Shells without drilling rotations: A representation theorem in the framework of the geometrically nonlinear 6-parameter resultant shell theory

In the framework of the geometrically nonlinear 6–parameter resultant shell theory we give a characterization of the shells without drilling rotations. These are shells for which the strain energy function W is invariant under the superposition of drilling rotations, i.e. W   is insensible to the arbitrary local rotations about the third director d3d3. For this type of shells we show that the strain energy density W   can be represented as a function of certain combinations of the shell deformation gradient FF and the surface gradient of d3d3, namely W(FTF,FTd3,FTGradsd3). For the case of isotropic shells we present explicit forms of the strain energy function W having this property.