Evolutionary algorithm and boundary element method for solving inverse problems of piezoelectricity

Abstract

The piezoelectric phenomenon is widely uitilized in many devices, for example, sensors and actuators, micro-electro-mechanical systems (MEMS), transducers [5]. An analysis of piezoelectric devices requires a solution of coupled mechanical and electrical partial differential equations. In this paper the boundary element method (BEM) is implemented to solve the coupled field problem in piezoelectrics. The method allows the analysis by discretization of the boundary only [1]. The piezoelectric material is modelled as two-dimensional: homogenous, transversal isotropic, linear elastic and dielectric [3]. In most boundary value problems, the governing equations have to be solved with the appropriate boundary conditions [3]. These problems are called direct. However, when the boundary conditions are incomplete on a certain boundary part, the boundary value problems are generally ill-posed, then the existence, uniqueness and stability of the solution is not always guaranteed. These problems are inverse problems. In this paper the Cauchy problem is considered [3]. Another inverse problem is identification of the material constants. For considered two-dimensional case, the physical properties of the piezoelectric material depend on the nine material constants: four elastic constants, three piezoelectric constants and two dielectric constants. A relatively big number of the constants and difficulties in obtaining the gradient information, cause, that the identification problem of the piezoelectric material constants is quite complicated. To solve the inverse problems the distributed evolutionary algorithm is used [2], [4]. Numerical examples will be presented and they will show that the boundary element formulation with evolutionary algorithm gives an efficient computational intelligence tool for solving inverse problems of piezoelectricity.