近年来，复合材料层合板结构被广泛地应用于航空航天、军工、建筑工程等领域。但是，由于其几何尺寸的不准确性、材料参数的分散性、载荷环境的波动性等不确定性因素的影响，可能会对复合材料层合板结构的可靠性和安全性，以及系统的输出响应产生重大影响。由于复合材料层合板的层间粘结不良、外部应力集中等因素，当复合材料层合板结构的能量释放速率达到层间断裂韧性时，就会发生分层。因此对复合材料层合板结构的分层可靠性进行分析具有重要的意义。目前，对于复合材料层合板结构的可靠性分析主要是采用一阶可靠性方法(First Order Reliability Method, FORM)、二阶可靠性方法(Second Order Reliability Method, SORM)和重要性抽样方法(Importance Sampling, IS)等传统可靠性分析方法，并将其和蒙特卡罗模拟(Monte Carlo simulation，MCS)对比。但是，当复合材料结构不确定性维度高且复杂时，这些方法不仅计算效率太低，而且不能保证其计算精度。相比于传统的可靠性分析方法，可以利用基于自适应Kriging模型集成策略和主动学习函数结合蒙特卡罗模拟(Adaptive Kriging-based Monte Carlo Simulation, AK-MCS)的方法，对复合材料层合板结构进行可靠性分析。而直接概率积分方法(Direct Probability Integral Method, DPIM)具有更高的计算效率和精度，特别是对于高维度和复杂的可靠性分析问题。所以，本文采用AK-MCS方法和DPIM对模式I、模式II和混合I/II模式下的复合材料层合板结构分层的可靠度进行了研究。结果表明：DPIM和AK-MCS与传统可靠性分析方法相比具有更高的计算精度和计算效率，但是DPIM以其高效的计算效率脱颖而出，尽管其精度略低于AK-MCS，但在处理随机变量更多、非线性程度更高的混合I/II模式下的层合板结构分层的可靠性时展现出明显优势。综合考虑精度与时效性的平衡，DPIM能够准确地评估复合材料结构的可靠度，保障其在航天航空装备等领域的安全运行。
Abstract
In recent years, composite laminated structures have been widely used in fields such as aerospace, military, and construction engineering. However, the uncertainty factors such as inaccuracies in geometric dimensions, variability in material properties, and fluctuations in loading environments may significantly impact the reliability and safety of composite laminated structures, as well as the output responses of the systems. Due to factors such as poor interlaminar bonding and external stress concentrations, delamination occurs in composite laminated structures when the rate of energy release reaches the interlaminar fracture toughness. Therefore, analyzing the delamination reliability of composite laminated structures is of significant importance. Currently, the reliability analysis of composite laminated structures mainly employs traditional methods such as first-order reliability method (FORM), second-order reliability method (SORM), and importance sampling (IS), often compared with Monte Carlo simulation (MCS). However, when the uncertainty dimensions and complexities of composite structures are high, these methods not only demonstrate low computational efficiency but also fail to ensure sufficient accuracy in their calculations.Compared to traditional reliability analysis methods, the integration of an adaptive Kriging model strategy and active learning functions combined with Monte Carlo simulation can be used for the reliability analysis of composite laminated structures. In particular, the Direct Probability Integral Method (DPIM) offers higher computational efficiency and accuracy, especially for high-dimensional and complex reliability analysis problems. Therefore, this study employs the AK-MCS method and DPIM to investigate the delamination reliability of composite laminated structures under Mode I, Mode II, and Mixed Mode I/II conditions. The results indicate that both DPIM and AK-MCS offer higher computational accuracy and efficiency compared to traditional reliability analysis methods. However, DPIM stands out due to its efficient computational performance. Although its accuracy is slightly lower than that of AK-MCS, DPIM demonstrates significant advantages in assessing the delamination reliability of laminated structures under the more complex and nonlinear conditions of Mixed Mode I/II. Considering the balance between accuracy and timeliness, DPIM can effectively evaluate the reliability of composite structures, ensuring their safe operation in fields such as aerospace and aviation equipment.
关键词
复合材料层合板 /
自适应Kriging模型 /
直接概率积分方法 /
可靠性分析
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Key words
Composite laminates；Adaptive Kriging method；Direct probability integral method /
Reliability analysis
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