“Optimizing contact-based assemblies” by Tozoni, Zhou and Zorin
Conference:
Type(s):
Title:
- Optimizing contact-based assemblies
Session/Category Title: Fabrication
Presenter(s)/Author(s):
Abstract:
Modern fabrication methods have greatly simplified manufacturing of complex free-form shapes at an affordable cost, and opened up new possibilities for improving functionality and customization through automatic optimization, shape optimization in particular. However, most existing shape optimization methods focus on single parts. In this work, we focus on supporting shape optimization for assemblies, more specifically, assemblies that are held together by contact and friction. Examples of which include furniture joints, construction set assemblies, certain types of prosthetic devices and many other. To enable this optimization, we present a framework supporting robust and accurate optimization of a number of important functionals, while enforcing constraints essential for assembly functionality: weight, stress, difficulty of putting the assembly together, and how reliably it stays together. Our framework is based on smoothed formulation of elasticity equations with contact, analytically derived shape derivatives, and robust remeshing to enable large changes of shape, and at the same time, maintain accuracy. We demonstrate the improvements it can achieve for a number of computational and experimental examples.
References:
1. Pierre Alart and Alain Curnier. 1991. A mixed formulation for frictional contact problems prone to Newton like solution methods. CMAME 92, 3 (Nov. 1991).
2. Grégoire Allaire and Francois Jouve. 2008. Minimum stress optimal design with the level set method. Engineering Analysis with Boundary Elements 32, 11 (2008), 909 — 918. Shape and Topological Sensitivity Analysis: Theory and Applications.
3. G Allaire, F Jouve, and H Maillot. 2004. Topology optimization for minimum stress design with the homogenization method. Structural and Multidisciplinary Optimization 28, 2-3 (2004), 87–98.
4. Ted Belytschko, Wing Kam Liu, and Brian Moran. 2000. Nonlinear Finite Elements for Continua and Structures. John Wiley & Sons, Ltd.
5. P. Beremlijski, J. Haslinger, J. Outrata, and R. Pathó. 2014. Shape Optimization in Contact Problems with Coulomb Friction and a Solution-Dependent Friction Coefficient. SIAM Journal on Control and Optimization 52, 5 (Jan. 2014), 3371–3400.
6. Éric Bonnetier and Charles Dapogny. 2020. An introduction to shape and topology optimization. (2020).
7. Robert Bridson, Ronald Fedkiw, and John Anderson. 2002. Robust Treatment of Collisions, Contact and Friction for Cloth Animation. ACM Trans. on Graph. 21 (05 2002).
8. Gilles Daviet, Florence Bertails-Descoubes, and Laurence Boissieux. 2011. A Hybrid Iterative Solver for Robustly Capturing Coulomb Friction in Hair Dynamics. ACM Trans. on Graph. 30 (12 2011).
9. B. Desmorat. 2007. Structural rigidity optimization with frictionless unilateral contact. International Journal of Solids and Structures 44, 3 (Feb. 2007), 1132–1144.
10. Ounan Ding and Craig Schroeder. 2020. Penalty Force for Coupling Materials with Coulomb Friction. IEEE Transactions on Visualization and Computer Graphics 26, 7 (2020), 2443–2455.
11. Christof Eck, Jiri Jarusek, Miroslav Krbec, Jiri Jarusek, and Miroslav Krbec. 2005. Unilateral Contact Problems : Variational Methods and Existence Theorems. CRC Press.
12. Moritz Geilinger, David Hahn, Jonas Zehnder, Moritz Bächer, Bernhard Thomaszewski, and Stelian Coros. 2020. ADD: Analytically Differentiable Dynamics for Multi-Body Systems with Frictional Contact. ACM Trans. Graph. 39, 6, Article 190 (Nov. 2020), 15 pages.
13. David Harmon, Etienne Vouga, Breannan Smith, Rasmus Tamstorf, and Eitan Grinspun. 2009. Asynchronous contact mnumpageechanics. In ACM Trans. on Graph. (TOG), Vol. 28. ACM.
14. Jaroslav Haslinger, Pekka Neittaanmaki, and Timo Tiihonen. 1986. Shape optimization in contact problems based on penalization of the state inequality. Aplikace matematiky 31, 1 (1986), 54–77. https://eudml.org/doc/15435
15. J. Herskovits, A. Leontiev, G. Dias, and G. Santos. 2000. Contact shape optimization: a bilevel programming approach. Structural and Multidisciplinary Optimization 20, 3 (Nov. 2000), 214–221.
16. Yixin Hu, Teseo Schneider, Bolun Wang, Denis Zorin, and Daniele Panozzo. 2020. Fast Tetrahedral Meshing in the Wild. ACM Trans. Graph. 39, 4, Article 117 (July 2020), 18 pages.
17. Xiaodong Huang and Yi-Min Xie. 2010. A further review of ESO type methods for topology optimization. Structural and Multidisciplinary Optimization 41, 5 (2010), 671–683.
18. Michel Jean and Jean Jacques Moreau. 1992. Unilaterality and dry friction in the dynamics of rigid body collections. In Proc. of Contact Mech. Int. Symp., Vol. 1.
19. Minchen Li, Zachary Ferguson, Teseo Schneider, Timothy Langlois, Denis Zorin, Daniele Panozzo, Chenfanfu Jiang, and Danny M Kaufman. 2020. Incremental potential contact: intersection-and inversion-free, large-deformation dynamics. ACM Transactions on Graphics (TOG) 39, 4 (2020), 49–1.
20. Haojie Lian, Asger N. Christiansen, Daniel A. Tortorelli, Ole Sigmund, and Niels Aage. 2017. Combined shape and topology optimization for minimization of maximal von Mises stress. Structural and Multidisciplinary Optimization 55, 5 (2017), 1541–1557.
