Optimal design of piezoelectric microstructures |
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Authors: | E C Nelli Silva J S Ono Fonseca N Kikuchi |
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Affiliation: | Department of Mechanical Engineering of Polytechnic School at the University of S?o Paulo, S?o Paulo, Brazil, BR Department of Mechanical Engineering and Applied Mechanics, The University of Michigan, Ann Arbor, MI, 48109-2125, USA, US
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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. |
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