Simultaneous Design of the Host Structure and the Polarisation Profile of Piezoelectric Sensors Applied to Cylindrical Shell Structures

Piezoelectric actuators and sensors are applied in many fields in order to produce forces or displacements with the aim of sensing, manipulating or measurement, among other functions. This study presents the numerical methodology to optimize the static response of a thick-shell structure consisting of piezoelectric sensors, based on the maximisation of the electric charge while controlling the amount of piezoelectric and material required. Two characteristic functions are involved, determining the topology of the sensor and the polarisation profile. Constraints over the reaction force are included in the optimisation problem in order to avoid singularities. The topology optimisation method is used to obtain the optimal results, where regularisation techniques (density filtering and projection) are used to avoid hinges. The minimum length scale can be controlled by the use of three different projections. As the main novelty, a displacement-controlled scheme is proposed in order to generate a robust algorithm for future studies including non-linearities.