Keywords: corotational method, beams, composite beams, shells, finite rotations, nonlinear analysis.

The corotational method is an alternative approach to derive efficient nonlinear finite elements, in particular for beams and shells. The idea is to decompose the large motion of the element into rigid body and pure deformational parts. Then, if an appropriate mesh size is taken, the deformational part can be assumed as small and can be modelled by using classical linear (or low order nonlinear) finite element formulations. One main interest of this method is that once the corotational framework has been derived, several local formulations can be used, giving different finite formulations well suited to different types of problems.

The purpose of this paper is to present a review of some new developments obtained during the last fifteen years utilizing the corotational method. In particularly, the development of corotational formulations for composite two-dimensional beams with interlayer slips and for dynamic two-dimensional and three-dimensional beams are addressed. Corotational formulations for plane, solid and shell elements also are presented and discussed.

Several corotational formulations can be found in the literature. All these formulations are based on the idea presented above. However, their implementations, especially for three-dimensional beams and shells, can be rather different. This paper focuses mainly on the recent work carried out in a collaboration between KTH, the Royal Institute of Technology in Sweden and INSA de Rennes in France.

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