Low-velocity impact response of functionally graded doubly curved panels with Winkler-Pasternak elastic foundation: An analytical approach

In this paper a nonlinear investigation is presented for impact response of functionally graded material (FGM) doubly curved panels which are resting on Winkler-Pasternak elastic foundation with simply supported end condition. The governing equations of the doubly curved panels are based on a Reddy's higher order shear deformation theory with the von Kármán-type of kinematic nonlinearity. Moreover, the effect of heat conduction is considered and material properties of panels are assumed to be temperature dependent and vary along the thickness according to Mori-Tanaka micromechanical model. In addition, by using a modified Hertz's contact law, the influence of material properties of the substrate layers on impact response is taken into account. The equations of motion are solved via an analytical procedure and a parametric polynomial solution is extracted. The influences of materials property gradient, initial velocity of the impactor, curvatures ratio, aspect ratio and the effect of elastic foundations on impact response of panels are discussed.