A Simulation-Based Fatigue Life Estimation Method for Nonlinear Systems under Non-Gaussian Loads

In the fields of durability and stochastic structural dynamics, it is customary to focus on linear structures subjected to Gaussian excitations. However, real-world engineering systems often exhibit nonlinear behavior and are exposed to non-Gaussian loads. Calculating fatigue life for such nonlinear systems under non-Gaussian loading presents many challenges such as complex nonlinear dynamics, multifaceted statistical characteristics, and time-dependent effects resulting in a very high computational effort. To overcome these hurdles, this research uses non-Gaussian Karhunen-Loeve expansion (NG-KLE) to not only predict the expected fatigue life but also obtain the Probability Density Function (PDF) of fatigue life. It integrates a sub-domain-based technique to significantly reduce the computational demands while preserving accuracy, by efficiently obtaining long time trajectories of random processes. This development is very useful for excitation signals that far exceed the process correlation length. The NG-KLE method serves as the main tool for characterizing the excitation process by estimating its non-Gaussian marginal distribution and autocorrelation function. A Karhunen-Loeve (KL) expansion is executed only for the first subdomain, and then extended to subsequent subdomains by establishing correlations between the KL expansion coefficients of adjacent subdomains. This innovative approach is adapted to non-Gaussian (NG) excitation, allowing for efficient characterization of both the input and output random processes using NG-KLE, enabling the generation of very long synthetic output random stress process samples. The fatigue life corresponding to each output stress trajectory contributes to the estimation of the PDF of fatigue life. The proposed generalized fatigue life estimation approach accommodates both Gaussian and non-Gaussian processes for both narrow and wide band signals. To demonstrate its effectiveness, we use a duffing oscillator system and a practical example involving a truck assembly modeled by the Finite Element Method (FEM).