Geodesic
On existence of solutions of nonlinear equilibrium problems on shallow inhomogeneous anisotropic shells of the Timoshenko type
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2019), pp. 45-61

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

We prove the existence of solutions to geometrically nonlinear boundary value problem for an elastic inhomogeneous anisotropic shallow shells with rigidly clamped edges under shear model S.P. Timoshenko. The boundary value problem is reduced to one nonlinear operator equation, the solvability of which is established using the principle of compressed maps. The investigation method is based on integral representations for generalized displacements containing arbitrary holomorphic functions determined by boundary conditions involving the theory of Cauchy type integrals with real densities.
Mots-clés : Timoshenko type shell
Keywords: equilibrium equations system, boundary problem, generalized shifts, generalized problem solution, integral images, singular integral equation, existence theorem. 
@article{IVM_2019_8_a4,
     author = {S. N. Timergaliev},
     title = {On existence of solutions of nonlinear equilibrium problems on shallow inhomogeneous anisotropic shells of the {Timoshenko} type},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {45--61},
     publisher = {mathdoc},
     number = {8},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2019_8_a4/}
}
TY  - JOUR
AU  - S. N. Timergaliev
TI  - On existence of solutions of nonlinear equilibrium problems on shallow inhomogeneous anisotropic shells of the Timoshenko type
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2019
SP  - 45
EP  - 61
IS  - 8
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2019_8_a4/
LA  - ru
ID  - IVM_2019_8_a4
ER  - 
%0 Journal Article
%A S. N. Timergaliev
%T On existence of solutions of nonlinear equilibrium problems on shallow inhomogeneous anisotropic shells of the Timoshenko type
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2019
%P 45-61
%N 8
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2019_8_a4/
%G ru
%F IVM_2019_8_a4
S. N. Timergaliev. On existence of solutions of nonlinear equilibrium problems on shallow inhomogeneous anisotropic shells of the Timoshenko type. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2019), pp. 45-61. http://geodesic.mathdoc.fr/item/IVM_2019_8_a4/