21. Miles Macklin, Kenny Erleben, Matthias Müller, Nuttapong Chentanez, Stefan Jeschke, and Viktor Makoviychuk. 2019. Non-Smooth Newton Methods for Deformable Multi-Body Dynamics. (07 2019).
22. Aymeric Maury, Grégoire Allaire, and François Jouve. 2017. Shape optimisation with the level set method for contact problems in linearised elasticity. (Jan. 2017). https://hal.archives-ouvertes.fr/hal-01435325
23. Jean Jacques Moreau. 1973. On Unilateral Constraints, Friction and PLasticity. New Variational Tech. in Math. Phys. (1973).
24. Miguel Otaduy, Rasmus Tamstorf, Denis Steinemann, and Markus Gross. 2009. Implicit Contact Handling for Deformable Objects. Comp. Graph. Forum 28 (04 2009).
25. Julian Panetta, Abtin Rahimian, and Denis Zorin. 2017. Worst-case stress relief for microstructures. ACM Transactions on Graphics 36, 4 (2017).
26. Daniele Panozzo, Philippe Block, and Olga Sorkine-Hornung. 2013. Designing Unreinforced Masonry Models. ACM Trans. Graph. 32, 4, Article 91 (July 2013), 12 pages.
27. Miha Polajnar, Franc Kosel, and Radovan Drazumeric. 2017. Structural optimization using global stress-deviation objective function via the level-set method. Structural and Multidisciplinary Optimization 55, 1 (2017), 91–104.
28. Michael Rabinovich, Roi Poranne, Daniele Panozzo, and Olga Sorkine-Hornung. 2017. Scalable locally injective mappings. ACM Transactions on Graphics (TOG) 36, 4 (2017), 1.
29. Jonathan Richard Shewchuk. 1996. Triangle: Engineering a 2D quality mesh generator and Delaunay triangulator. In Applied Computational Geometry Towards Geometric Engineering, Ming C. Lin and Dinesh Manocha (Eds.). Springer Berlin Heidelberg, Berlin, Heidelberg, 203–222.
30. FO Sonmez. 2009. Optimal shape design of shoulder fillets for flat and round bars under various loadings. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 223, 8 (2009), 1741–1754.
31. Ondrej Stava, Juraj Vanek, Bedrich Benes, Nathan Carr, and Radomir Mvech. 2012. Stress Relief: Improving Structural Strength of 3D Printable Objects. ACM Trans. Graph. 31, 4, Article 48 (July 2012), 11 pages.
32. David E Stewart. 2001. Finite-dimensional contact mechanics. Phil. Trans. R. Soc. Lond. A 359 (2001).
33. Stanisław Stupkiewicz, Jakub Lengiewicz, and Joze Korelc. 2010. Sensitivity analysis for frictional contact problems in the augmented Lagrangian formulation. Computer Methods in Applied Mechanics and Engineering 199, 33 (July 2010), 2165–2176.
34. Timothy Sun and Changxi Zheng. 2015. Computational Design of Twisty Joints and Puzzles. ACM Transactions on Graphics (Proceedings of SIGGRAPH 2015) 34, 4 (Aug. 2015). http://www.cs.columbia.edu/cg/twisty
35. Jane Tournois, Noura Faraj, Jean-Marc Thiery, and Tamy Boubekeur. 2021. Tetrahedral Remeshing. In CGAL User and Reference Manual (5.3 ed.). CGAL Editorial Board. https://doc.cgal.org/5.3/Manual/packages.html#PkgTetrahedralRemeshing
36. Francisca Gil Ureta, Chelsea Tymms, and Denis Zorin. 2016. Interactive Modeling of Mechanical Objects. Computer Graphics Forum 35, 5 (2016), 145–155. arXiv:https://onlinelibrary.wiley.com/doi/pdf/10.1111/cgf.12971
37. Laurent Van Miegroet and Pierre Duysinx. 2007. Stress concentration minimization of 2D filets using X-FEM and level set description. Structural and Multidisciplinary Optimization 33, 4-5 (2007), 425–438.
38. Mickeal Verschoor and Andrei C Jalba. 2019. Efficient and accurate collision response for elastically deformable models. ACM Trans. on Graph. (TOG) 38, 2 (2019).
39. Etienne Vouga, Mathias Höbinger, Johannes Wallner, and Helmut Pottmann. 2012. Design of Self-Supporting Surfaces. ACM Trans. Graph. 31, 4, Article 87 (July 2012), 11 pages.
40. Ziqi Wang, Peng Song, Florin Isvoranu, and Mark Pauly. 2019. Design and Structural Optimization of Topological Interlocking Assemblies. ACM Trans. Graph. 38, 6, Article 193 (Nov. 2019), 13 pages.
41. Qi Xia, Tielin Shi, Shiyuan Liu, and Michael Yu Wang. 2012. A level set solution to the stress-based structural shape and topology optimization. Computers & Structures 90 (2012), 55–64.
42. Jiaxian Yao, Danny M. Kaufman, Yotam Gingold, and Maneesh Agrawala. 2017. Interactive Design and Stability Analysis of Decorative Joinery for Furniture. ACM Transactions on Graphics (TOG) 36, 2, Article 20 (March 2017), 16 pages.
43. Haiming Zhao, Weiwei Xu, Kun Zhou, Yin Yang, Xiaogang Jin, and Hongzhi Wu. 2016. Stress-Constrained Thickness Optimization for Shell Object Fabrication. In Computer Graphics Forum. Wiley Online Library.
44. Yahan Zhou, Evangelos Kalogerakis, Rui Wang, and Ian R Grosse. 2016. Direct shape optimization for strengthening 3D printable objects. In Computer Graphics Forum, Vol. 35. Wiley Online Library, 333–342.


