A vector encoding for topology finding of structured quad-based patterns for surface structures

Topology-optimisation strategies for structural design of discrete surface structures result in unstructured patterns that require post-rationalisation to limit the number and complexity of the various structural elements. Fabrication-related objectives still demand further processing. Designers need topology exploration, before topology optimisation, following a generative-design approach that is decoupled from density tuning and shape design, to produce high-quality patterns. Such an approach allows to flexibly embed multiple design constraints, benefit from state-of-the-art form-finding algorithms and explore design trade-offs of the multiple requirements related to architecture, engineering and construction. This research investigates a parameterisation strategy to encode topological exploration of structured patterns based on quad meshes. The focus is set on singular vertices, which connect an irregular number of blocks, cables, or beams. Singularities are independent from pattern density and geometry, and have a fundamental influence on the qualitative and quantitative performance of the structure. We introduce an L-system encoding a quad-mesh grammar into a string that describes topological transformations of these singularities. Design applications to a net and a gridshell demonstrate the influence of singularities on the design of surface structures, and highlight the flexibility and generality of the approach in terms of geometrical processing and performance metrics. Beyond exploration, this parameterisation strategy opens to novel applications of search and optimisation methods for generative design of singularities in structural patterns.