In this paper, a novel approach to the design of piezoelectric plate and shell actuators using topology optimization is described. A new piezoelectric material model PEMAP-P (piezoelectric material with penalization and polarization) is proposed, which is an extension of the SIMP (solid isotropic material with penalization) model used for elastic materials. In addition to the pseudo-density ρ 1 , which describes the 'amount' of piezoelectric material in each finite element, a new design variable ρ 2 is introduced for the polarization of the piezoelectric material. The optimization problem consists in distributing the piezoelectric actuators in such a way as to achieve a maximum output displacement in a given direction at a given point of the structure, while simultaneously minimizing the structural compliance. Sequential linear programming (SLP) is used to solve the optimization problem. Examples are given demonstrating the potential of the proposed approach for the optimal design of piezoelectric actuators for multi-layer plate and shell structures.

Abstract. Among other applications piezoelectric transducers are widely used for acoustic wave generation and as resonators. These applications require goals in the transducer design such as high electromechanical energy conversion for a certain transducer vibration mode, specified resonance frequencies and narrowband or broadband response. In this work, we have proposed a method for designing piezoelectric transducers that tries to obtain these characteristics, based upon topology optimization techniques and the finite element method (FEM). This method consists of finding the distribution of the material and void phases in the design domain that optimizes a defined objective function. The optimized solution is obtained using sequential linear programming (SLP). Considering acoustic wave generation and resonator applications, three kinds of objective function were defined: maximize the energy conversion for a specific mode or a set of modes; design a transducer with specified frequencies and design a transducer with narrowband or broadband response. Although only two-dimensional plane strain transducer topologies have been considered to illustrate the implementation of the method, it can be extended to three-dimensional topologies. Transducer designs were obtained that conform to the desired design requirements and have better performance characteristics than other common designs.

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This paper addresses manufacturing constraints by means of a unified projection-based approach restricting the range of solutions to the topology optimization problem. A domain of design variables is considered, which is projected in a pseudo-density domain to obtain the solution. The relation between domains is defined by the projection and variable mappings according to each manufacturing constraint of interest. The following constraints are considered: minimum member size, minimum hole size, symmetry, extrusion, pattern repetition, turning, casting, forging, and rolling.