适用于含多个隐式极限状态方程的飞机结构系统安全分析新方法

工程复杂随机结构的概率安全分析中，最重要的两个步骤是建立所有失效模式的极限状态方程和计算所建立极限状态方程的失效概率。一般来说大型复杂工程结构的极限状态方程都是隐式的，且当材料参数、结构参数和外载荷等均为随机变量时，极限状态方程均为非线性的，为此文中提出了建立真实复杂结构多模式隐式极限方程的等效方法。该方法对于单个极限状态方程采用在均值点展开成线性项和高次项修正的方式，在概率等效的基础上，建立起原非线性隐式极限状态方程的概率等效线性显式极限状态方程。当结构系统所有极限状态方程都建立了其等效显式线性极限状态方程后，即可利用可得的可靠性分析方法来计算结构系统的等效失效概率。所提方法被用于真实飞机结构翼身连接接头的强度刚度多模式可靠性分析，与迭代响应面法计算结果的对比表明，所提方法具有较高的精度。并且所提方法可以与任何标准有限元程序相结合，而标准有限元程序是当今处理结构力学分析与设计的强有力的工具，文中方法提供了力学分析与概率安全分析相结合的合理连接，其应用前景将是十分广泛的。

A new safety analysis method for aircraft structural system with multiple implicit limit state equations

The two important steps for probabilistic safety analysis of the complex stochastic structure are identification of limit state equations in failure modes and calculation of failure probability.In general,the limit state equations of the large scale complex structure do not have explicit expressions.When the physical properties,geometrical parameters and loading are basic random variables,the limit state equations are nonlinear.In order to analyze the probability safety for this kind of complex structure,an new equivalent method was presented for a single implicit limit state.The advanced-mean-value-first-order method was employed to obtain the cumulative probability based on the linear expansion of the real limit state at the mean value point and the correction of the higher order terms.An equivalent linear limit state to the actual nonlinear implicit one was established on the criterion of the equal probability.After the equivalent limit states for all implicit nonlinear limit states were established,the equivalent failure probability of the structure system could be computed by the available methods.The presented method was applied to analyze the reliability of the wing-fuselage joint structure in a real aircraft.Comparison of the presented methods with the response surface method shows that the relative errors for these two methods are small.The presented method provides an incorporation of probabilistic analysis and the standard finite element software.Combined with the powerful mechanics tool,which is familiar to the engineering designer,the presented method can be definitely accepted as an attractive tool for the reliability analysis of the real complex structure.