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摘要:
飞行器结构安全系数是设计载荷与使用载荷之比，传统的统一安全系数设计方法取值主观、难以量化不确定性，易导致设计保守，制约先进飞行器性能。为解决这一限制，在保证可靠性设计要求的前提下，更好地挖掘材料性能与设计空间，有必要发展一种分区差异化安全系数设计方法。运用概率可靠性设计优化理论来研究结构系统的不确定性，建立结构可靠度与分区差异化安全系数之间的映射关系，提出平衡安全性与经济性的分区差异化安全系数设计方法。以工程型号简化的翼尖结构等为验证算例，显示在满足结构强度可靠度99%设计要求前提下，实现了结构绝大部分子区域的分区差异化安全系数均小于统一安全系数1.45，从而使得结构设计质量相对更轻达3.926 kg。
Abstract:The structural safety factor of an aircraft, defined as the ratio of design load to service load, is a key parameter in aircraft design. Traditional design methods rely heavily on engineering experience, leading to subjective safety factor values and insufficient objectivity in quantifying uncertainties. For advanced aircraft requiring refined design, the uniform safety factor applied across all components results in overly conservative designs that limit ultimate flight performance. In order to solve this limitation, it is necessary to develop a sub-regional differentiated safety factor design method to better explore the material properties and design space on the premise of ensuring the reliability design requirements. In this paper, probabilistic reliability design optimization theory is used to study the uncertainty of the structural system, and the mapping relationship between structural reliability and sub-regional differentiated safety factors is established, and the design method of sub-regional differentiated safety factors is developed. Using the simplified engineering model of the wing-tip structure as an example, it is demonstrated that, assuming the design requirement of 99% structural strength reliability is met, the sub-regional differentiated safety factors in the majority of the structure's subregions are less than the unified safety factor of 1.45, resulting in a relatively lighter design weight of up to 3.926 kg.
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图 1 典型飞机结构不同子区域组件的安全系数
Figure 1. Safety factors for components in different sub-regions of aircraft
图 2 基于结构可靠性的分区差异化安全系数设计过程
Figure 2. Process of sub-regional differentiated safety factors design based on structural reliability
图 4 统一安全系数方法与分区差异化安全系数方法的可行设计域
Figure 4. Feasible region of unified safety factor and sub-regional differentiated safety factor scheme
图 5 分区差异化安全系数对子区域1结构可靠度的影响
Figure 5. Feasible region of unified safety factor and sub-regional differentiated safety factor scheme
图 6 分区差异化安全系数对两子区域结构可靠度的影响
Figure 6. Influence of sub-regional differentiated safety factors of two sub-regions on reliability index
图 7 双层嵌套优化设计问题的参数映射关系
Figure 7. Parameter relationships of two-layer nested optimization
图 8 非正态分布的等价正态变换
Figure 8. Equivalent normal transformations of non-normal distributions
图 9 分区差异化安全系数与可靠性之间的映射关系
Figure 9. Relationship about reliability and sub-regional differentiated safety factors
图 10 分区差异化安全系数设计的主要流程
Figure 10. Main procedure of sub-regional differentiated safety factors design
图 12 结构强度安全系数迭代曲线
Figure 12. Structural strength safety factor iteration solution curves of wing
图 13 结构刚度安全系数迭代曲线
Figure 13. Structural stiffness safety factor iteration solution curves of wing
图 16 翼尖结构最大位移的概率密度分布
Figure 16. Probability density distribution of maximum displacement of wing tip structure
表 1 飞行器翼面结构的细节参数
Table 1. Detailed information of wing
弹性模量
$ E $/GPa泊松比 密度/
(kg·m−3)边界条件 后掠角/(°) 强度极限
$ {\sigma }_{\max } $/MPa110 0.33 4510 根部固支 40 ≤465 
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表 2 翼面结构分区差异化安全系数设计结果
Table 2. Results of sub-regional differentiated safety factors design
子区域 $ i $ 结构可靠度$ \eta _{i}^{j} $ 安全系数 $ f_{i}^{j} $ 强度$ \eta _{i}^{1} $ 刚度$ \eta _{i}^{2} $ 强度$ f_{i}^{1} $ 刚度$ f_{i}^{2} $ $ i=1 $ 1 0.9529 1.3027 1.2890 $ i=2 $ 0.9684 1 1.3434 1.3124 $ i=3 $ 1 1 1.3577 1.3561 $ i=4 $ 0.9508 0.9536 1.1701 1.2248
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表 3 统一安全系数设计与分区差异化安全系数设计结果对比
Table 3. Results comparison of traditional safety factor design and sub-regional differentiated safety factors design
子区域 $ i $ 安全系数$ f_{i}^{1} $ 结构可靠度$ R_{i}^{1} $ 传统安全
系数设计分区差异化
安全系数设计传统安全
系数设计分区差异化
安全系数设计1 1.45 1.249 1 0.999100 2 1.45 1.152 1 0.999720 3 1.45 1.305 1 0.995530 4 1.45 1.096 1 0.994800 5 1.45 1.311 1 0.996470 6 1.45 1.152 1 0.997200 7 1.45 1.297 0.99534 0.990740 8 1.45 1.413 1 0.999400 9 1.45 1.299 1 0.999940 10 1.45 1.210 1 0.994090 11 1.45 1.404 1 0.994930 12 1.45 1.261 1 0.993180 13 1.45 1.347 1 0.994490 14 1.45 1.449 1 0.996570 15 1.45 1.500 1 0.996160 16 1.45 1.500 1 0.994830 17 1.45 1.302 1 0.996290 18 1.45 1.402 1 0.997290 19 1.45 1.454 0.99697 0.990880 20 1.45 1.189 1 0.991960 21 1.45 1.246 1 0.992610 22 1.45 1.307 0.99410 0.990072 23 1.45 1.253 1 0.999970 24 1.45 1.352 1 0.991330 25 1.45 1.208 1 0.991290 26 1.45 1.247 1 0.999390 27 1.45 1.500 1 0.999110 28 1.45 1.451 1 0.999350 29 1.45 1.246 1 0.999190 30 1.45 1.303 1 0.998580 31 1.45 1.450 1 0.998380 32 1.45 1.401 1 0.999320
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表 4 统一安全系数设计与分区差异化安全系数设计结果质量对比
Table 4. Structural mass comparison of traditional safety factor design and sub-regional differentiated safety factors design
方法 结构质量/kg 统一安全系数设计 101.370 分区差异化安全系数设计 97.444
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