Similarity-driven topology finding of surface patterns for structural design

Structural design is a search for the best trade-off between multiple architecture, engineering, and construction objectives, not only mechanical efficiency or construction rationality. Producing hybrid designs from singleobjective optimal designs to explore multi-objective trade-offs is common in the design of structural forms, constrained to a single parametric design space. However, producing topological hybrids offers a more complex challenge, as a combinatorial problem that is not encoded as a finite set of real numbers but as an unbonded series of grammar rules. This paper presents a strategy for the generation of hybrid designs of quad-mesh pattern topologies for surface structures. Based on a quad-mesh grammar, an algebra is introduced to measure the distance between designs, find their similar features, and enumerate designs with different degrees of topological similarity. Structural design applications are shown to highlight the use of topologically hybrid designs as a surrogate for obtaining multi-objective trade-offs.