On the Existence of Solutions of Nonlinear Boundary Value Problems for Nonshallow Timoshenko-Type Shells with Free Edges

Abstract: We study the existence of solutions of a boundary value problem for a system of nonlinearsecond-order partial differential equations for the generalized displacements under given nonlinearboundary conditions that describes the equilibrium state of elastic nonshallow isotropicinhomogeneous shells of zero Gaussian curvature with free edges in the framework of theTimoshenko shear model. The research method is based on integral representations for generalizeddisplacements containing arbitrary functions that allow the original boundary value problem to bereduced to a nonlinear operator equation for generalized displacements in the Sobolev space. Thesolvability of the operator equation is established using the contraction mapping principle. © Pleiades Publishing, Ltd. 2023.