On the Existence of Solutions of Nonlinear Boundary Value Problems for Inhomogeneous Isotropic Shallow Shells of the Timoshenko Type with Free Edges

Abstract

Abstract: The paper deals with the study of solvability to geometrically nonlinear boundary value problem for elastic inhomogeneous isotropic shallow shells with free edges within S. P. Timoshenko shear model. The problem is reduced to one nonlinear equation relative to deflection of shell in Sobolev space. Solvability of equation is proved with the use of contracting mappings principle.