Topology Optimization Based on Structural Flexibility in the Periodic Loading

In structural design, the stiffest structure has been considered optimal. However, if the flexibility is implemented in some appropriate portions, a flexible structure provides higher performance than the stiffest structure. Furthermore, since flexible portions can provide a mechanical function to the structure, a new breed of jointless structural mechanisms known as compliant mechanism can be designed with structural flexibility. In this study, we present a methodology to provide the optimal structure accounting for structural flexibility in the case of periodic input loads. First, dynamic mutual mean compliance is introduced in order to define flexibility using a mutual energy concept. Second, a new multi-objective function incorporating the maximization of flexibility and stiffness is proposed. Next, an optimization procedure is constructed based on the homogenization design method and sequential linear programming (SLP). Finally, some examples are presented to confirm the problem specifications of the optimal configurations.