Structural topology optimization of compliant mechanisms (in cases where the ratio of the displacement at the input location to the displacement at the output location is included in an objective function)

In structural design, the stiffest structure is considered optimal. However, a structure having flexible parts offers certain advantages over a rigid structure in terms of mechanical function criteria. A typical mechanical example is compliant mechanisms, which use the design concept of structural flexibility to achieve a specified motion. In this paper, a new topology optimization method is constructed based on the continuous approximation assumption of material distributions for the design of compliant mechanisms. First, the relaxation scheme of a design domain based on this assumption is briefly discussed. Next, structural flexibility is formulated using a mutual energy concept. A new objective function taking the ratio of the displacement at the input location to the displacement at the output location into consideration is proposed. A multi-objective optimization problem is formulated and its algorithm is constructed using Sequential Linear Programming (SLP). Finally, several numerical examples are presented in order to confirm the validity of the method proposed here.