Nonconservative Components of Follower Forces in the Classical Shell Theory

An analysis of follower forces acting on shell structures is presented. Attention is focussed on the expressions of such forces as functions of the generalized displacements. Specific expressions for the follower forces are obtained, according to the order of magnitude of the strains and angles of rotation. For small strains the follower forces allow a decomposition into conservative and non-conservative components. This leads to the equations of dynamic stability of shell problems subjected to follower loads. The dynamic counterparts of Donnell-Mushtari-Vlasov stability equations are presented, by either retaining or omitting the prebuckling rotations.