A penalty function for enforcing maximum length scale criterion in topology optimization

Techniques for imposing a minimum length scale, or minimum feature size, in continuum topology optimization have been proposed in literature, with the motivation being stabilization of the maximum stiffness problem and satisfying manufacturing constraints. Imposing an upper bound on feature sizes, however, has not been investigated. This paper proposes a scheme for restricting the maximum length scale in topology optimization. In short, the design domain is searched and structural features larger than the prescribed maximum length scale are penalized. The scheme is implemented in the context of minimum compliance design together with an existing minimum length scale methodology. The resulting optimization problem is continuous and solved using the Method of Moving Asymptotes (MMA). Beam design examples are considered and solutions are shown to be near 0/1 (void/solid) topologies that satisfy the minimum and maximum length scale criteria. The designer thus gains complete control over member sizes and therefore additional influence over cost and manufacturability. Further, restricting maximum length scale can potentially be used to introduce structural redundancy into the design, as loads previously carried by few large members are often redistributed over an interconnected system of smaller members.