Optimal design of piezoelectric microstructures

Abstract

Application of piezoelectric materials requires an improvement in their performance characteristics which can be obtained by designing new topologies of microstructures (or unit cells) for these materials. The topology of the unit cell (and the properties of its constituents) determines the effective properties of the piezocomposite. By changing the unit cell topology, better performance characteristics can be obtained in the piezocomposite. Based on this idea, we have proposed in this work an optimal design method of piezocomposite microstructures using topology optimization techniques and homogenization theory. The topology optimization method consists of finding the distribution of material phase and void phase in a periodic unit cell, that optimizes the performance characteristics, subject to constraints such as property symmetry and stiffness. The optimization procedure is implemented using sequential linear programming. In order to calculate the effective properties of a unit cell with complex topology, a general homogenization method applied to piezoelectricity was implemented using the finite element method. This method has no limitations regarding volume fraction or shape of the composite constituents. Although only two-dimensional plane strain topologies of microstructures have been considered to show the implementation of the method, this can be extended to three-dimensional topologies. Microstructures obtained show a large improvement in performance characteristics compared to pure piezoelectric material or simple designs of piezocomposite unit cells.