Geometrically exact planar Euler-Bernoulli beam and time integration procedure for multibody dynamics

Abstract

Abstract A new formulation of geometrically exact planar Euler-Bernoulli beam in multi-body dynamics is proposed. For many applications, the use of the Euler-Bernoulli model is sufficient and has the advantage of being a nodal displacement-only formulation avoiding the integration of rotational degrees of freedom. In this paper, an energy momentum method is proposed for the nonlinear in-plane dynamics of flexible multi-body systems, including the effects of revolute joints with or without torsional springs. Large rotational angles of the joints are accurately calculated. Several numerical examples demonstrate the accuracy and the capabilities of the new formulation.

Keywords

• Multi-body dynamics
• Geometrically exact beam theory
• Euler-Bernoulli beam
• Energy-momentum method