Generation of correlated stress time histories from continuous turbulence Power Spectral Density for fatigue analysis of aircraft structures

The main purpose of the present work is to develop an efficient computational method for generating correlated stress time histories for aircraft structures under gust loads. Random gusts in any direction, which lead to random multiaxial loads on the aircraft structure are considered. A direct temporal simulation of stress using a finite element model is not possible due to computational burden. In order to overcome this, a new and efficient method based on Power Spectral Density functions (PSD) of stress is proposed. Since the PSD of the various stress components have not previously been correlated, a result enabling the direct generation of the correlation between them has been established, which is crucial for fatigue and damage tolerance analysis in several dimensions. Validation is performed by comparison with a direct (and costly) temporal simulation as well as Rice’s formulas. An example on a long range aircraft illustrates the relevance of the proposed approach. Although this method is presented with an application on a two dimensional stress tensor, it should be noted that it could be straightforwardly extended to any linear system with multiple input and output.