RELIABILITY OF UNCERTAIN LAMINATED SHELLS DUE TO BUCKLING AND SUPERSONIC FLUTTER

An objective of this paper is to study the supersonic flutter characteristics of initially compressed, laminated, thin shell structures using a 48-degree-of-freedom, doubly curved, quadrilateral, laminated, thin shell finite element developed on the basis of the Kirchhoff-Love thin shell theory and classical lamination theory. The aerodynamic pressure due to supersonic potential flow is described by the piston theory. Another objective of this paper is to study the reliability of initially compressed, laminated thin shells with structural uncertainties due to variabilities that occurred during fabrication. The two failure criteria considered are buckling and supersonic flutter. Interactive effects between the middle surface load and aerodynamic pressure for the uncertain shells are also studied. For buckling analysis, the structural uncertainties include modulus of elasticity, thickness, and fiber orientation of individual lamina, as well as geometric imperfections of the entire shell. For flutter analysis, additional uncertainties of mass densities of both the shell and the air, as well as the amplitudes of uniformly and linearly distributed middle surface loads, are considered. The stochastic element formulation is defined by including the effects of structural uncertainties and random middle surface loads. The stochastic solution procedure is developed based on the mean-centered, second-moment perturbation technique. To evaluate the validity and to demonstrate the applicability of the present formulation and solution procedure, a series of vibration, buckling, and supersonic flutter analyses of thin shells with structural uncertainties under random middle surface loads are performed. The results quantify the effects of these uncertain parameters on the reduction of the structural reliability and stability boundaries of initially compressed laminated shells. The results also provide physical insight into such design and fabrication problems with practical significance.