Invariant operators and separation of residual stresses

V. M. Gordienko<sup>ab

a</sup> Sobolev Institute of Mathematics SB RAS, 4 Koptyug av., 630090 Novosibirsk
^b Novosibirsk State University, 2 Pirogova str., 630090 Novosibirsk

Abstract: We consider the equations of linear elasticity in stresses for the three-dimensional 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 representable through the displacements. The construction of this decomposition is reduced to solving a series of Poisson equations.

Keywords: elasticity theory, strain tensor, stress tensor, deviator, residual stresses, Saint-Venant compatibility conditions.

UDC: 539.3

Received: 31.10.2016

DOI: 10.17377/sibjim.2017.20.404

 English version: Journal of Applied and Industrial Mathematics, 2017, 11:4, 521–526

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