Topology optimization of piezoelectric energy harvesting devices considering static and harmonic dynamic loads

Abstract

A topology optimization (TO) procedure is developed to design optimal layouts for piezoelectric energy harvesting devices (EHDs) by considering the effect of static and harmonic dynamic mechanical loads. To determine the optimal material distributions of a piezoelectric material considering the harmonic dynamic coupling effects between the electric energy and a structure for efficient EHDs, harmonic dynamic responses and the complex sensitivity analyses for various objectives related to the energy efficiency are calculated and derived. For the relaxation method of the density design variable for TO, material properties such as the anisotropic linear elasticity coefficients, piezoelectric coefficients, and permittivity coefficients are independently interpolated through the solid isotropic material with penalization (SIMP) approach with three penalization values. Through several numerical tests for various configurations of piezoelectric materials, it is found that depending on the choice of penalization value, complex behaviors of energies are possible and these in turn lead to a serious local optima issue in TO. Through several three-dimensional design problems, the validity and usefulness of the developed optimization procedure for efficient EHDs are demonstrated.