Nonlinear strain measures, shape functions and beam elements for dynamics of flexible beams

In this paper, we examine several aspects of the development of an explicit geometrically nonlinear beam element. These are: (i) linearization of the displacement field; (ii) the effect of a commonly adopted approximation for the nonlinear Lagrangian strain; and (iii) use of different-order shape fu nctions for discretization. The issue of rigid-body check for a nonlinear b eam element is also considered. An approximate check is introduced for an e lement based on an (approximate) intermediate strain measure. Several numer ical examples are presented to support the analysis. The paper concludes wi th a discussion on the use of explicit nonlinear beam elements for multibod y dynamics simulation.