S. N. Timergaliev, “On the problem of solvability of nonlinear boundary value problems for shallow isotropic shells of Timoshenko type in isometric coordinates”, Izv. Vyssh. Uchebn. Zaved. Mat., 2024, Number 1,Pages <nobr>50

This article is cited in 3 papers

On the problem of solvability of nonlinear boundary value problems for shallow isotropic shells of Timoshenko type in isometric coordinates

S. N. Timergaliev

Kazan State University of Architecture and Engineering, 1 Zelenaya str., Kazan, 420043 Russia

Abstract: The solvability of a boundary value problem for a system, which describes the equilibrium state of elastic shallow inhomogeneous isotropic shells with loose edges referred to isometric coordinates in the Timoshenko shear model and consists of five non-linear second-order partial differential equations under given non-linear boundary conditions, is studied. The boundary value problem is reduced to a nonlinear operator equation for generalized displacements in Sobolev space, the solvability of this equation is established with the help of the contraction mapping principle.

Keywords: shallow isotropic inhomogeneous shell of Timoshenko type, isometric coordinates, nonlinear boundary value problem, generalized solution, integral representation, holomorphic function, operator equation, existence theorem.

UDC: 517.958:539.3

Received: 26.01.2023
Revised: 26.01.2023
Accepted: 29.03.2023

DOI: 10.26907/0021-3446-2024-1-50-68