This article is cited in 17 papers

A method of integral equations in nonlinear boundary-value problems for flat shells of the Timoshenko type with free edges

S. N. Timergaliev

Kazan State Achitecture and Civil Engineering University, 1 Zelyonaya str., Kazan, 420043 Russia

Abstract: We prove the existence theorem for solutions of geometrically nonlinear boundary-value problems for elastic shallow isotropic homogeneous shells with free edges under shear model of S. P. Timoshenko. Research method consists in the reduction of the original system of equilibrium equations to a single nonlinear equation for the components of transverse shear deformations. The basis of this method are integral representations for the generalized displacements, containing an arbitrary holomorphic functions, which are determined by the boundary conditions involving the theory of one-dimensional singular integral equations.

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

UDC: 517.958:539.3

Received: 17.09.2015

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2017, 61:4, 49–64

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