Umbrella meshes

We present a computational inverse design framework for new class of volumetric deployable structures that have compact rest states and deploy into bending-active 3D target surfaces. Umbrella meshes consist elastic beams, rigid plates, hinge joints can be directly printed or assembled in zero-energy fabrication state. During deployment, as the beams varying heights rotate from vertical to horizontal configurations, entire structure transforms block curved surface. Meshes encode both intrinsic extrinsic curvature surface principle are free area expansion ratio bounds past auxetic material systems. build reduced physics-based simulation accurately efficiently model complex interaction between elastically deforming components. To determine mesh topology optimal shape parameters approximating given surface, we propose an optimization algorithm initialized with conformal flattening. Our minimizes structure's strain energy its deployed state optimizes actuation forces so final is stable equilibrium close desired few no external constraints. validate our approach by fabricating series physical models at various scales using different manufacturing techniques.