On finite element formulations for nearly incompressible linear elasticity

K. B. Nakshatrala, A. Masud, K. D. Hjelmstad

Research output: Contribution to journalArticlepeer-review

50 Scopus citations


In this paper we present a mixed stabilized finite element formulation that does not lock and also does not exhibit unphysical oscillations near the incompressible limit. The new mixed formulation is based on a multiscale variational principle and is presented in two different forms. In the first form the displacement field is decomposed into two scales, coarse-scale and fine-scale, and the fine-scale variables are eliminated at the element level by the static condensation technique. The second form is obtained by simplifying the first form, and eliminating the fine-scale variables analytically yet retaining their effect that results with additional (stabilization) terms. We also derive, in a consistent manner, an expression for the stabilization parameter. This derivation also proves the equivalence between the classical mixed formulation with bubbles and the Galerkin least-squares type formulations for the equations of linear elasticity. We also compare the performance of this new mixed stabilized formulation with other popular finite element formulations by performing numerical simulations on three well known test problems.

Original languageEnglish (US)
Pages (from-to)547-561
Number of pages15
JournalComputational Mechanics
Issue number4
StatePublished - Mar 2008
Externally publishedYes


  • Mixed methods
  • Multiscale formulation
  • Stabilized finite elements

ASJC Scopus subject areas

  • Computational Mechanics
  • Ocean Engineering
  • Mechanical Engineering
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics


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