Izv. Vyssh. Uchebn. Zaved. Mat., 2025 Number 3,Pages 71–88(Mi ivm10075)
On the existence of solutions to nonlinear boundary value problems for non-flat isotropic shells of Timoshenko type in arbitrary curvilinear coordinates
Abstract:
We study the solvability of a boundary value problem for a system of five nonlinear second-order partial differential equations under given nonlinear boundary conditions, which describes the equilibrium state of elastic non-flat inhomogeneous isotropic shells with loose edges in the framework of the Timoshenko shear model, assigned to arbitrary curvilinear coordinates. The boundary value problem is reduced to a nonlinear operator equation for generalized displacements in Sobolev space, the solvability of which is established using the contraction mapping principle.
Keywords:non-shallow isotropic inhomogeneous shell of Timoshenko type, arbitrary curvilinear coordinate, nonlinear boundary value problem, generalized solution, integral representation, holomorphic function, operator equation, existence theorem.
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