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Invariant operators and separation of residual stresses

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Abstract

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.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia

    V. M. Gordienko

  2. Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia

    V. M. Gordienko

Authors
  1. V. M. Gordienko
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Correspondence to V. M. Gordienko.

Additional information

Original Russian Text © V.M. Gordienko, 2017, published in Sibirskii Zhurnal Industrial’noi Matematiki, 2017, Vol. XX, No. 4, pp. 29–34.

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Gordienko, V.M. Invariant operators and separation of residual stresses. J. Appl. Ind. Math. 11, 521–526 (2017). https://doi.org/10.1134/S1990478917040093

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  • DOI: https://doi.org/10.1134/S1990478917040093

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