Spherical harmonic shape descriptors of nodal force demands for quantifying spatial truss connection complexity

The connections of a spatial truss structure play a critical role in the safe and efficient transfer of axial forces between members. For discrete connections, they can also improve construction efficiency by acting as registration devices that lock members in precise orientations. As more geometrically complex spatial trusses are enabled by computational workflows and the demand for material-efficient spanning systems, there is a need to understand the effects of global form on the demands at the connections. For large-scale structures with irregular geometry, customizing individual nodes to meet exact member orientations and force demands may be infeasible; conversely, standardizing all connections results in oversized nodes and a compromise in registration potential. We propose a method for quantifying the complexity of spatial truss designs by the variation in nodal force demands. By representing nodal forces as a geometric object, we leverage the spherical harmonic shape descriptor, developed for applications in computational geometry, to characterize each node by a rotation and translation-invariant fixed-length vector. We define a complexity score for spatial truss design by the variance in the positions of the feature vectors in higher-dimensional space, providing an additional performance metric during early stage design exploration. We then develop a pathway towards reducing complexity by clustering nodes with respect to their feature vectors to reduce the number of unique connectors for design while minimizing the effects of mass standardization.