Abstract
Application of piezoelectric materials, such as hydrophones and naval sonars, requires an improvement in their performance characteristics. This improvement can be obtained by designing new types of piezocomposite materials that possess a richer class of properties. The effective properties of a composite material depend on the topology of its unit cell (or microstructure) and the properties of its constituents. By changing the unit cell topology, better performance characteristics can be obtained in the piezocomposite. In this work, we have extended the optimal design method of piezocomposite microstructures proposed in the previous work [1] to three dimensional (3D) topologies, considering static applications such as hydrophones. This method uses topology optimization techniques and homogenization theory, and consists of finding the distribution of the material and void phases in a periodic unit cell that optimizes the performance characteristics of the piezocomposite. The optimization problem is subjected to constraints such as property symmetry and stiffness. An additional constraint was added in order to penalize the amount of intermediate densities generated in the final design. The optimized solution is obtained using Sequential Linear Programming (SLP). 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 (FEM). This homogenization method has no limitations regarding volume fraction or shape of the composite constituents. The main assumption is the periodicity of the unit cell. Microstructures obtained show a large improvement in performance characteristics compared to pure piezoelectric material or simple designs of piezocomposite unit cells. Finally, a hydrophone made of one layer of the unit cells obtained by using microstructure design is suggested. An FEM analysis is done to evaluate the performance improvement of such transducer.
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