Aerothermoelastic analysis of imperfect FG cylindrical shells in supersonic flow

Abstract

The supersonic panel flutter of functionally graded cylindrical shells under thermal loadings is investigated by considering the effects of various axisymmetric and asymmetric geometric imperfections. The problem is formulated using a nonlinear first-order shear deformation theory of shells with the first-order aerodynamic piston theory. The temperature is assumed to vary in the thickness direction according to the steady-state heat conduction equation. The semi-analytical finite element method (FEM), based on the field consistency redistribution approach is used to obtain discretized nonlinear aeroelastic equations. In the process of FEM, the imperfection functions are also discretized and efficiently approximated by the Hermitian polynomials in order to facilitate the required integrations. For analysis purpose, the deformations and stresses induced by the temperature rise are first computed by solving the nonlinear static aerothermoelastic equations using the Newton-Raphson method. The pseudo-arclength continuation method is also employed to detect the possible snap-through of the shell. The linearized stability equation about the equilibrium state is then used for determining the flutter boundaries. Numerous parametric studies are conducted to examine the effects of temperature rise and imperfections on the flutter boundaries, which show considerable effects of imperfections on changing the trend of variation of the flutter pressure with temperature.