Topology optimization of smart structures with embedded piezoelectric stack actuators using a composite geometry projection method

The design of smart structures is challenging because of the integrated electromechanical modelling and optimization of actuators, sensors and load-bearing structures. To simplify the design process, it is common to decouple some of the components and physics and develop each part separately, which could lead to suboptimal systems. To improve the overall design of active structures, we propose an integrated and fully coupled design methodology for a certain class of smart structures. Specifically, this paper presents a numerical framework for the simultaneous application of density-based topology optimization of multi-material conductive compliant mechanisms and a composite multi-layered geometry-projection method for the optimization of the size, position and orientation of embedded piezoelectric stack actuators. Their electromechanical properties are represented in a continuum-based setting by an orientation- and geometry-dependent equivalent material model and their activation depends on the distribution of conductive material in the structure. Furthermore, a novel constraint on the polarization of the actuators is proposed to avoid unwanted designs that could cause their mechanical degradation. A set of numerical examples is analysed and discussed. The proposed framework exhibits promising results, with significant improvements in comparison to a benchmark problem.