Multi-objective shape optimization for piezoceramics

This work first introduces a mathematical model which describes the property of a piezoelectrically excited in resonance under weak electric fields. The linear equation of motion for a general shape is given and solved numerically. Both usual shapes (e.g. a rectangular shape) and unusual ones (e.g. a shape with curved sides) are considered, and the results show that some curved side piezoceramics perform better than those with a rectangular shape when using a linear model for the dynamics. In the next step a multi-objective shape optimization problem for the design of piezoelectric actuators is introduced. Two objectives, the maximum amplitude (better performance) and the minimum curvature (simple manufacturing), need to be optimized at the same time. The optimization is conducted with a subdivision algorithm based on the software package GAIO and the corresponding Pareto-optimal solutions are obtained for a linear model.