Geodesic
General solutions of weakened equations in terms of stresses in the theory of elasticity
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2012), pp. 26-32
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The general solutions of some weakened systems of equations in terms of stresses in isotropic elasticity are analyzed. These systems which are not equivalent to the classic one, involve (besides the equilibrium equations) only three of six compatibility equations, namely either diagonal or off-diagonal ones. An equivalence of the formulations of quasistatic boundary-value problems in elasticity in terms of stresses based on such systems is discussed. 
@article{VMUMM_2012_6_a4,
     author = {D. V. Georgievskii},
     title = {General solutions of weakened equations in terms of stresses in the theory of elasticity},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {26--32},
     year = {2012},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2012_6_a4/}
}
TY  - JOUR
AU  - D. V. Georgievskii
TI  - General solutions of weakened equations in terms of stresses in the theory of elasticity
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2012
SP  - 26
EP  - 32
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2012_6_a4/
LA  - ru
ID  - VMUMM_2012_6_a4
ER  - 
%0 Journal Article
%A D. V. Georgievskii
%T General solutions of weakened equations in terms of stresses in the theory of elasticity
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2012
%P 26-32
%N 6
%U http://geodesic.mathdoc.fr/item/VMUMM_2012_6_a4/
%G ru
%F VMUMM_2012_6_a4
D. V. Georgievskii. General solutions of weakened equations in terms of stresses in the theory of elasticity. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2012), pp. 26-32. http://geodesic.mathdoc.fr/item/VMUMM_2012_6_a4/

[1] Georgievskii D.V., Pobedrya B.E., “O chisle nezavisimykh uravnenii sovmestnosti v mekhanike deformiruemogo tverdogo tela”, Prikl. matem. i mekhan., 68:6 (2004), 1043–1048 | MR

[2] Pobedrya B.E., Georgievskii D.V., “Equivalence of formulations for problems in elasticity theory in terms of stresses”, Russ. J. Math. Phys., 13:2 (2006), 203–209 | DOI | MR

[3] Pobedrya B.E., Chislennye metody v teorii uprugosti i plastichnosti, Izd-vo MGU, M., 1995 | MR

[4] Markenscoff X., “A note of strain jump conditions and Cesáro integrals for bonded and slipping inclusions”, J. Elasticity, 45:1 (1996), 45–51 | DOI | MR

[5] Volterra V., “Sur l'équilibre des corps elastiques multipliment connexes”, Ann. l'École Norm. Sup., 24 (1907), 401–517 | DOI | MR

[6] Kröner E., Kontinuumstheorie der Versetzungen und Eigenspannungen, Springer, Berlin, 1958 | MR

[7] Cesáro E., “Sulle formole del Volterra, fondamentali nella teoria delle distorsioni elastiche”, Rend. Acad. R. di Napoli, 12:1 (1906), 311–321

[8] Ciarlet P.G., Gratie L., Mardare C., “A generalization of the classical Cesáro–Volterra path integral formula”, C. r. Acad. sci. Paris. Ser. I, 347 (2009), 577–582 | DOI | MR

[9] Filonenko-Borodich M.M., Teoriya uprugosti, Fizmatgiz, M., 1959 | MR

[10] Pobedrya B.E., “Novaya postanovka zadachi mekhaniki deformiruemogo tverdogo tela v napryazheniyakh”, Dokl. AN SSSR, 253:2 (1980), 295–297 | MR

[11] Pobedrya B.E., “O staticheskoi zadache v napryazheniyakh”, Vestn. Mosk. un-ta. Matem. Mekhan., 2003, no. 3, 61–67

[12] Kucher V.A., Markenscoff X., Paukshto M.V., “Some properties of the boundary value problem of linear elasticity in terms of stresses”, J. Elasticity, 74:2 (2004), 135–145 | DOI | MR

[13] Li Shaofan, Gupta A., Markenscoff X., “Conservation laws of linear elasticity in stress formulations”, Proc. Roy. Soc. London. Ser. A. Math. Phys. and Eng. Sci., 461:2053 (2005), 99–116 | DOI | MR

[14] Borodachev N.M., “Resheniya prostranstvennoi zadachi teorii uprugosti v napryazheniyakh”, Prikl. mekhan., 42:8 (2006), 3–35 | MR