同时考虑构件刚度和预应力的索网结构刚度优化  

Stiffness optimization of cable-net structures simultaneously considering member’s stiffness and prestress

作　　者：陈璀 邓华[1] 姜晓东 诸德熙[1] CHEN Cui;DENG Hua;JIANG Xiao-dong;ZHU De-xi(Space Structures Research Center,Zhejiang University,Hangzhou 310058,China;Zhejiang Engineering Management Co.,LTD,Hangzhou 310012,China)

机构地区：[1]浙江大学空间结构研究中心,浙江杭州310058 [2]浙江工程建设管理有限公司,浙江杭州320012

出　　处：《空间结构》2019年第4期27-34,共8页Spatial Structures

基　　金：国家自然科学基金项目(51578493)

摘　　要：同时以单元轴向线刚度和力密度为设计变量,提出一种结构整体刚度的优化方法,使索网在特定荷载作用下能够满足多点位移限值的约束条件.针对索网结构的切线刚度矩阵,建立了以上两类设计变量分别与结构线弹性刚度和几何刚度的解析关系式.不考虑外荷载变化,推导了两类设计变量与结构位移的近似增量关系,并给出其灵敏度矩阵的解析表达式.针对给定荷载下的索网多点变形约束条件,借助灵敏度矩阵的特征空间性质,提出了一种结构刚度优化的数值策略,并指出优化设计变量与目标位移间存在的效率评价问题.以一个梯形平面马鞍形索网为算例,利用该方法对结构刚度进行优化以使索网在给定荷载下能够满足预先设定的位移场限值要求.计算结果不仅验证了算法的有效性,也反映出进行优化结果的效率评价是必要的.Simultaneously taking the element’s axial linear stiffness and force density as the design variables, an optimization method of structural overall stiffness was proposed to enable cable net to satisfy the constraint conditions of multi-point displacement limits under specific load. Based on the tangent stiffness matrix of cable-net structure, the analytical expressions between the two kinds of design variables and the structural linear elastic stiffness as well as geometric stiffness were established. The approximate incremental relationships between the two kinds of design variables and the structural displacement were also derived with constant external loads, and the analytical expression of the sensitivity matrix was given. For the constraint condition of multi-point displacements of cable net sustaining constant load, a numerical strategy for optimizing structural stiffness was put forward by means of the eigenspace of sensitivity matrix, and the problem of efficiency evaluation between optimal design variables and target displacement was also pointed out. A saddle-shaped cable net with trapezoidal plane was adopted as an illustrative example. Using the method put forward in this paper, its structural stiffness was optimized to satisfy the limit of the pre-set displacement field under a given load. The numerical results verify the validity of the optimization method, and reveal the necessity of evaluating the efficiency of the optimal solutions.

关 键 词：索网结构 刚度优化 构件刚度 预应力 灵敏度分析 

分 类 号：TU351[建筑科学—结构工程]