The geometric stiffness of thick shell triangular finite elements for large rotations

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6 Scopus citations


This paper is concerned with the development of the geometric stiffness matrix of thick shell finite elements for geometrically nonlinear analysis of the Newton type. A linear shell element that is comprised of the constant stress triangular membrane element and the triangular discrete Kirchhoff Mindlin theory (DKMT) plate element is 'upgraded' to become a geometrically nonlinear thick shell finite element. Perturbation methods are used to derive the geometric stiffness matrix from the gradient, in global coordinates, of the nodal force vector when stresses are kept fixed. The present approach follows earlier works associated with trusses, space frames and thin shells. It has the advantage of explicitness and clear physical insight. A special procedure, tailored to triangular elements is used to isolate pure rotations to enable stress recovery via linear elastic constitutive relations. Several examples are solved. The results compare well with those available in the literature.

Original languageEnglish
Pages (from-to)1378-1402
Number of pages25
JournalInternational Journal for Numerical Methods in Engineering
Issue number9
StatePublished - 26 Feb 2006


  • Geometric stiffness matrix
  • Mindlin plates
  • Nonlinear analysis
  • Thick shells

ASJC Scopus subject areas

  • Numerical Analysis
  • Engineering (all)
  • Applied Mathematics


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