基于等几何分析的柔性多体系统建模方法研究

近三十年来，柔性多体系统动力学取得长足进步，尤其是以绝对节点坐标方法(Absolute Nodal Coordinate Formulation, ANCF)为代表的非线性有限元已被用来处理复杂的柔性多体系统动力学问题.但绝对节点坐标方法采用斜率矢量作为广义坐标，导致系统自由度多，计算效率低.针对柔性多体系统，基于非均匀有理B样条(Non-Uniform Rational B-Splines, NURBS)曲线和曲面分别提出了Euler-Bernoulli细长梁单元和Kirchhoff-Love薄壳单元，在完全拉格朗日格式下，根据Green应变张量对单元变形进行描述，结合第二类Piola-Kirchhoff应力张量给出单元应变能公式，推导了单元的弹性力和弹性力雅可比矩阵表达式，最后通过静力学及动力学数值算例对提出的两类单元的性能进行对比和验证，为柔性多体系统建模提供了一种精确高效的新单元.

Research of flexible multibody system modeling based on isogeometrical analysis

In the last three decades, the research in flexible multibody dynamics has made substantial progress, in particular, the nonlinear finite element represented by the Absolute Nodal Coordinate Fromulation (ANCF) has been widely applied to deal with the system of flexible multibody dynamics. However, in this formulation the slope vectors are selected as the element node coordinate, the increased scale of the freedoms for the complex structures gives rise to the computational burden. Based on the above issues, the beam and shell elements described with Non-Uniform Rational B-Splines (NURBS) curves and surfaces have been proposed in the frame of Isogeometrical Analysis (IGA). Based on the total lagrangian formulation, the deformation of the elements is described with the Green strain, and the strain energy of the elements can be obtained. Besides, the elastic force and its Jacobian matrix of the elements are also deduced. Finally, four case studies including both static and dynamic problems are given to validate the proposed beam and shell elements. High efficient and accurate formulation has been proposed in the research of flexible multibody dynamics.