Structural Topology Optimization Considering Complexity

As topology optimization is a free-form approach to optimizing structural layout, it has a tendency to design structures that are topologically complex. In large-scale structures, this complexity drives construction costs significantly higher, potentially overtaking cost savings from reduced material usage. This work examines opportunities to incorporate complexity measures directly into the topology optimization of structures such that the designer gains control and may explore potential constructability-performance tradeoffs. In particular, the cost of topological and connection complexity is considered. The algorithm is formulated in a continuous form such that sensitivities are readily available for use with rapid gradient-based optimizers. The algorithm is demonstrated on static design problems and solutions. The tradeoffs between constructability, material usage, and performance are explored.