Rotational Invariants in Finite Element Formulation of Three-Dimensional Beam Theories

摘要

This paper presents a new nite element formulation of the `geometrically exact nitestrain beam theory'. The formulation employs the generalized virtual work principle in which the main role is played by strain vectors. A set of governing equations of the beam is developed in which the only unknown functions are the strain vectors. The consistency condition that the equilibrium and the constitutive internal force and moment vectors are equal, is enforced to be satis ed at the chosen points. The accuracy and the ef ciency of the derived numerical algorithm are demonstrated by several examples.