FINITE-ROTATION ELEMENTS FOR THE NON-LINEAR ANALYSIS OF THIN SHELL STRUCTURES

For the numerical analysis of shells undergoing finite rotations doubly curved finite shell elements are developed via the displacement formulation. The derivation starts from a consistent finite-rotation shell theory which is transformed by a variational procedure into an incremental formulation. Thus, the non-linearity can be treated by an incremental-iterative technique. The non-linear element matrices are obtained by a tensor-oriented procedure permitting a direct transformation of the initial equations into efficient numerical models. Unlike in the usual procedure, the KIRCHHOFF-LOVE assumption is treated as a subsidiary condition at the element level. This computer-oriented approach permits the elimination of the dependent rotational degrees of freedom without loss of accuracy. Finally, some examples are presented to demonstrate the ability of the resulting finite elements to deal with finite-rotation problems. © 1989.