Vol.17, No.2, 2007-Table of Contents
  • Application of Meshfree Method to Elastic-Plastic Fracture Mechanics Parameter Analysis
  • 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
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  • Five Different Formulations of the Finite Strain Perfectly Plastic Equations
  • 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
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  • Fictitious Domain Approach for Spectral/hp Element Method
  • 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
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  • A New Quasi-Unsymmetric Sparse Linear Systems Solver for Meshless Local Petrov-Galerkin Method (MLPG)
  • 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
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  • A General Partial Discretization Methodology for Interlaminar Stress Computation in Composite Laminates
  • 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
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