Integrated multi-material and multi-scale optimization of compliant structure with embedded movable piezoelectric actuators

Abstract

Piezoelectric actuators embedded in compliant structures have many potential applications, which call for effective design approaches. Existing optimization driven design methods focus on the piezoelectric actuator location or the macro topology of the host compliant structure while ignoring the possibility to exploit the use of multiple materials and hierarchical material design. In this study, an integrated, density-based multi-material and multi-scale optimization method for compliant structures with embedded movable piezoelectric actuators is proposed. The design variables in the optimization represent the location of the piezoelectric actuators and the layout of the macro/micro host structures. To mitigate the risk of suboptimal designs, the three sets of design variables are simultaneously optimized using gradient-based optimization where the gradients are computed using the adjoint method. A material interpolation model that describes the piezoelectric actuators, multiple lattice materials of the host structure as well as their coating layer is proposed. To illustrate the formulation, several compliant structures embedded with movable piezoelectric actuators are designed such that the displacement at an output port is maximized. Macro and micro volume fractions, and overlapping of piezoelectric actuators are constrained in the optimization.