Solvability of Nonlinear Equilibrium Problems for Elastic Thin Shells of Timoshenko-type

The solvability of a boundary value problem is studied for a system of five nonlinear second-order partial differential equations with nonlinear boundary conditions, describing the equilibrium state of elastic steep inhomogeneous anisotropic shells with free edges, within the framework of the Timoshenko shear model, expressed in arbitrary curvilinear coordinates. The method of analysis is based on reducing the original nonlinear boundary value problem to a nonlinear operator equation with respect to the generalized displacements in a Sobolev space, the solvability of which is established using the contraction mapping principle.