On the variational formulation of the extended thick anisotropic shells theory of I. N. Vekua type

摘要

A new variant of the I. N. Vekua-A. A. Amosov extended theory of thick anisotropic shells is constructed on the groundwork of the Lagrange variational formalism of analytical mechanics of continua and the dimensional reduction approach. The shell model consists in the set of field variables, the surface Lagrangian density, and the constraint equations defined on the two-dimensional manifold corresponding to the base surface. The supplementary constraints are derived from the boundary conditions on shell's faces. The field variables of the first kind are biorthogonal expansion's coefficients for the displacement vector. This constrained variational problem is solving by the Lagrange multipliers method that results the two-dimensional initial-boundary value problem of the general shell theory.