An energy-momentum method for in-plane geometrically exact Euler-Bernoulli beam dynamics

作者：Sansour Carlo^*; Tien Long Nguyen; Hjiaj Mohammed

来源：International Journal for Numerical Methods in Engineering, 2015, 102(2): 99-134.

DOI：10.1002/nme.4832

• nonlinear dynamics
• geometrically exact beam
• Euler-Bernoulli beam
• energy-momentum method
• time integration
• chaotic motions

Nonlinear geometrically exact rod dynamics is of great interest in many areas of engineering. In recent years, the research was focused towards Timoshenko-type rod theories where shearing is of importance. However, in many general model of mechanisms and spatial deformations, it is desirable to have a displacement-only formulation, which brings us back to the classical Bernoulli beam. While it is well known for linear analysis, the Bernoulli beam is not as common in geometrically exact models of dynamics, especially when we want to incorporate the rotational inertia into the model. This paper is about the development of an energy-momentum integration scheme for the geometrically exact Bernoulli-type rod. We will show that the task is achievable and devise a general framework to do so.

• 出版日期2015-4-13