Geodesic
Solution of the Beltrami equations for the infinite hollow cylinder under the axisymmetric deformation
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 11 (2018) no. 1, pp. 10-17.

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

In this paper, axisymmetric stresses of an infinitely long hollow circular cylinder are found from the strain compatibility equations that are reduced to a system of Bessel-type ordinary differential equations by the Fourier transform. The constants of integration of the expressions for the Fourier transforms of stresses are determined by the Fourier-transformed equilibrium equations and boundary conditions. Numerical results are given for the particular case of cylinder's load.
Keywords: infinitely long cylinder, axisymmetric deformation, Beltrami strain compatibility equations, equilibrium equations
Mots-clés : Fourier transform. 
@article{JSFU_2018_11_1_a1,
     author = {Petr I. Anferov and Christina Yu. Aturgasheva},
     title = {Solution of the {Beltrami} equations for the infinite hollow cylinder under the axisymmetric deformation},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {10--17},
     publisher = {mathdoc},
     volume = {11},
     number = {1},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2018_11_1_a1/}
}
TY  - JOUR
AU  - Petr I. Anferov
AU  - Christina Yu. Aturgasheva
TI  - Solution of the Beltrami equations for the infinite hollow cylinder under the axisymmetric deformation
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2018
SP  - 10
EP  - 17
VL  - 11
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2018_11_1_a1/
LA  - en
ID  - JSFU_2018_11_1_a1
ER  - 
%0 Journal Article
%A Petr I. Anferov
%A Christina Yu. Aturgasheva
%T Solution of the Beltrami equations for the infinite hollow cylinder under the axisymmetric deformation
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2018
%P 10-17
%V 11
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2018_11_1_a1/
%G en
%F JSFU_2018_11_1_a1
Petr I. Anferov; Christina Yu. Aturgasheva. Solution of the Beltrami equations for the infinite hollow cylinder under the axisymmetric deformation. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 11 (2018) no. 1, pp. 10-17. http://geodesic.mathdoc.fr/item/JSFU_2018_11_1_a1/

[1] M.A. Koltunov, Y.N. Vasilyev, V.A. Chernyh, Elasticity and strength of cylindrical bodies, Vysshaya Shkola, M., 1975 (in Russian)

[2] A.E. Love, Mathematical theory of elasticity, Cambridge Univ., Cambridge, 1927

[3] A.E. Love, A Treatise on the Mathematical Theory of Elasticity, Cambridge Univ., Cambridge, 1924 | MR

[4] S. Masao, O. Juhachi, “Problems on the finite hollow cylinders under the axially symmetrical deformations”, Bulletin of JSME, 11:48 (1968), 1000–1014 | DOI

[5] Y.N. Rabotnov, Mechanics of a deformed solid, Nauka, M., 1979 (in Russian)

[6] G. Lame, Lecons surla theorie de l'elastite, Gauthier-Villars, Paris, 1852

[7] S.P. Timoshenko, J.N. Goodier, Theory of Elasticity, Mc Graw-Hill, N.Y., 1970 | MR