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.