Nonlinear dynamic analysis and optimization of sandwich plate and shell panels with auxetic core and functionally graded Zr-MgO/Al facesheets

Abstract

In the present investigation, the geometric parameters (rib thickness, inclined cell angle, vertical cell rib length, and inclined cell rib length) of auxetic honeycomb core and material parameters (volume fraction coefficient) of the functionally graded Zr-MgO/Al facesheets of the sandwich plate and shell panels are optimized for the first time. The dynamic analysis is carried out considering a higher-order shear deformation theory and employing a $C_0$ eight-noded isoparametric element with nine degrees of freedom per node. The material properties of the functionally graded material (FGM) facesheets are graded in the thickness direction according to a basic power law distribution in terms of the volume fractions of the constituents. The artificial bee colony algorithm is used to optimize volume fraction coefficient and different parameters of the auxetic core of the sandwich panel. The mechanical properties of the original material and the geometrical features of the unit cells are used to determine the mechanical properties of the auxetic core. The equivalent elastic parameters and density of facesheets are obtained using two micromechanical models i.e., rule of mixture (RM) and Mori–Tanaka (MT) methods. The analysis is further extended to nonlinear vibration analysis of FGM sandwich plate and shell panels. Geometrical nonlinearity is taken into consideration using the von Kármán type nonlinear strain–displacement equations.