基于有限体积法的结构系统疲劳可靠性研究

In order to establish the fatigue failure mechanism of structural system, to improve the recognition efficiency of failure modes of structural system and the computational accuracy of structural system reliability, the finite volume method was used to study the fatigue reliability of structural system, which was significance to improve the computational accuracy and efficiency of fatigue reliability analysis of structural system. A numerical model for fatigue reliability analysis of structural systems based on finite volume method has been established; Based on S-N curve method and Miner’s theory, fatigue failure criteria of structural elements were analyzed. On this basis, according to estimate the carrying capacity of structural system, the critical failure cross sections of the structural system were confirmed, the fatigue failure mechanism of entity structure system was analyzed, the discrimination method of fatigue failure of structural system has been explored; An improved method of branch and bound method was established, taking the failure probability as the criterion, an efficient method for identifying the main failure modes of the structural system has been constructed; Based on the idea of dimensionality reduction, and according to the mapping relation between the element failure events and normal space, a precise expression method of the correlation degree between multiple element failure events and one element failure event has been constructed; An analytical method for correlation between units and major failure modes has been established; Finally, the analysis method of fatigue reliability of entity structure system has been established, the recognition efficiency of failure mode and the calculation accuracy of fatigue reliability of structural system were improved, and it provides theoretic foundation for fatigue reliability analysis of structural system.

针对结构系统疲劳失效机理难于建立、结构系统失效模式的识别效率和结构系统可靠度的计算精度不高等问题，基于有限体积法研究结构系统疲劳可靠性对于提高结构系统疲劳可靠性的计算精度和效率具有重要的意义。建立基于有限体积法分析结构系统疲劳可靠性的数值模型；基于S-N曲线法及Miner累积损伤理论分析结构单元的疲劳失效准则；在此基础上，通过判断结构系统承载能力，确定结构系统临界破坏截面，解析实体结构系统的疲劳失效机理，探寻结构系统疲劳失效的判别方法；建立分支限界法的改进方法，以失效概率为判据，构建结构系统主要失效模式的高效识别方法；基于降维思想，依据单元失效事件与正态空间映射关系，构建多个单元失效与一个单元失效事件相关程度的精确表述方法，建立单元之间及主要失效模式之间的相关性的分析方法；最终建立完善的实体结构系统疲劳可靠性分析方法，提高了结构系统失效模式的识别效率及结构系统疲劳可靠度的计算精度.

本项目基于有限体积法针对结构系统疲劳可靠性分析问题开展研究。针对金属结构疲劳失效特点，提出了金属结构元件的疲劳失效准则，建立了结构元件的等效功能函数；研究了金属结构系统的疲劳失效准则；当有n个结构元件失效后，结构损伤累积到一定程度，结构失效元件在结构局部表面形成了明显的裂纹时，认为结构局部的失效会导致整个结构系统的承载能力大幅度降低，不能满足原有结构的承载能力，导致结构系统失效，从而建立了金属结构系统疲劳失效的判别准则。基于金属材料的S-N曲线，元件的内力越大，其疲劳寿命就越小，元件累积损伤的越快，它的破坏概率就越大。选取一定范围的内力较大的元件作为每一级的临界失效元，可以大大缩小搜索范围。依据上述原则确定每一级的临界失效元，直到满足整个结构系统失效的准则，最终形成了高效识别结构系统主要失效模式的方法。从结构系统可靠性分析基本原理出发，通过单元失效事件与正态空间映射关系，研究了多个单元失效与一个单元失效事件相关程度的精确表述方法；分析多单元联合失效时状态矢量的变化规律；通过利用等效状态矢量描述多单元联合失效的方式，将一个单元与多单元间相关性分析问题转化为一个单元状态矢量与多个单元等效状态矢量间夹角余弦的计算问题，建立一个与多个单元间及主要失效模式间相关系数的计算方法。最终建立了结构系统疲劳可靠性分析方法，并编制了一套相应的计算机程序。并针对某航空发动机的涡轮叶片疲劳可靠性进行了分析，计算了涡轮叶片的疲劳可靠度和失效概率；对张弦双向网格型单层柱面网壳在承载力失效和变形失效两种失效形式下的的可靠度开展了研究，计算了失效概率、可靠指标及其灵敏度和相关性；对潜孔弧形钢闸门的可靠性进行了研究，计算了潜孔弧形钢闸门的可靠度，并对输出变量进行了灵敏度分析。. 本项目的研究成果可为结构系统疲劳可靠性提供理论依据，奠定了结构系统疲劳可靠性分析的理论基础。本项目编制的结构系统疲劳可靠性计算机程序适用于分析金属结构系统的疲劳可靠性问题，对解决工程中的疲劳可靠性问题具有较好的应用前景。