Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-22T22:06:15.891Z Has data issue: false hasContentIssue false
  • English
  • Français

Truss Parametrization of Topology Optimization Results with Curve Skeletons and Meta Balls

Published online by Cambridge University Press:  26 May 2022

M. Denk ,
K. Rother  and
K. Paetzold
M. Denk
Affiliation:
Universität der Bundeswehr München, Germany
K. Rother
Affiliation:
Munich University of Applied Sciences, Germany
K. Paetzold*
Affiliation:
Technische Universität Dresden, Germany
*
[email protected]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Truss-like shapes can occur in topology optimization described by an assembly of finite elements or its boundary represented as a polygon mesh. Such shape description does not cover a common engineering parametrization like the lines of a frame structure and its corresponding cross-section. This article addresses the truss-parametrization of such optimization using curve skeletons and Meta Balls. While the curve skeleton is common in the truss-parametrization, including Meta Balls can lead to an overall implicit and smooth shape description.

Keywords

topological optimisationreverse engineeringcomputer-aided design (CAD)
Type
Article
Information
Proceedings of the Design Society , Volume 2: DESIGN2022 , May 2022 , pp. 363 - 372
Creative Commons
Creative Common License - CCCreative Common License - BYCreative Common License - NCCreative Common License - ND
This is an Open Access article, distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives licence (http://creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is unaltered and is properly cited. The written permission of Cambridge University Press must be obtained for commercial re-use or in order to create a derivative work.
Copyright
The Author(s), 2022.

