Set-In-Stone: Worst-Case Optimization of Structures Weak in Tension

We propose a structural optimization that jointly optimizes an ornament’s strength-to-weight ratio and balance under self-weight, thermal, wind, and live loads.

Formwork limits the geometric complexity of concrete structures. Binder jetting is a promising alternative. While weaker, the build material displays a similar behavior to concrete: it is weak under tension and strong under compression. To use large-scale binder jetting at the scale of available build tray sizes, we introduce a structural and mass property optimization that accounts for the difference in the compressive and tensile strength of the material. We base our formulation on the three-parameter Bresler Pister criterion and introduce a failure potential that measures the distance to the failure surface defined by this criterion. Besides self-weight, we support wind, live, and thermal loads. To optimize structures under unknown wind and live loads, we devise a worst-case optimization where we first identify the loads that lead to the highest stresses from a parameterized set, minimizing them by hollowing the interior. Discretizing the design space with extended finite elements and evolving a level set, we represent the interface between material and void space exactly, supporting topological changes. Optimizing the strength-to-weight ratio and center of mass of models, we demonstrate applications in art, furniture design, and architectural ornamentation.