基于逐点去约束法的索桁张拉结构形状判定及自应力模态求解方法  

Method of Shape Determination and Solving Self-stress Mode of Cable-truss Tensile Structure Based on Constraints Move Method

作　　者：薛素铎[1] 鲁建 李雄彦[1] 刘人杰 XUE Suduo;LU Jian;LI Xiongyan;LIU Renjie(Spatial Research Centre,Beijing Univ.of Technol.,Beijing 100124,China;Civil Eng.College Inst.,Yantai Univ.,Yantai 264000,China)

机构地区：[1]北京工业大学空间结构研究中心,北京100124 [2]烟台大学土木工程学院,山东烟台264000

出　　处：《工程科学与技术》2020年第2期47-53,94,共8页Advanced Engineering Sciences

基　　金：国家自然科学基金项目(51778017);北京市自然科学基金项目(8172011)。

摘　　要：索桁张拉结构是索杆张拉结构中最有竞争力的空间结构型式之一,其形状判定和自应力模态求解是设计时的两个关键问题。通过对前人研究成果的整理与分析可知:索杆张拉结构的形状判定大都根据平衡矩阵理论进行求解,而平衡矩阵理论一般需要编程,不易被掌握;已有的求解自应力模态方法大都不能在有限元软件上直接应用。针对这些问题,提出基于合理位形改进的逐点去约束法以求解索桁张拉结构的合理形状和自应力模态。该方法首先基于索桁张拉结构所具有的独特的拓扑关系,从合理位形出发推导了形状判定的简洁判断公式。然后 ,通过对逐点去约束法的研究,提出改进的逐点去约束法以求解索桁张拉结构的自应力模态。本文方法基于先形状判断后自应力模态求解的思路,可一次性确定结构的合理形状和自应力模态,回避了原方法中先求解自应力模态后判断形状的反复求解的缺点;同时不使用原方法中的生死单元技术,保证了求解过程的收敛;消除了因生死单元技术而产生的累计误差,提高了计算精度;避免了坐标转换,简化了求解流程;改进的方法可在有限元软件上直接应用。算例表明改进的方法具有系统的求解流程,且收敛快、精度高,为索桁张拉结构的形状判定与自应力模态求解提供了一种思路。Cable-truss tensile structure is one of the most competitive spatial structures of cable-strut tensile structures.The shape determination and algorithm for self-stress modes are two key problems in design.Based on sorting and analyzing of the previous research results,it showed that most of the shape determinations of cable-strut tensile structure were solved according to the equilibrium matrix theory,which was difficult to be mastered due to the necessity of programming.Most of the existed methods to solve the self-stress mode cannot be directly used in the finite element software.To solve these problems,an improved constraints moved method based on reasonable configuration was proposed to determine the rational shape and solve the self-stress mode of cable-truss tensile structures.The method proposed was firstly based on the special topological relation of cable truss structure,and a simple formula for shape determination was derived from the rational shape.Meanwhile the method was proposed based on the idea that is shape determination first and then solving self-stress mode,which could ensure reasonable shape and self-stress mode one time and avoid the defect of solving self-stress mode firstly and then repetitively determining shape of the original method.Besides,the proposed method did not use the life-and-death unit technology of the original method,which ensured the convergence of solution process.The accumulative error caused by the technology of life-and-death unit technology was eliminated and the calculation precision was improved.The coordinate transformation was avoided and the solving process was simplified.The new method could be directly applied to the finite element software.Numerical calculations showed that the proposed method had a systematic solution flow and high convergence accuracy.The proposed method offered a new idea to determine shape and solve self-stress mode of the cable-truss tensile structures.

关 键 词：索桁张拉结构 改进的逐点去约束法 有限元软件 形状判定 求解自应力模态 

分 类 号：TU394[建筑科学—结构工程]