“Design and volume optimization of space structures” by Jiang, Tang, Seidel and Wonka

  • ©Caigui Jiang, Chengcheng Tang, Hans-Peter Seidel, and Peter Wonka



Session Title:

    Work it, Make it Better, Stronger


    Design and volume optimization of space structures




    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.


    1. Wolfgang Achtziger and Mathias Stolpe. 2007. Truss topology optimization with discrete design variables–guaranteed global optimality and benchmark examples. Structural and Multidisciplinary Optimization 34, 1 (2007), 1–20. Google ScholarCross Ref
    2. Shmuel Agmon. 1954. The relaxation method for linear inequalities. Canadian Journal of Mathematics 6 (1954).Google Scholar
    3. MOSEK ApS. 2016. The MOSEK C optimizer API manual Version 7.1(Revision 62). http://docs.mosek.com/7.1/capi/index.htmlGoogle Scholar
    4. Phillipe Block and John Ochsendorf. 2007. Thrust Network Analysis: A New Methodology For Three-Dimensional Equilibrium. J. Int. Assoc. Shell and Spatial Structures 48, 3 (2007), 167–173.Google Scholar
    5. CV Camp and M Farshchin. 2014. Design of space trusses using modified teaching-learning based optimization. Engineering Structures 62 (2014), 87–97. Google ScholarCross Ref
    6. Wai-Fah Chen and Eric M Lui. 2005. Handbook of Utructural Engineering. Crc Press.Google Scholar
    7. Fernando de Goes, Pierre Alliez, Houman Owhadi, and Mathieu Desbrun. 2013. On the Equilibrium of Simplicial Masonry Structures. ACM Trans. Graph. 32 (2013). Google ScholarDigital Library
    8. William S Dorn. 1964. Automatic design of optimal structures. Journal de mecanique 3 (1964).Google Scholar
    9. Robert M Freund. 2004. Truss design and convex optimization. Massachusetts Institute of Technologi (2004).Google Scholar
    10. Chi-Wing Fu, Chi-Fu Lai, Ying He, and Daniel Cohen-Or. 2010. K-set tilable surfaces. ACM Trans. Graph. 29 (2010), #44,1–6.Google Scholar
    11. Mathieu Huard, Philippe Bompas, and Michael Eigensatz. 2014. Planar panelization with extreme repetition. In Advances in Architectural Geometry 2014, Philippe Block and others (Eds.). Springer.Google Scholar
    12. Caigui Jiang, Chengcheng Tang, Marko Tomičić, Johannes Wallner, and Helmut Pottmann. 2014. Interactive Modeling of Architectural Freeform Structures – Combining Geometry with Fabrication and Statics. In Advances in Architectural Geometry 2014, Philippe Block and others (Eds.). Springer.Google Scholar
    13. Caigui Jiang, Chengcheng Tang, Amir Vaxman, Peter Wonka, and Helmut Pottmann. 2015. Polyhedral Patterns. ACM Trans. Graph. 34 (2015). Google ScholarDigital Library
    14. Caigui Jiang, Jun Wang, Johannes Wallner, and Helmut Pottmann. 2014. Freeform Honeycomb Structures. Comput. Graph. Forum 33 (2014).Google Scholar
    15. Yoshihiro Kanno and Xu Guo. 2010. A mixed integer programming for robust truss topology optimization with stress constraints. Internat. J. Numer. Methods Engrg. 83, 13 (2010), 1675–1699. Google ScholarCross Ref
    16. A Kaveh, B Farhmand Azar, and S Talatahari. 2008. Ant colony optimization for design of space trusses. International Journal of Space Structures 23, 3 (2008), 167–181. Google ScholarCross Ref
    17. H Kawamura, H Ohmori, and N Kito. 2002. Truss topology optimization by a modified genetic algorithm. Structural and Multidisciplinary Optimization 23, 6 (2002), 467–473. Google ScholarCross Ref
    18. Timothy Langlois, Ariel Shamir, Daniel Dror, Wojciech Matusik, and David IW Levin. 2016. Stochastic structural analysis for context-aware design and fabrication. ACM Transactions on Graphics (TOG) 35, 6 (2016), 226.Google ScholarDigital Library
    19. LJ Li, ZB Huang, and F Liu. 2009. A heuristic particle swarm optimization method for truss structures with discrete variables. Computers & Structures 87, 7 (2009), 435–443. Google ScholarDigital Library
    20. Dong C Liu and Jorge Nocedal. 1989. On the limited memory BFGS method for large scale optimization. Mathematical Programming (1989).Google Scholar
    21. Yang Liu, Hao Pan, John Snyder, Wenping Wang, and Baining Guo. 2013. Computing Self-Supporting Surfaces By Regular Triangulation. ACM Trans. Graph. 32 (2013). Google ScholarDigital Library
    22. Yang Liu, Helmut Pottmann, Johannes Wallner, Yong-Liang Yang, and Wenping Wang. 2006. Geometric modeling with conical meshes and developable surfaces. ACM Trans. Graph. 25, 3 (2006), 681–689. Google ScholarDigital Library
