T. Nishioka¹, Y. Kobayashi¹, T. Fujimoto¹

CMES-Computer Modeling in Engineering & Sciences, Vol.17, No.3, pp. 231-238, 2007, DOI:10.3970/cmes.2007.017.231

Abstract First, for growing cracks in elastic-plastic materials, an incremental variational principle is developed to satisfy the boundary conditions near newly created crack surfaces. Then using this variational principle, a moving finite element method is formulated and developed, based on the Delaunay automatic triangulation. Furthermore, theoretical backgrounds on numerical prediction for fracture path of curving crack using T* integral are explained. Using the automatic moving finite element method, fracture-path prediction simulations are successfully carried out. More >

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 More >

A.N. Guz¹, O.V. Menshykov^1,2, 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 >

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… More >

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 More >

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 More >

Weiran Yuan¹, Pu Chen^1,2, Kaishin Liu^1,3

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 More >

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. More >

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… More >

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… More >