Three-dimensional aero-thermo-elasticity analysis of functionally graded cylindrical shell panels

Abstract

In the present paper, the aero-thermo-elastic behavior of a finite (three-dimensional) cylindrical curved panel geometry made from functionally graded material under high supersonic airflow is investigated. A generalized differential quadrature formulation is adopted while a steady-state through-the-thickness thermal field is also assumed. The geometry curvature and structural nonlinearity effects are included based on von Karman–Donnell strain–displacement relations. The nonlinear piston theory of third order is utilized in order to predict the unsteady aerodynamics loads induced from surrounding supersonic air stream. The functionally graded material is considered with temperature-dependent properties distributed in the thickness according to a power law function. Derived from the equilibrium equations, the aero-thermo-elastic governing equations are reduced to number of ordinary differential equations through using of the generalized differential quadrature method where the structure response is derived using fourth-order Runge–Kutta technique. The contribution of some parameters including flow Mach number, flow dynamic pressure, thickness temperature gradient, and functionally graded material volume fraction index on the flutter response as well as route-to-chaos behavior are reviewed. The calculated results are compared with those available in the literature wherever available and the accuracy and quality of the adopted generalized differential quadrature formulation in analyzing the aero-thermo-elastic behavior of three-dimensional functionally graded curved panels is shown. It reveals that using a three-dimensional approach, if any of Mach number and panel’s upper surface temperature is increased, the route-to-chaos behavior is reached through quasi-periodic motions.