Geodesic
Invariant operators and separation of residual stresses
Sibirskij žurnal industrialʹnoj matematiki, Tome 20 (2017) no. 4, pp. 29-34

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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. 
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     author = {V. M. Gordienko},
     title = {Invariant operators and separation of residual stresses},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {29--34},
     publisher = {mathdoc},
     volume = {20},
     number = {4},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2017_20_4_a3/}
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V. M. Gordienko. Invariant operators and separation of residual stresses. Sibirskij žurnal industrialʹnoj matematiki, Tome 20 (2017) no. 4, pp. 29-34. http://geodesic.mathdoc.fr/item/SJIM_2017_20_4_a3/