    23. Yang Liu, Wenping Wang, Bruno Lévy, Feng Sun, Dong-Ming Yan, Lin Lu, and Chenglei Yang. 2009. On centroidal voronoi tessellation–energy smoothness and fast computation. ACM Trans. Graph. 28 (2009). Google ScholarDigital Library
    24. J Clerk Maxwell. 1870. On Reciprocal Figures, Frames, and Diagrams of Forces. Transactions of the Royal Society of Edinburgh 26, 01 (1870).Google ScholarCross Ref
    25. Anthony George Maldon Michell. 1904. The limits of economy of material in frame-structures. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 8 (1904).Google Scholar
    26. Daniele Panozzo, Philippe Block, and Olga Sorkine-Hornung. 2013. Designing Unreinforced Masonry Models. ACM Trans. Graph. 32 (2013). Google ScholarDigital Library
    27. Chi-Han Peng, Michael Barton, Caigui Jiang, and Peter Wonka. 2014. Exploring Quadrangulations. ACM Trans. Graph. 33 (2014). Google ScholarDigital Library
    28. Nico Pietroni, Davide Tonelli, Enrico Puppo, Maurizio Froli, Roberto Scopigno, and Paolo Cignoni. 2015. Statics aware grid shells. Comput. Graph. Forum 34, 2 (2015), 627–641. Google ScholarDigital Library
    29. Romain Prévost, Emily Whiting, Sylvain Lefebvre, and Olga Sorkine-Hornung. 2013. Make it stand: balancing shapes for 3D fabrication. ACM Trans. Graph. 32, 4 (2013), 81. Google ScholarDigital Library
    30. MH Rasmussen and Mathias Stolpe. 2008. Global optimization of discrete trusstopology design problems using a parallel cut-and-branch method. Computers & Structures 86, 13 (2008), 1527–1538.Google ScholarDigital Library
    31. Adriana Schulz, Ariel Shamir, David IW Levin, Pitchaya Sitthi-Amorn, and Wojciech Matusik. 2014. Design and fabrication by example. ACM Trans. Graph. 33, 4 (2014), 62. Google ScholarDigital Library
    32. Jeffrey Smith, Jessica Hodgins, Irving Oppenheim, and Andrew Witkin. 2002. Creating models of truss structures with optimization. ACM Trans. Graph. 21 (2002). Google ScholarDigital Library
    33. Mathias Stolpe and Krister Svanberg. 2003. Modelling topology optimization problems as linear mixed 0–1 programs. Internat. J. Numer. Methods Engrg. 57, 5 (2003), 723–739. Google ScholarCross Ref
    34. Chengcheng Tang, Pengbo Bo, Johannes Wallner, and Helmut Pottmann. 2016a. Inter-active design of developable surfaces. ACM Trans. Graph. 35, 2 (2016), 12.Google ScholarDigital Library
    35. Chengcheng Tang, Martin Kilian, Pengbo Bo, Johannes Wallner, and Helmut Pottmann. 2016b. Analysis and design of curved support structures. In Advances in Architectural Geometry 2016, Sigrid Adriaenssens, Fabio Gramazio, Matthias Kohler, Achim Menges, and Mark Pauly (Eds.). VDF Hochschulverlag, ETH Zürich, 8–23.Google Scholar
    36. Chengcheng Tang, Xiang Sun, Alexandra Gomes, Johannes Wallner, and Helmut Pottmann. 2014. Form-finding with Polyhedral Meshes Made Simple. ACM Tran. Graph. 33 (2014).Google Scholar
    37. Nobuyuki Umetani, Takeo Igarashi, and Niloy J Mitra. 2012. Guided exploration of physically valid shapes for furniture design. ACM Trans. Graph. 31, 4 (2012), 86–1. Google ScholarDigital Library
    38. Etienne Vouga, Mathias Höbinger, Johannes Wallner, and Helmut Pottmann. 2012. Design of self-supporting surfaces. ACM Trans. Graph. 31, 4 (2012). Google ScholarDigital Library
    39. Weiming Wang, Tuanfeng Y Wang, Zhouwang Yang, Ligang Liu, Xin Tong, Weihua Tong, Jiansong Deng, Falai Chen, and Xiuping Liu. 2013. Cost-effective printing of 3D objects with skin-frame structures. ACM Trans. Graph. 32, 6 (2013).Google ScholarDigital Library
    40. Dong-Ming Yan, Bruno Lévy, Yang Liu, Feng Sun, and Wenping Wang. 2009. Isotropic remeshing with fast and exact computation of restricted Voronoi diagram. Comput. Graph. Forum 28 (2009). Google ScholarCross Ref
    41. Tomás Zegard and Glaucio H Paulino. 2014. GRAND-Ground structure based topology optimization for arbitrary 2D domains using MATLAB. Structural and Multidisciplinary Optimization 50 (2014).Google Scholar
    42. Tomás Zegard and Glaucio H Paulino. 2015. GRAND3-Ground structure based topology optimization for arbitrary 3D domains using MATLAB. Structural and Multidisciplinary Optimization 52, 6 (2015), 1161–1184. Google ScholarDigital Library
    43. Xin Zhao, Cheng-Cheng Tang, Yong-Liang Yang, and Helmut Pottmann. 2013. Intuitive Design Exploration of Constrained Meshes. In Advances in Architectural Geometry 2012, Lars Hesselgren and others (Eds.). Springer, 305–318. Google ScholarCross Ref

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