改进的动力松弛法及其在张拉整体结构找形中的应用

Modified Dynamic Relaxation Method and Its Application in Form-finding of Tensegrity Structures

针对目前常规动力松弛法存在收敛效率低和收敛不稳定的问题,采用中心差分法对动能极值点附近的运动进行精细化划分,通过节点坐标修正的策略使节点的运动准确地回溯至所定位的动能极值点处,改善常规动力松弛法收敛性能的同时扩大了算法的稳定收敛的区域。最后以六杆张拉整体结构和螺旋塔型张拉整体结构为例,对比了多种常规动力松弛法在此类结构找形问题上的求解效果。结果表明:本文所提出的改进方法相较于常规方法和抛物线拟合法在处理此类结构找形问题时,算法效率上提升了17%~58%,算法稳定收敛区间扩大了25%~41%,验证了该方法在复杂张拉整体结构找形分析过程中的准确性和有效性,同时为张拉整体结构在实际工程的应用进行初始形态找寻提供了理论支撑。

To solve the problem of low convergence efficiency and unstable convergence of normal dynamic relaxation methods,the central difference method is utilized to accurately segment the motion near the extreme points of kinetic energy.Through the strategy of node coordinate correction,the node’s motion can be accurately traced back to the located extreme points of kinetic energy,which improves the convergence performance of the normal dynamic relaxation method and expands the stable convergence region of the algorithm.Finally,a six-strut tensegrity structure and a spiral tower tensegrity structure are taken as two illustrative examples,and the results of various conventional dynamic relaxation methods are compared in dealing with the form-finding problem for such structures.The results show that the modified method proposed in this paper improves the algorithm efficiency by about 17%~58%and expands the stable convergence range by about 25%~41%compared with conventional methods and the parabola fitting method,which verifies the accuracy and effectiveness of this method in the form-finding analysis of tensegrity structures,and also,provides theoretical support for determining the initial shape of tensegrity structures in practical engineering.