This article is cited in 15 papers

On existence of solutions to geometrically nonlinear problems for shallow shells of the Timoshenko type with free edges

S. N. Timergaliev

Chair of Mathematics, Naberezhnye Chelny Institute (Branch), Kazan (Volga Region) Federal University, 68/19 Mira Ave., Naberezhnye Chelny, 423810 Russia

Abstract: We study the geometrically nonlinear physically linear boundary-value problems solvability for shallow isotropic elastic shells within the framework of S. P. Timoshenko shift model. The method of study consists in reducing of the equilibrium equations reference system to one nonlinear differential equation relative to deflection. In this case the significant role is played by integral representations for the tangential shifts and the angle of rotations, which are reduced with the attraction of the general solutions of the inhomogeneous Cauchy–Riemann equation. The solvability of equation relative to deflection is established with the use of of principle of contraction mappings.

Keywords: Timoshenko type shell, equilibrium equations system, boundary problem, generalized shifts, generalized problem solution, integral images, Sobolev spaces, operator, integral equations, holomorphic functions, existence theorem.

UDC: 517.958+539.3

Received: 30.09.2012

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2014, 58:3, 31–46

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