On the existence of solutions of nonlinear boundary value problems for nonshallow Timoshenko-type shells with free edges

We study the existence of solutions of a boundary value problem for a system of nonlinear second-order partial differential equations for the generalized displacements under given nonlinear boundary conditions that describes the equilibrium state of elastic nonshallow isotropic inhomogeneous shells of zero Gaussian curvature with free edges in the framework of the Timoshenko shear model. The research method is based on integral representations for generalized displacements containing arbitrary functions that allow the original boundary value problem to be reduced to a nonlinear operator equation for generalized displacements in the Sobolev space. The solvability of the operator equation is established using the contraction mapping principle.