A DRILL ROTATION FORMULATION FOR GEOMETRICALLY EXACT SHELLS

This paper considers the formulation of classical nonlinear shell models which incorporate an additional rotation degree of freedom called the drill rotation. This class of models correspond to convenient reformulations of classical shell theory, and not to higher order (Cosserat) theories. In the present context, the additional local equation for the drill rotation is a constraint condition which identifies the rotation of the mid-surface of the shell with the drill rotation. The remaining equations are those of the classical model. Proper account of the geometry of the mid-surface in a finite deformation setting makes the actual formulation of this additional equation nontrivial. A variational formulation of the shell equations incorporating drill rotation is constructed by introducing an additional Lagrange multiplier term. In sharp contrast with formulations based on the so-called Biot stress, here the Lagrange multiplier enforcing the constraint vanishes at equilibrium, allowing for a regularized variational principle which reproduces the proper set of shell balance equations for any value of the regularization parameter.