An analytical solution for the static bending of smart laminated composite and functionally graded plates with and without porosity

Abstract

In this paper, an analytical solution for smart laminated composite and functionally graded material plates with and without through-thickness porosity is presented. The kinematics of the deformation in smart structures is modelled through the newly proposed five non-polynomial higher-order shear deformation theories. The relative performance and accuracy of the different theories are assessed for the static bending response of the smart structures under a combined electromechanical loading. The proposed theories assume a nonlinear variation of the transverse shear strain through the thickness of the plate with transverse shear stress-free top and bottom surfaces. The governing differential equations of the plate derived through Hamilton’s principle are solved by Navier’s solution technique with simply supported boundary conditions. To demonstrate the accuracy and applicability of the proposed higher-order shear deformation theories, a wide range of numerical examples for static bending under mechanical and electrostatics loads are considered. The accuracy of the present theories is compared against the three-dimensional elasticity solution, and thereafter, several benchmark solutions for the functionally graded plates with and without porosity are reported. © 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.