保持承载刚度的张拉整体结构预应力降低方法  

An approach for relieving prestress of tensegrities with constant load-bearing stiffness

作　　者：诸德熙[1,2] 邓华[1,2] 王玮 ZHU Dexi;DENG Hua;WANG Wei(Space Structures Research Center,Zhejiang University,Hangzhou 310058,China;Zhejiang Provincial Key Laboratory of Spatial Structures,Zhejiang University,Hangzhou 310058,China;Beijing Institute of Architectural Design(Group)Co.,Ltd,Beijing 100045,China)

机构地区：[1]浙江大学空间结构研究中心,浙江杭州310058 [2]浙江大学浙江省空间结构重点实验室,浙江杭州310058 [3]北京市建筑设计研究院有限公司,北京100045

出　　处：《建筑结构学报》2022年第4期95-102,共8页Journal of Building Structures

基　　金：国家自然科学基金项目(51878599)。

摘　　要：几何刚度对张拉整体结构承载刚度的贡献通常与弹性刚度的贡献量级相当,但仅依靠高预应力保证结构承载刚度效果一般。而通过调整结构形状提高弹性刚度并替换部分几何刚度的贡献,可以在保持张拉整体结构承载刚度不变的前提下降低预应力。为此,将杆件原长变化作为基本变量,分析了该变量与单元内力、节点位移以及弹性和几何刚度矩阵的增量关系。建立了反映指定节点的受荷位移增量和单元原长变化量关系的灵敏度矩阵,指出由该灵敏度矩阵的零空间基向量线性组合而成的单元原长增量不会导致承载刚度的变化,但可以调整结构形状和预应力。以结构预应力下降为目标,提出了一种逐步调整结构形状的计算方法以使承载刚度中的几何刚度分量不断被增长的弹性刚度分量所替换。以一个张拉整体悬臂结构为算例,令其末端节点在给定荷载作用下的位移保持不变。分析结果表明:利用所建议的方法可以实现刚度分量的替换并显著降低该结构的预应力;将单元原长变化视为主动驱动,张拉整体具备主动调整形状和单元内力以保持承载刚度的自适应能力。The contribution of geometric stiffness to the load-bearing stiffness of tensegrities is generally equal to that of elastic stiffness,but it is usually not effective to rely on high prestress to ensure the structural load-bearing stiffness.By adjusting the structural shape to increase the elastic stiffness and replace the contribution of part of the geometric stiffness,the prestress can be relieved while maintaining the load-bearing stiffness of tensegrities.Adopting the variation of member rest lengths as the basic variable,its incremental relationships with the element internal forces,the node displacements,and the elastic and geometric stiffness matrices were analyzed.The sensitivity matrix reflecting the relationship between the load-induced displacement increment of the designated nodes and the variation of member rest lengths was established.It is pointed out that the increment of element rest lengths constructed by the linear combination of the nullspace basis vectors of the sensitivity matrix will not cause the change of the load-bearing stiffness,but can adjust the structural shape and prestress.To reduce the prestress of tensegrities,a numerical strategy was proposed by gradually adjusting the structural shape so that the geometric stiffness component in the load-bearing stiffness was partially replaced by the increasing elastic stiffness component.A tensegrity cantilever was employed as an illustrative example,and the displacement of its end nodes under the given loads was required to keep constant.The results show that the structural prestress can be significantly relieved by adjusting the stiffness components using the proposed strategy.The illustrative example also shows the adaptability of tensegrity on maintaining the load-bearing stiffness by adjusting the shape and the element internal forces,if variations of member rest lengths are considered as actuation.

关 键 词：张拉整体结构 承载刚度 刚度分量替换 预应力降低 自适应结构 

分 类 号：TU311.1[建筑科学—结构工程]