Consistent numerical formulation of eccentric follower loads applied to shell structures Part I: Theoretical derivation

An advanced numerical formulation for the geometrically nonlinear finite element analysis of the shell structures under nonconservative loads is proposed in the present paper. The nonconservative follower loads are efficiently implemented by the load correction stiffness matrix(LCSM). The implications and assumptions adopted to derive LCSM are thoroughly explored in this study to take reasonable approach for the problem. The formulations derived here can consider the loads applied to the arbitrary locations of the shell elements. The second order rotations are additionally incorporated into the displacement field of an element and the combined effect with the present nonconservative loads is included. It is demonstrated that the nonconservative loads and the improved displacement field all contribute to the tangent stiffness matrix, by which beneficial effects on the convergence behavior can be expected. In the companion paper, the present theory successfully finds its good and important application in the analysis of prestressed concrete shell structure under nonconservative loads. It will be seen in the companion paper that the proposed theory provides very efficient and accurate method for the realistic analysis of prestressed concrete shell structures under nonconservative follower loads.