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分析结构的数学失效过程,给出随机结构系统可靠性分析流程框图。对具有多随机变量结构可靠性分析中的力学模型选取、安全余量的建立、安全余量的敏度分析等问题进行了研究。对于空间理想弹塑性梁板体系,以随机有限元计算结构系统的响应量;通过对主要失效模式方程的线性化研究,计算各主要失效模式安全余量之间的相关系数;进行安全余量与可靠性指标对随机变量的敏度分析,推导了基于Taylor展开的随机有限元的可靠度迭代公式中的功能函数对点位移的导数表达式。文章最后以翼盒结构为例,分析结果表明,研究可提高具有多随机变量结构系统可靠性分析的计算精度,为复杂结构系统可靠性分析奠定一定的理论基础。
Analyze the mathematic failure process of the structure and give the block diagram of the reliability analysis of the random structure system. The mechanical model selection, the construction of safety margin and the sensitivity analysis of safety margins in structural reliability analysis with multiple random variables are studied. For the space ideal elastic-plastic beam plate system, the response of the structural system is calculated by stochastic finite element method. The correlation coefficient between the safety margin of each main failure mode is calculated through the linearization of the main failure mode equations. The safety margin and Reliability Index Based on the sensitivity analysis of random variables, the derivation of function derivative to point displacement in the reliability iteration formula of stochastic finite element based on Taylor expansion is derived. Finally, taking the wing box structure as an example, the analysis results show that the research can improve the calculation accuracy of the reliability analysis of the structural system with multiple random variables, and lay a theoretical foundation for the reliability analysis of complex structural systems.