Simultaneous determination of stochastic dynamic responses and reliabilities for geometrically nonlinear thin shells

Simultaneously determining the random vibration responses and dynamic reliabilities of thin shell coupling geometric nonlinearity and multisource uncertainties is an intractable task. A novel non-intrusive framework based on direct probability integral method (DPIM) is proposed in the present study, which offers an efficient and competitive solution tool to tackle this challenging issue. New framework incorporating DPIM with adaptive schemes can address efficiently stochastic dynamic responses and reliability determination of geometrically nonlinear thin shells in a unified way. Adaptive choosing strategy of the smoothing parameter of Dirac function and the number of representative points is adopted. Importantly, a judgment criterion is established to adaptively perform nonlinear theory and linear theory of large deflection for thin shell, which breaks the limitation of using a single nonlinear or linear theory and results in more accurate responses. Finally, several numerical examples demonstrate that the proposed framework possesses high accuracy and efficiency when compared to Monte Carlo simulation (MCS) and quasi-MCS for computing stochastic deflection and stress responses and dynamic reliabilities. The transform of probability density function of deflection responses from unimodal to bimodal distribution implies that the stochastic P-bifurcation occurs in random vibration of nonlinear thin shell. The remarkable effects of sound pressure level of noise excitation, power spectral density of random excitation, random parameter variability and boundary conditions on uncertainty quantification of thin shells are revealed.