Optimum design of flextensional piezoelectric actuators into two spatial dimensions

R Amigo (1) , S.M. Giusti (2) , A.A. Novotny (3) , E.C.N. Silva (1) , J. Sokolowski (4)

1 Department of Mechanical Engineering, Sao Paulo University
2 Universidad Nacional de Córdoba [Argentina]
3 LNCC / MCT - Laboratorio Nacional de Computação Cientifica [Rio de Janeiro]
4 IECL - Institut Élie Cartan de Lorraine

In control of distributed parameter systems the piezoelectric actuators are of com-mon use. The topology optimization of a multiphysic model in piezoelectricity is considered. The topological derivative of a tracking-type shape functional is derived in its closed form for the pur-pose of shape optimization of piezoelectric actuators. The optimum design procedure is applied to a micromechanism which transforms the electrical energy supplemented via its piezoceramic part into elastic energy of an actuator. The domain decomposition technique and the Steklov-Poincaré pseudo-differential boundary operator are employed in the asymptotic analysis of the shape func-tional defined on a part of the boundary of the elastic body under consideration. The proposed method of sensitivity analysis is general and can be used for the purpose of the shape-topological optimization for a broad class of multiphysics models. The numerical results confirm the efficiency of proposed approach to optimum design in multiphysics. 1. Introduction . In this paper we are interested in the optimal design of piezo-electric actuators, which consist of multi-flexible structures actuated by piezoceramic devices that generate an output displacement in a specified direction on the boundary of the actuated part [5, 27]. The multi-flexible structure transforms the piezoceramic output displacement by amplifying and changing its direction. This kind of mecha-nism can be manufactured at a very small scale. Therefore, the spectrum of appli-cations of such microtools becomes broader in recent years including microsurgery, nanotechnology processing, cell manipulation, among others. Yet, the development of microtools requires the design of actuated multi-flexible structures which are able to produce complex movements originated from simple expansion/contraction of the piezoceramic actuator. The performance of microtools can be strongly enhanced by optimizing the actuated multi-flexible structures with respect to their shape and their topology [6, 7, 8]. The shape sensitivity analysis of such coupled models has been fully developed in [19] and [18] for quasi-electrostatic layered piezoelectric devices and for non-stationary elastic, piezoelectric and acoustic coupled system, respectively. For the mathematical theory concerning coupled PDEs systems the reader may refer to e.g., [17, 20, 21]. However, a more general approach to deal with shape and topology optimization design is based on the topological derivative. In fact, this relatively new concept

Mots clés: Topology design AMS subject classifications 35J30; Steklov-Poincaré operator; Asymptotic analysis; 74P15; 74K20; Dirichlet-to-Neumann map; 49Q10; Do-main decomposition; Piezoelectric actuator; 49Q12; Topological derivative

Domaines: Mathématiques [math]

R Amigo, S.M. Giusti, A.A. Novotny, E.C.N. Silva, J. Sokolowski. Optimum design of flextensional piezoelectric actuators into two spatial dimensions. SIAM Journal on Control and Optimization, 2016, 54 (2), pp.760-789. ⟨10.1137/151004860⟩. ⟨hal-01103189⟩