Variation-based cracked laminate analysis revisited and fundamentally extended

Shuguang Li*, Farrukh Hafeez

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

36 Citations (Scopus)


The analyses of cracked laminates based on a variational principle and related approaches are appraised in this paper. The limitations of the existing methodology on the analyses of more general laminate configurations have been identified. It has been revealed that the limiting factor is the lack of boundary conditions for uncracked laminae. Natural boundary conditions have then been derived from the variational principle to meet the need. Such boundary conditions are mathematically sound but cannot be simply interpreted from the physical construction of the problem intuitively. A well posed boundary value problem has thus been formulated for laminates containing however many cracked and uncracked laminae. Appropriate mathematical tools can then be employed to solve the boundary value problem. The capability of analysing cracked laminates has been enhanced significantly, as a result.

Original languageEnglish
Pages (from-to)3505-3515
Number of pages11
JournalInternational Journal of Solids and Structures
Issue number20
Early online date17 Apr 2009
Publication statusPublished - 1 Oct 2009


  • Cracked laminate analysis
  • Natural boundary conditions
  • Periodic conditions
  • Total complementary potential energy
  • Translational symmetry
  • Variational approach

ASJC Scopus subject areas

  • Mechanical Engineering
  • Mechanics of Materials
  • Materials Science(all)
  • Condensed Matter Physics
  • Applied Mathematics
  • Modelling and Simulation


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