Optimization of the Polarization Profile of Conical-Shaped Shells Piezoelectric Sensors

Conical shell structures are frequently submitted to severe static and dynamic mechanical loads that can result in situations that affect the service of the systems that are part of, or even cause catastrophic failures. For this reason, a common solution is to design an active deformation control system, usually using piezoelectric patches strategically distributed along the surface of the shell structure. Moreover, these elements may be part of an energy recovery system. This paper details the methodology to topologically optimize the placement of piezoelectric elements through a characteristic function, analysing static and free vibration loading cases by means of the finite element method. Then, the optimal arrangement of the electrode with different polarization profiles is distributed throughout the entire structure. The nature of the loading cases studied corresponds to a general situation where static loads and dynamics vibration are considered. The objective function of the problem only depends linearly on the displacement fields, and therefore, the optimal electrode profile can be obtained for any combination of loads. As a consequence, this technique allows for maximising the electric charge obtained, which results in a greater capacity for monitoring, actuation and/or energy harvesting.