Solvability of Boundary Value Problems of the Dynamics of Nonlinear Viscoelastic Shells

摘要

The general initial-boundary value problem of the nonlinear theory of viscoelastic shells of the Koiter type is considered in curvilinear coordinates. A generalized solution to the problem is defined on the basis of mechanical variational principles. Two theorems on the existence of generalized solutions in energy spaces are established. The results on existence are obtained by the application of the Faedo-Galerkin method.