Linear buckling analysis of cracked plates by SFEM and XFEM

Pedro M. Baiz, Sundararajan Natarajan, Stéphane P A Bordas, Pierre Kerfriden, Timon Rabczuk

Research output: Contribution to journalArticle

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In this paper, the linear buckling problem for isotropic plates is studied using a quadrilateral element with smoothed curvatures and the extended finite element method. First, the curvature at each point is obtained by a nonlocal approximation via a smoothing function. This element is later coupled with partition of unity enrichment to simplify the simulation of cracks. The proposed formulation suppresses locking and yields elements which behave very well, even in the thin plate limit. The buckling coefficient and mode shapes of square and rectangular plates are computed as functions of crack length, crack location, and plate thickness. The effects of different boundary conditions are also studied.

Original languageEnglish
Pages (from-to)1213-1238
Number of pages26
JournalJournal of Mechanics of Materials and Structures
Issue number9-10
Publication statusPublished - 2011 Dec 1
Externally publishedYes



  • Buckling
  • Extended finite element method (XFEM)
  • Fracture
  • Mindlin
  • Partition of unity methods (PUM)
  • Reissner
  • Shear deformable plate theory

ASJC Scopus subject areas

  • Mechanics of Materials
  • Applied Mathematics

Cite this

Baiz, P. M., Natarajan, S., Bordas, S. P. A., Kerfriden, P., & Rabczuk, T. (2011). Linear buckling analysis of cracked plates by SFEM and XFEM. Journal of Mechanics of Materials and Structures, 6(9-10), 1213-1238.