On shape optimization for an evolution coupled system

Guenter Leugering (1) , A.A. 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

A shape optimization problem in three spatial dimensions for an elasto-dynamic piezoelectric body coupled to an acoustic chamber is introduced. Well-posedness of the problem is established and first order necessary optimality conditions are derived in the framework of the boundary variation technique. In particular, the existence of the shape gradient for an integral shape functional is obtained, as well as its regularity, sufficient for applications e.g. in modern loudspeaker technologies. The shape gradients are given by functions supported on the moving boundaries. The paper extends results obtained by the authors, where a similar problem was treated without acoustic coupling.

Mots clés: shape sensitivity analysis; piezoelectricity; electromechanical interaction

Domaines: Equations aux dérivées partielles [math.AP]

Guenter Leugering, A.A. Novotny, Augusto Perla Menzala, Jan Sokolowski. On shape optimization for an evolution coupled system. Applied Mathematics and Optimization, 2011, 64 (3), pp.441-446. ⟨10.1007/s00245-011-9148-7⟩. ⟨hal-00609020⟩