Set-in-stone: worst-case optimization of structures weak in tension.

Large-scale binder jetting provides a promising alternative to manual sculpting of sandstone. The weak build material, however, severely limits its use in architectural ornamentation. 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. To account for the difference in the tensile and compressive strength of the build material, we turn the Bresler-Pister criterion into a failure potential, measuring the distance to failure. Integrated into an XFEM-based level set formulation, we minimize this potential by changing the topology and shape of the internal structure. To deal with uncertainties in the location of live loads, and the direction of wind loads, we first estimate loads that lead to the weakest structure, then minimize the potential of failure under identified worst-case loads. With the help of first-order optimality constraints, we unify our worst-case load estimation and structural optimization into a continuous optimization. We demonstrate applications in art, furniture design, and architectural ornamentation with three large-scale 3D printed examples.