Multi-objective structural optimisation of piezoelectric materials

Abstract

In this paper we use computational structural optimisation to consider the multi-objective design of piezoelectric materials for both stiffness and piezoelectric properties. We design new single-poled piezoelectric materials to maximise a linear combination of the effective hydrostatic coupling constant, d̄h, and effective bulk modulus, B̄E. We utilise the Solid Isotropic Material with Penalisation (SIMP) method and derive the sensitivities of the homogenised piezoelectric properties using an adjoint method. Our optimisation results suggest that the hydrostatic coupling constant and bulk modulus cross-property space is convex. Furthermore, the optimised materials have competitive piezoelectric figures of merit when the optimisation objective prioritises d̄h, and this indicates their suitability for sensor and hydrophone applications. While computational design of piezoelectric materials is a sparse research field, our work demonstrates the potential of structural optimisation for discovering piezoelectric meta-materials with enhanced properties.