RUS  ENG
Full version
JOURNALS // Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika // Archive

Izv. Vyssh. Uchebn. Zaved. Mat., 2015 Number 5, Pages 49–61 (Mi ivm8999)

This article is cited in 7 papers

Solvability of geometrically nonlinear boundary-value problems for shallow shells of Timoshenko type with pivotally supported edges

S. N. Timergaliev, A. N. Uglov, L. S. Kharasova

Chair of Mathematics, Naberezhnye Chelny Branch of Kazan Federal University, 68/19 Mira Ave., Naberezhnye Chelny, 423810 Russia

Abstract: 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.

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

UDC: 517.958+539.3

Received: 28.11.2013


 English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2015, 59:5, 41–51

Bibliographic databases:


© Steklov Math. Inst. of RAS, 2024