plan area of the three dimensional (3D) laminate. The primary dependent variables in the ODEs are those which occur naturally on a plane z=a constant. An effective numerical integration (NI) technique is utilized for tackling the two-point BVP in an efficient manner. Numerical studies on cross-ply and angle-ply composite… More >

  • Open Access

    ARTICLE

    A New Quasi-Unsymmetric Sparse Linear Systems Solver for Meshless Local Petrov-Galerkin Method (MLPG)

    Weiran Yuan1, Pu Chen1,2, Kaishin Liu1,3

    CMES-Computer Modeling in Engineering & Sciences, Vol.17, No.2, pp. 115-134, 2007, DOI:10.3970/cmes.2007.017.115

    Abstract In this paper we propose a direct solution method for the quasi-unsymmetric sparse matrix (QUSM) arising in the Meshless Local Petrov-Galerkin method (MLPG). QUSM, which is conventionally treated as a general unsymmetric matrix, is unsymmetric in its numerical values, but nearly symmetric in its nonzero distribution of upper and lower triangular portions. MLPG employs trial and test functions in different functional spaces in the local domain weak form of governing equations. Consequently the stiffness matrix of the resultant linear system is a QUSM. The new solver for QUSM conducts a two-level unrolling technique for LDU factorization method and can be… More >

  • Open Access

    ARTICLE

    Fictitious Domain Approach for Spectral/hp Element Method

    L. Parussini 1

    CMES-Computer Modeling in Engineering & Sciences, Vol.17, No.2, pp. 95-114, 2007, DOI:10.3970/cmes.2007.017.095

    Abstract We propose a fictitious domain method combined with spectral/hp elements for the solution of second-order differential problems. This paper presents the formulation, validation and application of fictitiuos domain-spectral/hp element algorithm to one- and two-dimensional Poisson problems. Fictitious domain methods allow problems formulated on an intricate domain Ω to be solved on a simpler domain Π containing Ω. The Poisson equation, extended to the new domain Π, is expressed as an equivalent set of first-order equations by introducing the gradient as an additional indipendent variable, and spectral/hp element method is used to develop the discrete model. Convergence of relative energy norm… More >

  • Open Access

    ARTICLE

    Five Different Formulations of the Finite Strain Perfectly Plastic Equations

    Chein-Shan Liu 1,2

    CMES-Computer Modeling in Engineering & Sciences, Vol.17, No.2, pp. 73-94, 2007, DOI:10.3970/cmes.2007.017.073

    Abstract The primary objectives of the present exposition focus on five different types of representations of the plastic equations obtained from an elastic-perfectly plastic model by employing different corotational stress rates. They are (a) an affine nonlinear system with a finite-dimensional Lie algebra, (b) a canonical linear system in the Minkowski space, (c) a non-canonical linear system in the Minkowski space, (d) the Lie-Poisson bracket formulation, and (e) a two-generator and two-bracket formulation. For the affine nonlinear system we prove that the Lie algebra of the vector fields is so(5,1), which has dimensions fifteen, and by the Lie theory the superposition… More >

  • Open Access

    ARTICLE

    Application of Meshfree Method to Elastic-Plastic Fracture Mechanics Parameter Analysis

    S. Hagihara1, M. Tsunori2, T. Ikeda3, N. Miyazaki3

    CMES-Computer Modeling in Engineering & Sciences, Vol.17, No.2, pp. 63-72, 2007, DOI:10.3970/cmes.2007.017.063

    Abstract The element-free Galerkin (EFG) method is applied to the calculation of elastic-plastic fracture mechanics parameters such as the J-integral and T*-integral. The fields of displacement, strain and stress for a crack problem are obtained using the elastic-plastic EFG method. Then the elastic-plastic fracture mechanics parameters J-integral and T*-integral are calculated from path and domain integrals. In the finite element analysis, paths for the path integral and domains for the domain integral are selected depending on finite element mesh division. On the other hand, they can be arbitrarily selected in the EFG method, and we can use a simple integral path… More >

  • Open Access

    ARTICLE

    General Corotational Rate Tensor and Replacement of Material-time Derivative to Corotational Derivative of Yield Function

    K. Hashiguchi1

    CMES-Computer Modeling in Engineering & Sciences, Vol.17, No.1, pp. 55-62, 2007, DOI:10.3970/cmes.2007.017.055

    Abstract Constitutive equation describing the mechanical properties of material has to be formulated in an identical form independent of coordinate systems by which it is described even if there exist any mutual configuration and/or mutual rotation between the material and coordinate systems. This mechanical requirement is attained by describing rate variables as corotational rate tensors with objectivity in constitutive equations in rate form. Besides, in order to use the material-time derivative of yield condition as a consistency condition it has to be replaced to the corotational derivative. In this note a general corotational rate for tensors in arbitrary order having the… More >

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