Solvability of Nonlinear Equilibrium Problems for Timoshenko-type Shallow Shells in Curvilinear Coordinates

We prove the existence of solutions to the boundary value problem of equilibrium of elastic shallow inhomogeneous isotropic shells with free edges in the framework of Timoshenko beam model. The research is conducted in arbitrary curvilinear coordinates. The boundary value problem is reduced to a nonlinear operator equation with respect to generalized displacements in a Sobolev space. The solvability of the operator equation is established with the help of the contraction mapping principle.