Shape sensitivity analysis of a quasi-electrostatic piezoelectric system in multilayered media - Leugering, Günter; Novotny, A. A.; Perla Menzala, G.; Sokolowski, J. (Mathematical Methods in the Applied Sciences, 2010)
The optimization of shape and topology of piezo-patches or layered piezo-electrical material attached to structural parts, such as 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 optimization with the SIMP-method, time-varying piezoelectric material has not been investigated with respect to the 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 with a class of shape functional. More general layers can be dealt with similar approach.