References

Adam, G.A.O., Zimmer, D., 2015. On design for additive manufacturing: evaluating geometrical limitations. Rapid Prototyp. J. 21, 662–670. 10.1108/RPJ-06-2013-0060CrossRefGoogle Scholar
Alexe, A., Barthe, L., Cani, M.P., Gaildrat, V., 2007. Shape Modeling by Sketching Using Convolution Surfaces, in: ACM SIGGRAPH 2007 Courses, SIGGRAPH ’07. Association for Computing Machinery, New York, NY, USA, pp. 39-es. 10.1145/1281500.1281550Google Scholar
Amroune, A., Cuillière, J.-C., François, V., 2022. Automated Lofting-Based Reconstruction of CAD Models from 3D Topology Optimization Results. Comput.-Aided Des. 145, 103183. 10.1016/j.cad.2021.103183CrossRefGoogle Scholar
Angles, B., Tarini, M., Wyvill, B., Barthe, L., Tagliasacchi, A., 2017. Sketch-Based Implicit Blending. ACM Trans Graph 36. 10.1145/3130800.3130825CrossRefGoogle Scholar
Bandara, K., Rüberg, T., Cirak, F., 2016. Shape optimisation with multiresolution subdivision surfaces and immersed finite elements. Comput. Methods Appl. Mech. Eng. 300, 510–539. 10.1016/j.cma.2015.11.015CrossRefGoogle Scholar
Bendsoe, M.P., Sigmund, O., 2004. Topology Optimization: Theory, Methods, and Applications, 2nd ed. Springer-Verlag, Berlin Heidelberg. 10.1007/978-3-662-05086-6Google Scholar
Bendsøe, M.P., Sigmund, O., 1999. Material interpolation schemes in topology optimization. Arch. Appl. Mech. 69, 635–654. 10.1007/s004190050248Google Scholar
Blinn, J.F., 1982. A Generalization of Algebraic Surface Drawing. ACM Trans. Graph. 1, 235–256. 10.1145/357306.357310CrossRefGoogle Scholar
Bloomenthal, J., Shoemake, K., 1991. Convolution Surfaces, in: Proceedings of the 18th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH ’91. Association for Computing Machinery, New York, NY, USA, pp. 251–256. 10.1145/122718.122757CrossRefGoogle Scholar
Bloomenthal, J., Wyvill, B., 1997. Introduction to Implicit Surfaces. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA.Google Scholar
Blum, H., 1967. A Transformation for Extracting New Descriptors of Shape, in: Wathen-Dunn, W. (Ed.), Models for the Perception of Speech and Visual Form. MIT Press, Cambridge, pp. 362–380.Google Scholar
Bremicker, M., Chirehdast, M., Kikuchi, N., Papalambros, P.Y., 1991. Integrated Topology and Shape Optimization in Structural Design∗. Mech. Struct. Mach. 19, 551–587. 10.1080/08905459108905156CrossRefGoogle Scholar
Burger, W., Burge, M.J., 2009. Principles of Digital Image Processing, Undergraduate Topics in Computer Science. Springer London, London. 10.1007/978-1-84800-191-6CrossRefGoogle Scholar
Catmull, E., Clark, J., 1978. Recursively generated B-spline surfaces on arbitrary topological meshes. Comput.-Aided Des. 10, 350–355. 10.1016/0010-4485(78)90110-0CrossRefGoogle Scholar
Christiansen, A.N., Bærentzen, J.A., Nobel-Jørgensen, M., Aage, N., Sigmund, O., 2015. Combined shape and topology optimization of 3D structures. Comput. Graph., Shape Modeling International 2014 46, 25–35. 10.1016/j.cag.2014.09.021Google Scholar
Cuillière, J.-C., François, V., Nana, A., 2018. Automatic construction of structural CAD models from 3D topology optimization. Comput.-Aided Des. Appl. 15, 107–121. 10.1080/16864360.2017.1353726CrossRefGoogle Scholar
Dede, E., 2009. Multiphysics Topology Optimization of Heat Transfer and Fluid Flow Systems. Presented at the COMSOL Users Conference, Boston, USA.Google Scholar
Denk, M., Klemens, R., Paetzold, K., 2021a. Beam-colored Sketch and Image-based 3D Continuous Wireframe Reconstruction with different Materials and Cross-Sections, in: Stelzer, R., Krzywinski, J. (Eds.), Entwerfen Entwickeln Erleben in Produktentwicklung Und Design 2021. Presented at the Entwerfen Entwickeln Erleben, TUDpress, Dresden, pp. 345–354. 10.25368/2021.33Google Scholar
Denk, M., Rother, K., Paetzold, K., 2021b. Fully Automated Subdivision Surface Parametrization for Topology Optimized Structures and Frame Structures Using Euclidean Distance Transformation and Homotopic Thinning, in: Pfingstl, S., Horoschenkoff, A., Höfer, P., Zimmermann, M. (Eds.), Proceedings of the Munich Symposium on Lightweight Design 2020. Springer Berlin Heidelberg, Berlin, Heidelberg, pp. 18–27. 10.1007/978-3-662-63143-0_2CrossRefGoogle Scholar
Denk, M., Rother, K., Paetzold, K., 2021c. Subdivision Surfaces Mid-Surface Reconstruction of Topology Optimization Results and Thin-Walled Shapes using Surface Seletons, in: Proceedings of the 21th International Conference on Engineering Design. Presented at the International Conference on Engineering Design (ICED21), Cambridge University Press, Goethenburg, pp. 2771–2780. 10.1017/pds.2021.538Google Scholar
