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

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. [ABSTRACT FROM AUTHOR]

We study solvability of a geometrically nonlinear, physically linear boundary-value problems for elastic shallow homogeneous isotropic shells with pivotally supported edges in the framework of S. P. Timoshenko's shear model. The purpose of work is the proof of the theorem on existence of solutions. Research method consists in reducing the original system of equilibrium equations to one nonlinear differential equation for the deflection. The method is based on integral representations for displacements, which are built with the help of the general solutions of the nonhomogeneous Cauchy-Riemann equation. The solvability of equation relative to deflection is established with the use of principle of contraction mappings. [ABSTRACT FROM AUTHOR]