Stochastic dynamic analysis of composite plates in thermal environments using nonlinear autoregressive model with exogenous input in polynomial chaos expansion surrogate

Abstract

The application of composite materials has increased manifolds in aerospace and high-speed vehicle industries, where structures experience dynamic loads along with temperature variation. To ensure safety of these structures, the stochastic dynamic analysis in varying thermal environments is essential. The generalized polynomial chaos (gPC) expansion method is a well-known metamodel used to quantify uncertainties in engineering systems instead of using the direct Monte Carlo simulation. Though the gPC expansion method is used extensively for engineering systems, its classical version has some limitations while implementing in dynamical systems. The accuracy of the gPC expansion method reduces in delayed time domain and can be improved to some extent by increasing the order of polynomial, which though is computationally intensive. Furthermore, the classical gPC expansion method is suitable for low-dimensional problems having independent random parameters. To overcome these limitations in the classical gPC expansion method, a system identifier, i.e., nonlinear autoregressive model with exogenous input (NARX) is coupled with it to avoid response degeneration in delayed time domain. The temperature-dependent material properties of composite lamina can be random and correlated, however the classical gPC expansion method is unable to accommodate the correlated random parameters. To address these challenges, the NARX-gPC expansion method is modified to conduct stochastic dynamic analysis of composite plates using correlated random material properties of the composite lamina in varying thermal environments. The study indicates that the correlation has a significant effect on the stochastic dynamic response at low and high temperatures for cross-ply laminates in comparison with angle-ply laminates, which is not captured through uncorrelated random material properties. The prediction efficiency of the developed surrogate by using the adaptive NARX-gPC expansion method is established even though it is trained using data in a shorter time domain, thereby computational performance is enhanced. Additionally, this surrogate is implemented effectively for higher order randomness in the input parameters.