A Modal‐Based Framework for Topology Optimization of Compliant Mechanisms With Optimal Actuator Sizing

ABSTRACT

The design of compliant mechanisms with integrated actuation requires consistent treatment of structural topology, actuator dimensions, and actuator placement. This work presents a coupled optimization framework based on modal formulations that combines the optimization of structural topology and linear actuators into a unified design approach. The method minimizes actuator volume while ensuring prescribed deformations by explicitly capturing the interaction between modal stiffness and actuator‐induced work. A scalable actuator model reflects the proportional dependence of actuator properties on geometric dimensions as exhibited by piezoelectric stack actuators, enabling flexible sizing and placement. The coupling is formulated through a modal stiffness to coordinate the adjustment of structural compliance and actuator effort. Analytical investigations reveal a characteristic dependence of actuator volume on this stiffness, including the existence of a unique volume minimum. Motivated by these findings, the coupled framework combines a modal‐synthesis approach for topology design with an analytical procedure for volume‐optimal actuator sizing, governed by an outer golden‐section search that varies the modal stiffness to minimize the resulting actuator volume. Demonstrated across several case studies – including classical single‐input‐single‐output mechanisms, problems with mechanical amplification requirements, robustness against external loads, and shape‐adaptive structures – the proposed framework systematically reduces actuator volume while maintaining the prescribed deformation behavior.