Stochastic dynamic analysis of multi-layer functionally graded material cylinders using direct probability integral method with improved smoothing technique

Abstract

Uncertainties are inherently inevitable in the application of functionally graded materials (FGMs) structures. Existing analysis methods face challenges in terms of accuracy and efficiency when addressing these uncertainties, especially for dynamic problems. To this end, this paper proposes a direct probability integral method with improved smoothing technique (DPIM-IST) for the stochastic dynamic analysis of FGM cylinders. Subsequently, an adaptive framework is constructed based on the maximum entropy principle to determine the variable smoothing parameters at each representative point. To search for the proper smoothing parameter vector, a hybrid grey wolf optimizer is employed, which combines the grey wolf optimizer and BFGS method. Moreover, the dynamic responses at each representative point are evaluated by utilizing the differential quadrature method and Newmark algorithm. Several numerical and multiphase and multi-layer FGM hollow cylinder examples, involving nonlinear performance functions with Gaussian and non-Gaussian parameters, are investigated to validate the accuracy of the proposed DPIM-IST.