基于奇异值分解张拉整体结构找形方法  

Form-finding method for tensegrity structures based on singular value decomposition

作　　者：罗阿妮 曹紫莺 刘贺平[1] LUO Ani;CAO Ziying;LIU Heping(College of Mechanical and Electrical Engineering,Harbin Engineering University,Harbin 150001,China)

机构地区：[1]哈尔滨工程大学机电工程学院,黑龙江哈尔滨150001

出　　处：《哈尔滨工程大学学报》2024年第5期957-963,共7页Journal of Harbin Engineering University

基　　金：国家自然科学基金项目(51835002,51875111);黑龙江省自然科学基金项目(LH2019E023,LH2020E062)。

摘　　要：张拉整体结构是由一组不连续的受压单元包含于连续受拉单元组成的稳定自平衡结构,为了寻找自平衡状态下的构型,引入奇异值分解的方法,将寻找张拉整体结构的自平衡构型问题转化为最小奇异值的判定。通过广义节点坐标和构件之间的连接关系建立结构的数学模型;引入力密度的概念,对张拉整体结构进行受力分析,列写包含平衡矩阵的平衡方程;对平衡矩阵进行奇异值分解,利用分解获得的最小奇异值判断平衡方程是否有解,对张拉整体结构是否存在自平衡构型进行初步判定,再依据获得的力密度的均匀性(同组构件力密度大小相等)和正负属性(杆的力密度小于0,索的力密度大于0)对结构自平衡状态进一步判断;通过实例分析对该找形方法的可行性进行了验证,结果表明:该方法可以找到张拉整体结构自平衡构型。本文为寻找自平衡张拉整体结构提供了一种思路。Tensegrity structures are stable self-equilibrium structures comprising a group of discontinuous compres-sion elements within continuous tension elements.To find the self-equilibrium configuration,the singular value de-composition(SVD)method is introduced to transform the problem of finding the self-equilibrium configuration of the tensegrity structure into the determination of the minimum singular value.First,the mathematical model of the structure is established by the connection relationship between the generalized node coordinate and the component.Second,the concept of force density is introduced to analyze the stress of the tensegrity structure,and the equilibri-um equation,including the equilibrium matrix,is written.Next,the equilibrium equation is solved by SVD,and the minimum singular value is used to initially determine whether there is a solution to the equilibrium equation and a self-equilibrium configuration of the tensegrity structure.According to the uniformity of force density(the mem-bers in the same group are equal in force density)and the positive and negative properties(the force density of the rod is<0,and the force density of the cable is>0),the self-equilibrium state of the structure is further judged.Finally,the feasibility of this form-finding method is verified by example analysis,and the result shows that the self-equilibrium configuration of the tensegrity structure can be calculated by this method.This study provides a way to find the self-equilibrium tensegrity structure.

关 键 词：张拉整体结构 找形方法 节点坐标 连接矩阵 平衡矩阵 平衡方程 奇异值分解 力密度 

分 类 号：TP242[自动化与计算机技术—检测技术与自动化装置]