Bending of Piezo-Electric FGM Plates by a Mesh-Free Method

Abstract

Unified formulation for bending of elastic piezoelectric plates is derived with incorporating the assumptions of three plate bending theories, such as the Kirchhoff-Love theory, 1st order and 3rd order shear deformation plate theory. The functional gradation of material coefficients in the transversal as well as in-plane direction is allowed and the plate thickness can be variable. Both the governing equations and the boundary conditions are derived from the variational formulation of 3D electro-elasticity. For numerical solution a mesh-free method is developed with using the Moving Least Square approximation for spatial variations of field variables. The high order derivatives of field variables are eliminated by decomposing the original governing partial differential equations (PDE) into the system of PDEs with not higher than 2nd order derivatives. The numerical simulations are presented for illustration of coupling effects and verification of the developed theoretical and numerical formulations.