A level set approach for optimal design of smart energy harvesters

The proliferation of Micro-Electro-Mechanical Systems (MEMS), portable electronics and wireless sensing networks has raised the need for a new class of devices with self-powering capabilities. Vibration-based piezoelectric energy harvesters provide a very promising solution, as a result of their capability of converting mechanical energy into electrical energy through the direct piezoelectric effect. However, the identification of fast, accurate methods and rational criteria for the design of piezoelectric energy harvesting devices still poses a challenge. In this work, a level set-based topology optimization approach is proposed to synthesize mechanical energy harvesting devices for self-powered micro systems. The energy harvester design problem is reformulated as a variational problem based on the concept of topology optimization, where the optimal geometry is sought by maximizing the energy conversion efficiency of the device. To ensure computational efficiency, the shape gradient of the energy conversion efficiency is analytically derived using the material time derivative approach and the adjoint variable method. A design velocity field is then constructed using the steepest descent method, which is further integrated into level set methods. The reconciled level set (RLS) method is employed to solve multi-material shape and topology optimization problems, using the Merriman-Bence-Osher (MBO) operator. Designs with both single and multiple materials are presented, which constitute improvements with respect to existing energy harvesting designs.