On graded elements for multiphysics applications

Abstract

Recently, the functionally graded material (FGM) concept has been explored inpiezoelectric materials to improve properties and to increase the lifetime of bimorphpiezoelectric actuators. For instance, elastic, piezoelectric, and/or dielectric properties maybe graded along the thickness of a piezoceramic. Thus, the gradation of piezoceramicproperties influences the performance of piezoactuators. The usual FGM modelling usingtraditional finite element formulation and discretization into layers gives a highlydiscontinuous stress distribution, which is undesirable. In this work, we focus onnonhomogeneous piezoelectric materials using a generalized isoparametric formulationbased on the graded finite element concept, in which the properties change smoothly insidethe element. This approach provides a continuum material distribution, whichis appropriate to model FGMs. Both four-node quadrilaterals and eight-nodequadrilaterals for piezoelectric FGMs were implemented using the graded finite elementconcept. A closed form two-dimensional analytical model of piezoelectric FGMs isalso developed to check the accuracy of these finite elements and to assess theinfluence of material property gradation on the behavior of piezoelectric FGMs. Thepaper discusses and compares the behavior of piezoelectric graded elements underfour loading conditions with respect to the analytical solutions (derived in thiswork) considering exponential variation of elastic, piezoelectric, and dielectricproperties separately. The analytical solutions provide benchmark problems to verifynumerical procedures (such as the finite element method and the boundary elementmethod).