基于等几何配点法的柔索非线性动力学分析

Nonlinear dynamic analysis for cables based on the isogeometric collocation method

针对柔索结构非线性动力学问题,提出了基于非均匀有理B样条(NURBS)的等几何配点法.利用哈密顿原理建立了耦合三个平动自由度和一个扭转自由度的柔索非线性运动方程,基于等参元的思想,利用NURBS基函数的高阶连续性和配点离散强形式的控制偏微分方程组,采用Newmark-β时间积分与修正的Newton-Raphson非线性迭代法求解离散动力学方程.通过与传统有限元法计算结果对比,验证了该数值方法的准确性和高效性.进一步分析了等几何配点法典型的收敛特性,表明该方法能有效处理非线性动力学问题.

The isogeometric collocation （IGA-C） method based on non-uniform rational B-splines was proposed for the nonlinear dynamic analysis of cable structures .The nonlinear equations of motion of cables ,which coupled three translational and one torsional degrees of freedom were formulated by em-ploying the Hamilton principle .Taking advantage of the high-continuity properties of NURBS basis functions and collocation points ,the IGA-C method was adopted to discretize the strong form of gov-erning partial differential equations within an isoparametric framework .The Newmark-βtime integra-tion algorithm in conjunction with the modified Newton-Raphson nonlinear iteration strategy was uti-lized to solve those discretized dynamic equations .The accuracy and high efficiency of the present nu-merical method were demonstrated by comparing with the results obtained from the traditional finite element method .The characteristic convergence behavior of the IGA-C method was investigated .The results show that the method can effectively deal with the nonlinear dynamic problems .