Reliability-Based Aircraft Structural Design Pays, Even with Limited Statistical Data

摘要

Probabilistic structural design tends to apply higher safety factors to inexpensive or lightweight components, because it is a more efficient way to achieve a desired level of safety. We show that even with limited knowledge about stress probability distributions, we can increase the safety of an airplane by following this paradigm. We find that a small perturbation of the deterministic design is sufficient to maximize safety for the same weight. The structural optimization for safety of a representative system composed of a wing, a horizontal tail, and a vertical tail is used to demonstrate the paradigm. We find that moving a small amount of material from the wing to the tails leads to substantially increased structural safety. Because aircraft companies often apply additional safety factors beyond those mandated by the Federal Aviation Administration, this opens the door to obtaining probabilistic designs that also satisfy the Federal Aviation Administration code-based rules for deterministic design. We also find that the ratio of probabilities of failure of the probabilistic design and the deterministic design is insensitive to even very large errors in the stress probability distribution or probability-of-failure estimate of the deterministic design. Finally, we find that for independent components subject to the same failure mode, the probabilities of failure at the probabilistic optimum are approximately proportional to the weight. So a component that is 10 times lighter than another should be designed to be about 10 times safer. This phenomenon is proved for normal distributions of stress and failure stress, but was found in an example to approximately hold also for the lognormally distributed stress.