基于体系可靠度的桁架结构优化设计研究

发布时间：2019-02-22 09:34

【摘要】：结构的优化设计不只是追求结构的重量最小或者是造价最低，更重要的是要保证结构优化后的安全性。对桁架这类具有明显失效历程的结构优化设计，需要考虑结构的体系可靠性。本文探讨了结构构件及体系可靠性分析方法，提出了适用于工程结构的体系可靠性优化方法，最后对标准十杆平面桁架和钢桁梁结构进行了体系可靠性优化分析。具体研究内容如下： (1)探讨了结构构件可靠度和结构体系可靠度的分析方法，并对各种方法的适用范围和优缺点进行说明。在JC法、MC法和窄界限法的理论基础上，在MATLAB平台上编制了可靠度计算软件。为结构体系可靠性优化设计中体系可靠性求解问题打下基础。 (2)提出基于遗传算法和神经网络的结构体系可靠性优化设计方法。该方法首先由BP神经网络映射出随机变量与结构受力关系，采用Monte Carlo Method得出各失效模式的可靠指标；然后由β约界法得出结构失效树，采用PNET(概率网络估算技术)法计算体系可靠指标；最后以选取的目标体系可靠指标为约束条件，以罚函数的方式引入遗传算法，在MATLAB平台实现优化设计。 (3)通过十杆平面桁架和钢桁梁的算例分析，表明该方法可适用于此类结构的优化设计。参数分析表明：传统确定性优化和构件层次可靠性优化不能保证上述结构的体系可靠性，随着目标体系可靠指标和变异系数的增大，其对优化结果影响越大。 (4)建立了钢桁梁结构体系可靠性优化数学模型，对某悬索桥的桁架式主梁结构进行了体系可靠性优化分析。分析结果表明：该结构的最初失效状态表现为腹杆的压应力屈曲失效，最终失效状态表现为纵、横梁跨中弯曲失效。适当减小某钢桁梁结构的纵、横梁截面面积和增加腹杆面积，可在保证体系可靠度的情况下减小结构重量，也可在结构重量不变的情况下提高结构体系可靠指标。
[Abstract]:The optimal design of the structure is not only to seek the minimum weight or the lowest cost of the structure, but also to ensure the safety of the optimized structure. The structural reliability should be considered in the optimal design of truss with obvious failure history. In this paper, the reliability analysis method of structural members and systems is discussed, and the system reliability optimization method suitable for engineering structures is put forward. Finally, the system reliability optimization analysis of standard ten-bar plane truss and steel truss structure is carried out. The main contents of this paper are as follows: (1) the reliability analysis methods of structural components and structural systems are discussed, and the applicability, advantages and disadvantages of these methods are explained. Based on the theory of JC method, MC method and narrow bound method, the reliability calculation software is developed on MATLAB platform. It lays a foundation for the system reliability solution in the structural system reliability optimization design. (2) A reliability optimization design method based on genetic algorithm and neural network is proposed. Firstly, the BP neural network is used to map out the relationship between random variables and structural forces, and the reliability index of each failure mode is obtained by Monte Carlo Method. Then the structure failure tree is obtained by 尾 -reduction method, and the reliability index of the system is calculated by PNET (probabilistic network estimation technique). Finally, taking the selected reliability index of the target system as the constraint condition, the genetic algorithm is introduced in the form of penalty function, and the optimal design is realized on the MATLAB platform. (3) through the example analysis of ten bar plane truss and steel truss, it is shown that this method can be applied to the optimization design of this kind of structure. The parameter analysis shows that traditional deterministic optimization and component hierarchical reliability optimization can not guarantee the reliability of these structures. With the increase of reliability index and coefficient of variation of the target system, the greater the impact on the optimization results. (4) the reliability optimization mathematical model of steel truss beam structure is established, and the system reliability optimization analysis of the truss girder structure of a suspension bridge is carried out. The results show that the initial failure state of the structure is the buckling failure of the compressive stress of the web bar, and the ultimate failure state is the longitudinal failure and the mid-span bending failure of the beam. Reducing the cross section area of a steel truss beam and increasing the area of web bar can reduce the weight of the structure under the condition of ensuring the reliability of the system, but also improve the reliability index of the structure system when the weight of the structure remains unchanged.
【学位授予单位】：长沙理工大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：TU318

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