自适应索杆张力结构的理论研究与试验

发布时间：2018-01-07 18:36

本文关键词：自适应索杆张力结构的理论研究与试验　出处：《浙江大学》2014年博士论文　论文类型：学位论文

【摘要】：变长度单元自适应索杆张力结构,是以主动单元长度变化为调控手段,通过改变结构几何形态以提高适应环境变化能力的一类智能结构。本文以变长度单元自适应索杆张力结构的形态控制为目标,从索杆张力结构受力特性出发,围绕主动单元调控长度计算和最优数量及位置分布等关键技术进行了深入研究。综合运用平衡矩阵分解理论、非线性规划理论、以及非线性有限元理论对变长度单元自适应索杆张力结构的力学基础进行了系统分析,推导了结构对单元长度变化的非线性响应计算公式,并提出了求解策略。所提出的理论分析方法及算法适用于任意荷载工况下的任意类型索杆张力结构,为自适应索杆张力结构的分析提供了理论基础。以张力结构形状和内力控制为目标,以主动单元长度调控量为未知量,基于非线性有限元理论,推导了目标响应与主动单元长度调控量的增量关系式,提出了增量迭代求解策略及误差反馈迭代求解策略。进一步,考虑单元内力约束及主动单元调控长度限制等条件,建立了自适应索杆张力结构的形态非线性优化控制数学模型,从目标响应与主动长度调控量之间的有限元增量关系出发,提出了基于序列二次规划法SQP的求解策略。基于有限元平衡方程,推导了结构响应对主动单元长度变化的灵敏度计算公式,同时建立了自适应行为中的形状控制、内力控制以及刚度控制等多目标函数对所有主动单元调控量的一阶、二阶灵敏度矩阵,为序列二次规划法求解策略提供了梯度信息。利用所推导灵敏度公式,对Geiger索穹顶和张拉整体结构进行结构响应的灵敏度分析,探讨了索单元及杆单元类型分别作为主动单元的调控效率,提出了在不同自适应目标下,两类结构中主动单元的选择准则,为主动单元的布设提供参考。基于精确可控条件,利用线性方程组的性质,通过对调控增量计算系数矩阵的分析,揭示了主动单元数量及位置与方程组解之间的数学关系,提出了主动单元数量与位置的布设准则。建立了以调控增量最小为目标的最优位置优化数学模型,提出了基于遗传算法的求解策略。进一步,以最小化形态控制误差、主动单元调控长度以及主动单元数量为目标函数,建立了以主动单元分布向量和调控长度为变量的混合变量多目标优化控制模型,提出了基于非支配排序遗传算法NSGA-Ⅱ和序列二次规划法SQP的分层求解策略。该算法获得的结果能直观地显示各目标函数最优解之间的矛盾关系,为决策者制定最合理方案提供了理论参考。在理论分析基础上,设计了具有长度可调单元的Geiger索穹顶模型进行试验研究,考察了模型在张拉成形过程、调控响应过程、以及加载调节过程中的结构响应。试验结果数据分析表明,试验模型的预应力分布情况与理论计算值一致,结构对于各类主动单元的长度变化响应灵敏度与理论分析趋势保持一致,由理论控制方案指导进行的荷载态形态调控试验结果良好,验证了本文理论计算模型的正确性。根据本文所提出的相关算法策略,采用MATLAB软件编制了相应程序,所有程序均具有通用性,能对任意给定几何拓扑和约束等条件的索杆张力结构进行系统分析和调控计算,为索杆张力结构的调控提供了有效的数值分析工具。
[Abstract]:Variable length unit Adaptive Cable strut structure, is the active unit length change control means, through a kind of intelligent structure to improve the ability to adapt to the changing environment and change the structure of geometry. In this paper, the adaptive variable length unit of cable strut structure shape control as the goal, starting from the stress characteristics of cable strut structure, around the key the technology of active control unit length calculation and the optimal number and location are studied deeply.
The comprehensive use of the equilibrium matrix decomposition theory, nonlinear programming theory and nonlinear finite element theory has carried on the system analysis of cable strut structure on the mechanical basis of variable length unit adaptive calculation formula of nonlinear response of structure of unit length variation is deduced, and puts forward the solving strategy. Any type of theoretical analysis method and the proposed algorithm is applicable to arbitrary load conditions of cable strut structure, provides a theoretical basis for the adaptive analysis of cable strut structure.
The tension structure and internal control as the goal, to active unit length regulation is unknown, based on nonlinear finite element theory, the target response increment with active unit length regulation volume formula, proposed an iterative solving strategy and error feedback incremental iteration strategy. Further, considering the constraint element internal forces and active unit the regulation length constraints, an adaptive nonlinear optimal control mathematical model of cable strut structure form, starting from the target response finite element incremental and the relationship between the amount of active length regulation, a sequence of two quadratic programming method solving strategy based on SQP.
Finite element equilibrium equation is deduced based on structural response sensitivity of active unit length variation formula, and establish the shape control of adaptive behavior in the internal control and stiffness control objective function for all active unit control quantity of one order, two order sensitivity matrix, provide gradient information to sequence two a programming method for solving strategy. Using the derived sensitivity formula, analysis on sensitivity of structure response of cable dome and tensegrity structure of Geiger, discusses the cable element and bar element types were used as control efficiency of active unit, put forward the different adaptive target selection criteria, active elements of two kinds of structure, provide the reference for the layout of active units.
The precise control based on the properties of the linear equations, through the analysis and calculation of the coefficient matrix of the incremental regulation, reveals the mathematical relationship between the solutions of the active element number and position and equations, the author proposes the layout criterion on active unit quantity and location. To establish a control of optimal location optimization model for minimizing the increment and put forward solving strategy based on genetic algorithm. Further, to minimize the error of shape control, active control unit length and active element number as the objective function, is established with the active unit distribution vector and regulation length control model of multi-objective optimization of mixed variables, the non dominated sorting genetic algorithm II NSGA- and sequence two planning method of SQP hierarchical solving strategy based on the results of the algorithm can visually display the contradiction between the objective function optimal solution, as will The policy makers provide the theoretical reference for the most reasonable plan.
On the basis of theoretical analysis, design with adjustable length unit of Geiger cable dome model were studied. The studied model in stretch forming process, the regulation of response, response of structure and the loading in the regulation process. The experimental data analysis results show that the prestress distribution test and theoretical calculation value of the model, structure the length change of all kinds of active element sensitivity trend is consistent with theoretical analysis, the theoretical guidance of the load control scheme forms regulation experiment results verify the correctness of the calculation model of the theory in this paper.
According to the algorithm proposed by this paper, and the corresponding program is designed by MATLAB software, all procedures are universal, for any given topology and geometric constraint conditions of the cable strut structure system analysis and control calculation, provide an effective analysis tool for the numerical control of cable strut structure.

【学位授予单位】：浙江大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TU399

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