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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{SJIM_2017_20_4_a3,
     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/}
}
TY  - JOUR
AU  - V. M. Gordienko
TI  - Invariant operators and separation of residual stresses
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2017
SP  - 29
EP  - 34
VL  - 20
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2017_20_4_a3/
LA  - ru
ID  - SJIM_2017_20_4_a3
ER  - 
%0 Journal Article
%A V. M. Gordienko
%T Invariant operators and separation of residual stresses
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2017
%P 29-34
%V 20
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2017_20_4_a3/
%G ru
%F SJIM_2017_20_4_a3
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/

[1] Sedov L. I., Mekhanika sploshnoi sredy, v. 1, Nauka, M., 1973 | MR

[2] Krutkov Yu. A., Tenzor funktsii napryazhenii i obschie resheniya v statike teorii uprugosti, Izd-vo AN SSSR, M.–L., 1949

[3] Godunov S. K., Mikhailova T. Yu., Predstavleniya gruppy vraschenii i sfericheskie funktsii, Nauch. kniga, Novosibirsk, 1998 | MR

[4] Bondar V. D., Osnovy teorii uprugosti, izd. NGU, Novosibirsk, 2004

[5] Leibenzon L. M., Kurs teorii uprugosti, Gostekhizdat, M.–L., 1947 | MR

[6] Godunov S. K., Romenskii E. I., Elementy mekhaniki sploshnykh sred i zakony sokhraneniya, Nauch. kniga, Novosibirsk, 1998

[7] Borisenko A. I., Tarapov I. E., Vektornyi analiz i nachala tenzornogo ischisleniya, Vischa shkola, Kharkov, 1978 | MR

[8] Birger I. A., Ostatochnye napryazheniya, Gostekhizdat, M., 1963