Shape Sensitivity Analysis of a Quasi-Eletrostatic Piezoelectric System in Multilayered Media

Guenter Leugering (1) , Andre Novotny (2) , Augusto Perla Menzala (2) , Jan Sokolowski (3)

1 University of Erlangen Nuremberg, Department of Mathematics
2 LNCC / MCT - Laboratorio Nacional de Computação Cientifica [Rio de Janeiro]
3 IECN - Institut Élie Cartan de Nancy

The optimization of shape and topology of piezo-patches or layered piezo-electrical material attached to structural parts, like elastic bodies, plates and shells plays a major role in the design of smart structures, as piezo-mechanic-acoustic devices in loudspeakers or energy harvesters. While the design for time-harmonic motions is genuinely frequency-dependent, as has been reported in the literature in the context of density optimizaiton with the SIMP-method, time-varying piezoelectric material has not been investigated with respect to optimal design so far. Therefore, shape sensitivities for layered piezoelectric material and time-varying loads and charges are derived in this paper. In particular, we provide the shape-derivatives for nested piezo-layers associated to a class of shape functional. More general layers can be dealt with similarly.

Mots clés: piezoelectricity; electromechanical interaction; shape sensitivity analysis

Domaines: Equations aux dérivées partielles [math.AP]

Guenter Leugering, Andre Novotny, Augusto Perla Menzala, Jan Sokolowski. Shape Sensitivity Analysis of a Quasi-Eletrostatic Piezoelectric System in Multilayered Media. 2009. ⟨hal-00419760⟩