Discrete level set method enhanced by conformal mapping: an efficient approach for topology optimization of piezoelectric energy harvesters.

To improve the efficiency of topology optimization for piezoelectric energy harvesters (PEHs), this paper proposes a discrete level set method enhanced by conformal mapping. By mapping the PEH onto a 2D regular domain, the original 3D topology optimization problem is simplified as a 2D problem by using a scalar function. Then re-meshing and barycentric interpolation theory are used to simplify the solution of the driving equation and resolve the issue of inconsistent discretization between the level set function and the finite element model. Moreover, based on the proposed method, the finite element expression of the piezoelectric shell element is derived, taking into account the piezoelectric material coupling effect and polarization direction. This leads to an accurate numerical solution for the optimization process. Resultantly, numerical examples demonstrate that proposed method enables the optimization using a simple discretization, while effectively preserving surface characteristics of PEHs. Hence, this method offers a new approach for the structural optimization of PEHs. [ABSTRACT FROM AUTHOR]