Denk, M., Rother, K., Paetzold, K., 2020. Multi-Objective Topology Optimization of Heat Conduction and Linear Elastostatic using Weighted Global Criteria Method, in: Proceedings of the 31st Symposium Design for X (DFX2020), DFX. Presented at the DfX Symposium 2020, The Design Society, Bamberg, pp. 91–100. 10.35199/dfx2020.10Google Scholar
Denk, M., Rother, K., Zinßer, M., Petroll, C., Paetzold, K., 2021d. Nodal cosine sine material interpolation in multi objective topology optimization with the global criteria method for linear elasto static, heat transfer, potential flow and binary cross entropy sharpening., in: Proceedings of the 23th International Conference on Engineering Design. Presented at the International Conference on Engineering Design, Cambridge University Press, Götheburg, pp. 2247–2256. 10.1017/pds.2021.486Google Scholar
Gao, J., Luo, Z., Xiao, M., Gao, L., Li, P., 2020. A NURBS-based Multi-Material Interpolation (N-MMI) for isogeometric topology optimization of structures. Appl. Math. Model. 81, 818–843. 10.1016/j.apm.2020.01.006CrossRefGoogle Scholar
Hitoshi, N., Makoto, H., Toshiyuki, K., Toru, K., Isao, S., Koichi, O., 1985. Object modeling by distribution function and a method of image generation. 電子通信学会論文誌 D 68, 718–725.Google Scholar
Hubert, E., Cani, M.-P., 2012. Convolution surfaces based on polygonal curve skeletons. J. Symb. Comput., Advances in Mathematics Mechanization 47, 680–699. 10.1016/j.jsc.2011.12.026Google Scholar
Joo, Y., Lee, I., Kim, S.J., 2018. Efficient three-dimensional topology optimization of heat sinks in natural convection using the shape-dependent convection model. Int. J. Heat Mass Transf. 127, 32–40. 10.1016/j.ijheatmasstransfer.2018.08.009CrossRefGoogle Scholar
Karpenko, O., Hughes, J.F., Raskar, R., 2002. Free-form sketching with variational implicit surfaces. Comput. Graph. Forum 21, 585–594.CrossRefGoogle Scholar
Lee, T.C., Kashyap, R.L., Chu, C.N., 1994. Building Skeleton Models via 3-D Medial Surface Axis Thinning Algorithms. CVGIP Graph. Models Image Process. 56, 462–478. 10.1006/cgip.1994.1042Google Scholar
Mayer, J., Wartzack, S., 2020. Ermittlung eines Skelettierungsverfahrens zur Konvertierung von Topologieoptimierungsergebnissen, in: Proceedings of the 31st Symposium Design for X (DFX2020). Presented at the Symposium Design for X 2020, Bamberg, pp. 111–120. 10.35199/dfx2020.12CrossRefGoogle Scholar
Morgenthaler, D.G., 1981. Three-dimensional Simple Points: Serial Erosion, Parallel Thinning, and Skeletonization. University of Maryland.Google Scholar
Nana, A., Cuillière, J.-C., Francois, V., 2017. Automatic reconstruction of beam structures from 3D topology optimization results. Comput. Struct. 189, 62–82. 10.1016/j.compstruc.2017.04.018CrossRefGoogle Scholar
Pan, J., Yan, S., Qin, H., 2016. Interactive Dissection of Digital Organs Based on Metaballs, in: Proceedings of the 33rd Computer Graphics International. Presented at the CGI ’16: Computer Graphics International, ACM, Heraklion Greece, pp. 13–16. 10.1145/2949035.2949039Google Scholar
Sobiecki, A., Jalba, A., Telea, A., 2014. Comparison of curve and surface skeletonization methods for voxel shapes. Pattern Recognit. Lett. 47, 147–156. 10.1016/j.patrec.2014.01.012CrossRefGoogle Scholar
Stangl, T., Wartzack, S., 2015. Feature based interpretation and reconstruction of structural topology optimization results, in: Weber, M., Husung, C., Cascini, S., Cantamessa, G., Marjanovic, M., Bordegoni, D. (Ed.), Proceedings of the 20th International Conference on Engineering Design (ICED15). Design Society, p. Vol. 6, 235–245.Google Scholar
Tagliasacchi, A., Delame, T., Spagnuolo, M., Amenta, N., Telea, A., 2016. 3D Skeletons: A State-of-the-Art Report. Comput. Graph. Forum 35, 573–597. 10.1111/cgf.12865CrossRefGoogle Scholar
Wyvill, G., McPheeters, C., Wyvill, B., 1986. Data structure for soft objects. Vis. Comput. 2, 227–234. 10.1007/BF01900346CrossRefGoogle Scholar
Xia, Y., Langelaar, M., Hendriks, M., 2020. Optimization-based three-dimensional strut-and-tie model generation for reinforced concrete. Comput.-Aided Civ. Infrastruct. Eng. 10.1111/mice.12614CrossRefGoogle Scholar
Xu, T.-C., Wu, E.-H., 2016. View-space meta-ball approximation by depth-independent accumulative fields, in: SIGGRAPH ASIA 2016 Technical Briefs, SA ’16. Association for Computing Machinery, New York, NY, USA, pp. 1–4. 10.1145/3005358.3005389Google Scholar
Yin, G., Xiao, X., Cirak, F., 2020. Topologically robust CAD model generation for structural optimisation. Comput. Methods Appl. Mech. Eng. 369, 113102. 10.1016/j.cma.2020.113102CrossRefGoogle Scholar