Topology design of slender piezoelectric actuators with repetitive component patterns

This article presents a study on topology optimization of planar piezoelectric actuators assembled with repetitive component patterns. Repetitive configuration has the advantage of ease of engineering implementation, especially for relatively slender structures. For realizing this concept in the design of piezoelectric actuators, topology optimization techniques are employed for seeking the optimal layout within the design domain of the structural components. The design objective is to maximize the work delivered by the displacement output port, while constraints are imposed on the actuation energy consumption and the material volume. Both the distributions of the actuation voltage and the topologies of the host layer and the piezoelectric layers are optimized. Power-law penalization functions are used to suppress intermediate values of material densities and actuation voltage. Numerical techniques for a sensitivity analysis of structural response are presented, and the proposed optimization problem is solved with a gradient-based mathematical programming approach. Two numerical examples are given to demonstrate the applicability of the proposed approach. Compared with the method directly treating the whole design domain, this approach is shown to have a better convergence behavior and is able to provide final topologies that are better acceptable from engineering point of view.