Reliability and nonlinear supersonic flutter of uncertain laminated plates

Abstract

It is the intent of this paper to study the geometrically nonlinear supersonic flutter characteristics of laminated composite thin-plate structures using a 48 degree-of-freedom rectangular plate element developed on the basis of the classical lamination theory. The aerodynamic pressure due to supersonic potential flow is simplified using the quasisteady first-order piston theory. Another intent is to study the reliability of laminated thin plates with structural uncertainties due to possible variabilities that occurred during the fabricating process. Interactive effects between the in-plane load and aerodynamic pressure for the uncertain plates are also studied. The stochastic finite element formulation is accomplished by including the effects of structural uncertainties. The stochastic solution procedure is based on the mean-centered second-moment perturbation technique. To evaluate the validity and to demonstrate the applicability of the present developments, a series of nonlinear free vibration and supersonic flutter analyses of isotropic and laminated composite thin plates are performed. The results quantify the effects of geometric nonlinearity on the mechanical behavior and structural reliability of the present laminated plates. Efforts are made to interpret the results so as to provide physical insight into the problems. Conversely, the present method and results may help to provide limits for the random variables to control the fabrication process.