Shape optimization of piezoelectric energy harvesters based on isogeometric analysis and particle swarm optimization

Shape optimization of piezoelectric energy harvesters (PEH) is deemed to be one of the most effective methods to enhance energy efficiency. In this paper, we propose a novel shape optimization approach for PEH by combining isogeometric analysis (IGA) and particle swarm optimization (PSO). Based on the Kirchhoff–Love plate theory and Hamilton’s principle, an IGA formula is modeled for a bimorph PEH. Meanwhile, two optimization models with maximum average open-circuit voltage as the objective function are established, and the difference between the two is whether frequency constraint is considered or not. Then, we set the coordinates of control points to be design variables and utilize PSO to solve optimization problems. The numerical examples are performed to verify the accuracy and convergence of the IGA model and systematically compare the computational efficiency between PSO and genetic algorithm (GA). Furthermore, the shape optimization is executed for three different structures, and the effect of thickness ratio and frequency constraint on the optimized shapes are further analyzed. The results show that maximum output power and power density of the optimized design respectively increase by 184.7 and \(36.4{{\% }}\), compared with the initial design. More importantly, the presented method can realize the integrated analysis of modeling, simulation, and optimization for PEH.