Geometrically exact 3D beam theory: implementation of a strain-invariant finite element for statics and dynamics

Abstract

Geometrically exact 3D beam theory has been used as a basis for development of a variety of finite element formulations. It has recently become apparent that the important requirement of objectivity of adopted strain measures, although provided by the theory itself, does not automatically extend to a finite element formulation. In this paper we present a new finite element formulation of the geometrically exact 3D beam theory, specifically designed to preserve the objectivity of the adopted strain measures. In order to do so the current local rotations are interpolated in a manner similar to that adopted in co-rotational approaches. However, no approximations typical for co-rotational approaches are introduced into the procedure, so in contrast to co-rotational formulations, the present formulation fully preserves the geometric exactness of the theory. A range of numerical examples serves to illustrate the problem and to assess the formulation.