Classic finite elements for simulation of piezoelectric smart structures

Abstract

Several authors have focused on the construction of the adapted or specific finite elements to take into ac-count the electromechanical coupling of piezoelectric ma-terials, in adding the electric degrees of freedom DOF. The computation times can be expensive in this case. Some authors have eliminated the electric potential DOF by “compensation by condensation”. It can justify a gain computation time.This work shows that the classic finite elements (without electrical DOF) are sufficient for solving a thin piezoelectric smart structure. The classic finite elements (mechanical only) are sufficient, we must just introduce correctly the modified elasticity matrix and the electric force induced from imposed potential. The electric load is computed from the obtained displacement. We have shown that the modified terms are the same as those used in the “compensation by condensation” method. We have avoided the computation times by “compensation by con-densation” steps and sensibly reduced the computation time.