Accurate stress extraction for nearly incompressible materials by the displacement formulation of the P-version FEM

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Abstract

Direct methods for computing the pointwise stresses for nearly incompressible elastic materials fail to provide meaningful results when applied to the displacement formulation of the finite element method (FEM). A new extraction method for accurate computation of pointwise stresses for nearly incompressible elastic materials is presented. It is based on the complementary energy principle applied over a local domain in the postprocessing phase in conjunction with the p-version finite element solution. It is shown that accurate pointwise stresses are obtained, that the relative error in the pointwise stresses converges at a rate which is as fast as the relative error measured in the energy norm or faster, and importantly, the extracted stresses are virtually independent of Poisson's ratio. Numerical results for two problems, one having a smooth solution and the other containing a singular point, are provided.

Original languageEnglish
Pages (from-to)807-826
Number of pages20
JournalCommunications in Numerical Methods in Engineering
Volume12
Issue number12
DOIs
StatePublished - Dec 1996
Externally publishedYes

Keywords

  • Complementary energy
  • Elasticity
  • Finite element method
  • Incompressible materials
  • P-version
  • Stress extraction

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