3D FEM analysis of piezoelectric inclusions in the plate with varied supports and materials

Abstract

The purpose of this article is to present a finite element method solution that consists in the development of numerical models for smart composite materials with inclusions made of piezoelectric materials embedded in a non-piezoelectric matrix with varied support conditions. The plate is subjected to bending force from its upper surface. The analysis of the electrostatic problem is investigated across eight distinct support conditions, considering a range of materials. For all support conditions, the cases where the plate comprises a single piezoelectric inclusion (Problem 1), two different types of twin piezoelectric inclusions (Problem 2-3), and quadruplet piezoelectric inclusions (Problem 4) are discussed separately to obtain maximum electric potential.In each instance, the total volume of inclusions within the plate remains consistent. The piecewise homogeneous body model is used in the mathematical formulation of the problems within the framework of the exact 3D equations of the electroelasticity theory. Ideal contact conditions exist at the interface between the matrix material and the piezoelectric inclusions. This study constitutes the first attempt to quantify the influence of various boundary conditions and the quantity of piezoelectric inclusions within the plate on the electric potential generated by these inclusions, employing the three-dimensional exact equations of electroelasticity theory. The results of the comparison for the four specified problems, examining the impact of different support conditions, matrix materials, inclusion materials, and certain geometric characteristics of the plate, are provided and analyzed. It is established that the position, material, and quantity of piezoelectric inclusions considerably affect the electric potential, and the boundary conditions at the front and back surfaces of the plate significantly influence the variation in electric potential more than those at the lateral surfaces. It is necessary to fasten more the front and back surfaces in order to get a high electric potential.