Invariant operators and separation of residual stresses

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We consider the equations of linear theory of elasticity in stresses for the threedimensional space. Solutions are decomposed into sums of stationary solutions not satisfying the compatibility condition (residual stresses) and nonstationary solutions satisfying the compatibility condition and hence represented through the displacements. The construction of this decomposition is reduced to solving a series of Poisson equations.

Original languageEnglish
Pages (from-to)521-526
Number of pages6
JournalJournal of Applied and Industrial Mathematics
Issue number4
Publication statusPublished - 1 Oct 2017


  • deviator
  • elasticity theory
  • residual stresses
  • Saint-Venant compatibility conditions
  • strain tensor
  • stress tensor

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