A recursive formulation based on corotational frame for flexible planar beams with large displacement

Abstract

A forward recursive formulation based on corotational frame is proposed for flexible planar beams with large displacement. The traditional recursive formulation has been successfully used for flexible mutibody dynamics to improve the computational efficiency based on floating frame, in which the assumption of small strain and deflection is adopted. The proposed recursive formulation could be used for large displacement problems based on the corotational frame. It means that the recursive scheme is used not only for adjacent bodies but also for adjacent beam elements. The nodal relative rotation coordinates of the planar beam are used to obtain equations with minimal generalized coordinates in present formulation. The proposed formulation is different from absolute nodal coordinate formulation and the geometrically exact beam formulation in which the absolute coordinates are used. The recursive scheme and minimal set of dynamic equations lead to a high computational efficiency in numerical integration. Numerical examples are carried out to demonstrate the accuracy and validity of this formulation. For all of the examples, the results of the present formulation are in good agreement with results obtained using commercial software and the published results. Moreover, it is shown that the present formulation is more efficient than the formulation in ANSYS based on GEBF.