Finite Element Models for Linear Electroelastic Dynamics

Abstract

In the last decades, much attention has been focused on finite element modeling of electroelastic structural elements (see for example the survey in [1]). For most contributions in the covered literature, the reference variational framework is the extended Hamilton’s principle and the finite element formulations involve mechanical displacement and electric potential as independent variables. Although these conventional finite element models are the most used in practice, they are often too stiff and susceptible to mesh distortion. To improve element accuracy, bubble or incompatible modes have been used for displacement and electric potential. An attractive alternative to enhance element performance is offered by mixed variational formulations [2]–[4]. Recently, a mixed approach has been successfully employed by Cannarozzi and Ubertini [5] to develop hybrid finite elements for static analysis, which involve stress and electric flux density as additional independent variables. These elements have been classified as hybrid in the sense of the original hybrid model proposed by Pian [6] for elasticity. In fact, the additional variables must satisfy locally the field balance equations and the corresponding primary variables (displacement and electric potential) turn out to be defined on the element boundary only. At the interelements, continuity requirements on the additional variables are relaxed, so that the parameters of their approximations can be condensed out at the element level. This leads to finite element equations involving only nodal displacements and electric potentials, which can be handled using standard finite element procedures.