Multi-material topology optimization of piezoelectric composite structures for energy harvesting

Energy harvesting is an essential technology for enabling low-power, maintenance-free electronic devices, and thus has attracted much attention in recent years. In this paper, we propose a multi-material topology optimization approach for the design of energy harvesting piezoelectric composite structures. The energy conversion efficiency of piezoelectric composite structure is maximized by optimally distributing elastic, piezoelectric and void materials. To this end, a multi-material interpolation model is particularly established. In order to improve gradient-based mathematical programming algorithms, analytical sensitivities of topological design variables are derived using the adjoint method. An additional constraint on structural compliance is considered in design to maintain the load-carrying capability and improve the convergence. A variety of numerical experiments are performed to test our approach on a benchmark composite beam with piezoelectric layers. The proposed approach has been shown effective in increasing the energy conversion efficiency by the simultaneous distribution of the piezoelectric and non-piezoelectric materials. The performance calibration of the optimized design and the reconstructed topologies based on computer-aided design demonstrate the effectiveness of the proposed method under both static and harmonic load conditions.