Geodesic
Solvability of geometrically nonlinear boundary-value problems for shallow shells of Timoshenko type with pivotally supported edges
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2015), pp. 49-61

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We study the solvability of a geometrically nonlinear, physically linear boundary-value problems for elastic shallow homogeneous isotropic shells with pivotally supported edges in the framework of S. P. Timoshenko's shear model. The purpose of work is the proof of the theorem on existence of solutions. Research method consists in reducing the original system of equilibrium equations to one nonlinear differential equation for the deflection. The method is based on integral representations for displacements, which are built with the help of the general solutions of the nonhomogeneous Cauchy–Riemann equation. The solvability of equation relative to deflection is established with the use of principle of contraction mappings.
Mots-clés : Timoshenko type shell, Sobolev spaces
Keywords: equilibrium equations system, boundary-value problem, generalized shifts, generalized problem solution, integral images, operator, integral equations, holomorphic functions existence theorem. 
@article{IVM_2015_5_a5,
     author = {S. N. Timergaliev and A. N. Uglov and L. S. Kharasova},
     title = {Solvability of geometrically nonlinear boundary-value problems for shallow shells of {Timoshenko} type with pivotally supported edges},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {49--61},
     publisher = {mathdoc},
     number = {5},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2015_5_a5/}
}
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S. N. Timergaliev; A. N. Uglov; L. S. Kharasova. Solvability of geometrically nonlinear boundary-value problems for shallow shells of Timoshenko type with pivotally supported edges. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2015), pp. 49-61. http://geodesic.mathdoc.fr/item/IVM_2015_5_a5/