【作者】 李莎；

【导师】 董石麟； 肖南；

【作者基本信息】 浙江大学 ， 结构工程， 2014， 博士

【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。更多还原

【Abstract】 An adaptive cable-strut tensile structure with length-adjustable members is defined as a smart structure which can actively adjust its configuration to improve its adaptability to the variation of operational environments by changing the length of members. Aiming at the shape control of adaptive cable-strut tensile structure and based on its mechanical characteristics, this thesis has conducted intensive research on the key technologies, including the calculation of length changes, minimum quantity and optimal placement of adjustable members.By synthetically utilizing the decomposition theory of equilibrium matrix, nonlinear programming theory and nonlinear finite element theory, the mechanism of adaptive cable-strut structures has been analyzed systematically. The formulae on structural nonlinear responses to the length changes of members are derived and the solving strategy is provided. The proposed methods and strategies are appropriate for any type of cable-strut tensile structures under any load cases, providing the theoretical basis for the analysis on adaptive cable-strut tensile structures.With the shape and internal forces control as the objectives, and taking the length changes of active members as the unknowns, the incremental relation between the target responses and length changes has been derived based on NFEM. Both the incremental iterative strategy and the error feedback iterative strategy are proposed for solutions of this problem. Further, taking the constraints on internal forces and limited length changes of active members into account, a nonlinear shape control optimization model has been established. Based on the relation between target response and length changes, an sequential quadratic programming algorithm(SQP) has been proposed.Based on the finite element equilibrium equation, the sensitivity of structure responses to length changes has been derived. Furthermore, the first and second order sensitivities of objective functions on shape control, internal forces control and stiffness control are derived, providing the gradient information for the SQP algorithm. The sensitivity analyses proposed are applied to a Geiger cable dome and a tensegrity structure respectively, the control efficiency of active cables and active bars is discussed, and a criteria for the selection of active members is proposed.Moreover, based on precisely controllable conditions and the property of linear equations, the coefficient matrix for calculation of incremental length changes has been studied, and the mathematic relationship between the solutions of equations and active members’number and placement is revealed. The criteria for the layout of active members are proposed. An optimization model for the placement of active members with the minimum length changes as the objective has been established. A genetic algorithm(GA) is proposed to solve the problem. Further, a multi-objective control model with the minimum shape errors, minimum length changes and minimum number of active members as objectives has been established. A hybrid algorithm is proposed to solve the problem, which is composed by non dominant sorting genetic algorithm(NSGA-Ⅱ) and SQP. Results from the proposed algorithm show the restriction between different optimal solutions, providing reference for deciders to make an optimal plan.Based on the proposed theory, a small model of a Geiger cable dome with adjustable members was designed to carry on the experiment investigation. The pre-stressing progress, length adjusting and structure responding progress, and shape control progress were all investigated. Results show that, the experimental pre-stress was consistent with the theoretical model; the experimental trend of sensitivity analysis was consistent with theoretical analysis; the favorable control effect on the model guided by analytical scheme verified the validity of theoretical algorithms.According to the strategies and algorithms proposed in thesis, computer programs for the analysis and control of adaptive cable-strut structures are developed based on MATLAB. It’s capable to apply systematic analysis and control on any cable-strut structure with given topology by such programs.更多还原