This article is cited in 8 papers

On existence of solutions of nonlinear equilibrium problems on shallow inhomogeneous anisotropic shells of the Timoshenko type

S. N. Timergaliev

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

Abstract: We prove the existence of solutions to geometrically nonlinear boundary value problem for an elastic inhomogeneous anisotropic shallow shells with rigidly clamped edges under shear model S.P. Timoshenko. The boundary value problem is reduced to one nonlinear operator equation, the solvability of which is established using the principle of compressed maps. The investigation method is based on integral representations for generalized displacements containing arbitrary holomorphic functions determined by boundary conditions involving the theory of Cauchy type integrals with real densities.

Keywords: Timoshenko type shell, equilibrium equations system, boundary problem, generalized shifts, generalized problem solution, integral images, singular integral equation, existence theorem.

UDC: 517.958:539.3

Received: 19.06.2018
Revised: 19.06.2018
Accepted: 27.03.2019

DOI: 10.26907/0021-3446-2019-8-45-61

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2019, 63:8, 38–53

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