REFINED THEORIES OF ELASTIC ANISOTROPIC SHELLS ACCOUNTING FOR SMALL STRAINS AND MODERATE ROTATIONS

A geometrically non-linear theory of elastic anisotropic shells based upon discarding Kirchhoff-Love assumptions is developed in this paper. The theory incorporates transverse (normal and shear) deformation as well as the higher-order effects and accounts for small strains and moderate rotations of the normal. The theory is given in a complete Lagrangian description while the equations of motion and the boundary conditions are obtained through the Hamilton variational principle. Appropriate specializations of the obtained results are performed revealing that they cover a large number of cases separately treated in the specialized literature but considered here in a unified manner.