Determination of stress intensity factors by the finite element discretized symplectic method

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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  • A. Y T Leung
  • Zhenhuan Zhou
  • Xinsheng Xu


Original languageEnglish
Pages (from-to)1115-1122
Journal / PublicationInternational Journal of Solids and Structures
Issue number5
Online published16 Dec 2013
Publication statusPublished - 1 Mar 2014


When rewriting the governing equations in Hamiltonian form, analytical solutions in the form of symplectic series can be obtained by the method of separation of variable satisfying the crack face conditions. In theory, there exists sufficient number of coefficients of the symplectic series to satisfy any outer boundary conditions. In practice, the matrix relating the coefficients to the outer boundary conditions is ill-conditioned unless the boundary is very simple, e.g.; circular. In this paper, a new two-level finite element method using the symplectic series as global functions while using the conventional finite element shape functions as local functions is developed. With the available classical finite elements and symplectic series, the main unknowns are no longer the nodal displacements but are the coefficients of the symplectic series. Since the first few coefficients are the stress intensity factors, post-processing is not required. A number of numerical examples as well as convergence studies are given. © 2013 Elsevier Ltd. All rights reserved.

Research Area(s)

  • Finite element discretized symplectic method, Method of separation of variables, Stress intensity factor