Finite Rotations in the Nonlinear Theory of Thin Shells

Abstract

The theory of finite rotations in thin shells is developed and many shell relations in terms of finite rotations are presented. Three forms of geometric boundary conditions and energetically compatible static boundary conditions are constructed. Various sets of Eulerian and Lagrangean shell equations are discussed and their consistent simplification within the first-approximation geometrically non-linear theory of isotropic elastic shells is given. A classification of shell problems with small, moderate, large and finite rotations is proposed and appropriate sets of simplified shell equations are presented.