The derivation of dual extremum and complementary stationary principles in geometrical non-linear shell theory

Abstract

In non-linear elasticity dual extremum principles can be formulated for some class of elastic deformations, for which uniqueness of the solution is assured. These results are used in the present paper to derive extremal variational principles for geometrical non-linear shells with moderate rotations. Furthermore two complementary variational principles are considered, which are stationary principles without any extremum property. The proposed theorems are valid also for the special cases of linear plates and shells, for the non-linear von Karman plate theory and for non-linear Donnell-Marguerre type shells.