We study the design and optimization of statically sound and materially efficient space structures constructed by connected beams. We propose a systematic computational framework for the design of space structures that incorporates static soundness, approximation of reference surfaces, boundary alignment, and geometric regularity. To tackle this challenging problem, we first jointly optimize node positions and connectivity through a nonlinear continuous optimization algorithm. Next, with fixed nodes and connectivity, we formulate the assignment of beam cross sections as a mixed-integer programming problem with a bilinear objective function and quadratic constraints. We solve this problem with a novel and practical alternating direction method based on linear programming relaxation. The capability and efficiency of the algorithms and the computational framework are validated by a variety of examples and comparisons.
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledgements: We thank the anonymous reviewers for their insightful comments and suggestions for improving the paper. This research was supported by the KAUST Office of Sponsored Research, the Visual Computing Center (VCC) at KAUST and by the Max Planck Center for Visual Computing and Communication. Chengcheng Tang would like to thank the support of NSF grant IIS-1528025, a Google Focused Research Award, a gift from the Adobe Corporation, and a hardware donation from NVIDIA. The authors would like to thank Helmut Pottmann, Leonidas Guibas, Renjie Chen, Lorenzo Greco, and Qingyun Sun for discussions, Virginia Unkefer and Olga Diamanti for proofreading, and Marko Tomicic for creating the renderings used in Figure 1 and Figure 3 (middle).