A higher-order equilibrium finite element method

K. Olesen, B. Gervang, J. N. Reddy, M. Gerritsma

Research output: Contribution to journalArticleScientificpeer-review

3 Citations (Scopus)


In this paper, a mixed spectral element formulation is presented for planar, linear elasticity. The degrees of freedom for the stress are integrated traction components, ie, surface force components. As a result, the tractions between elements are continuous. The formulation is based on minimization of the complementary energy subject to the constraints that the stress field should satisfy equilibrium of forces and moments. The Lagrange multiplier, which enforces equilibrium of forces, is the displacement field and the Lagrange multiplier, which enforces equilibrium of moments, is the rotation. The formulation satisfies equilibrium of forces pointwise if the body forces are piecewise polynomial. Equilibrium of moments is weakly satisfied. Results of the method are given on orthogonal and curvilinear domains, and an example with a point singularity is given.

Original languageEnglish
Pages (from-to)1262-1290
Number of pages29
JournalInternational Journal for Numerical Methods in Engineering
Issue number12
Publication statusPublished - 2018


  • Curvilinear coordinates
  • Interelement continuity of the tractions
  • Mixed finite element formulation
  • Pointwise equilibrium of forces
  • Stress singularity

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