Analysis of coupling effects in FGM piezoelectric plates by a meshless method

摘要

In this paper we derive a unified formulation for bending of piezoelectric plates with taking into account 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 complies the rule of mixture. For numerical solution of a rather complex boundary value problems a strong form meshless 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 lower order derivatives. The time integration is carried out by the Wilson theta- method. Results of several numerical experiments are presented for illustration of coupling effects in bending of FGPM plates under stationary and/or transient voltage loading.