On Using Rotations as Primary Variables in the Nonlinear Theory of Thin Elastic Shells

Abstract

We discuss such a formulation of the non-linear theory of thin shells in which finite rotations are among independent fields of the boundary value problem. We show that in the general case of finite shell strains the surface bending tensor and the internal couple resultant tensor are non-symmetric in general, when defined with respect to the rotated base. Transforming the surface principle of virtual work we derive several strong and weak boundary value problems. In particular, we construct global variational principles of the total potential energy, Hu—Washizu and Simmonds—Danielson type. For a homogeneous, isotropic, rubber-like shell it is shown that the simplest approximation to the strain energy function does not contain the skew-symmetric part of the bending tensor.