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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.
Received: 26.01.2023 Revised: 26.01.2023 Accepted: 29.03.2023
Citation:
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, no. 1, 50–68
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https://www.mathnet.ru/eng/ivm9949 https://www.mathnet.ru/eng/ivm/y2024/i1/p50
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Abstract page: | 66 | Full-text PDF : | 1 | References: | 22 | First page: | 17 |
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