非线性几何精确梁理论研究综述

Advances of geometrically exact 3D beam theory

几何精确梁理论是处理几何非线性梁的一种重要方法,该法能够高效并准确地处理梁的大变形与大转动问题。阐述了该法的2种有限转动参数化形式,其中一种是最新形式;阐述了两大类有限转动插值方法的选取方式,并指出这两类方法的优缺点;阐述了求解动力学方程的2种积分方法的选择,并比较2种方法优势与缺陷。说明该法在处理几何非线性梁问题时具有较少的单元节点自由度与较高的计算效率等优点,但同时存在着转动参数的奇异性、单元应变客观性等问题。因此该法尚不完善,仍值得学者们做进一步研究。

Geometrically exact 3D beam theory can describe the large detormatlon and rotation ol the beam and effectively deals with geometric nonlinear beam problems. The development of geometrically exact 3D beam theory is reviewed. Two methods of parameterizing finite rotation are demonstrated, one o~ which is newly mentioned. Two interpolation methods of the finite rotation are also described~ advantages and disadvantages of those two methods are pointed out. Selection of to two integration methods to solve the dynamic equations is also discussed, and strength and weakness of those two methods are also elaborated. It is indicated that the geometrically exact 3D beam theory has the merits of less general coordinates and higher calculation efficiency when deal- ing with geometric nonlinear beam problems in the meantime, the problems of rotation parameter singularity and unit strain ob- iectivity also exist which need more future investigations.