Bending analysis of five-layer curved functionally graded sandwich panel in magnetic field: closed-form solution

Abstract

In this paper, an exact closed-form solution for a curved sandwich panel with two piezoelectric layers as actuator and sensor that are inserted in the top and bottom facings is presented. The core is made from functionally graded (FG) material that has heterogeneous power-law distribution through the radial coordinate. It is assumed that the core is subjected to a magnetic field whereas the core is covered by two insulated composite layers. To determine the exact solution, first characteristic equations are derived for different material types in a polar coordinate system, namely, magneto-elastic, elastic, and electro-elastic for the FG, orthotropic, and piezoelectric materials, respectively. The displacement-based method is used instead of the stress-based method to derive a set of closed-form real-valued solutions for both real and complex roots. Based on the elasticity theory, exact solutions for the governing equations are determined layer-by-layer that are considerably more accurate than typical simplified theories. The accuracy of the presented method is compared and validated with the available literature and the finite element simulation. The effects of geometrical and material parameters such as FG index, angular span along with external conditions such as magnetic field, mechanical pressure, and electrical difference are investigated in detail through numerical examples.