Structural optimization considering flexibility (1st Report, Formulation of equation and application to compliant mechanisms)

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 structural performance criteria. Moreover, flexible parts can offer mechanical function to the structure. A relatively new breed of mechanisms, compliant mechanisms, uses the design concept of structural flexibility to achieve a specified motion. In this paper, an optimization design procedure taking structural flexibility into consideration is proposed and applied to compliant mechanism design. First, structural flexibility is formulated using variational calculus, and a new multi-objective function is constructed. This objective function incorporates both maximum flexibility and minimum compliance using the homogenization method. Next, the optimization problem is solved using the Finite Element Method (FEM) and Sequential Linear Programming (SLP). Finally, some design examples of compliant mechanisms are presented, which confirm that the concept of flexible structure design can be used to design compliant mechanisms.