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SUBDIVISION SURFACE MID-SURFACE RECONSTRUCTION OF TOPOLOGY OPTIMIZATION RESULTS AND THIN-WALLED SHAPES USING SURFACE SKELETONS

Published online by Cambridge University Press:  27 July 2021

Martin Denk ,
Klemens Rother  and
Kristin Paetzold
Martin Denk*
Affiliation:
Bundeswehr University Munich, Institute for Technical Product Development
Klemens Rother
Affiliation:
Munich University of Applied Sciences, Institute for Material and Building Research
Kristin Paetzold
Affiliation:
Bundeswehr University Munich, Institute for Technical Product Development
*
Denk, Martin, Bundeswehr University Munich, Insitute for Technical Product Development, Germany, [email protected]

Abstract

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Polygon meshes and particularly triangulated meshes can be used to describe the shape of different types of geometry such as bicycles, bridges, or runways. In engineering, such polygon meshes can occur as finite element meshes, resulting from topology optimization or laser scanning. This article presents an automated parameterization of polygon meshes into a parametric representation using subdivision surfaces, especially in topology optimization. Therefore, we perform surface skeletonization on a volumetric grid supported by the Euclidian distance transformation and topology preserving and shape-preserving criterion. Based on that surface skeleton, an automated conversation into a Subdivision Surface Control grid is established. The final mid-surface-like parametrization is quite flexible and can be changed by variating the control gird or the local thickness.

Keywords

Computational design methodsComputer Aided Design (CAD)Lightweight designSkeletonisationTopology Optimization
Type
Article
Information
Proceedings of the Design Society , Volume 1: ICED21 , August 2021 , pp. 2771 - 2780
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), 2021. Published by Cambridge University Press

References

Adam, G.A.O., Zimmer, D., 2015. On design for additive manufacturing: evaluating geometrical limitations. Rapid Prototyp. J. 21, 662–670. https://doi.org/10.1108/RPJ-06-2013-0060CrossRefGoogle Scholar
Agathos, A., Pratikakis, I., Perantonis, S., Sapidis, N., Azariadis, P., 2007. 3D Mesh Segmentation Methodologies for CAD applications. Comput.-Aided Des. Appl. 4, 827–841. https://doi.org/10.1080/16864360.2007.10738515CrossRefGoogle 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. https://doi.org/10.1016/j.cma.2015.11.015CrossRefGoogle Scholar
Ben Makhlouf, A., Louhichi, B., Mahjoub, M.A., Deneux, D., 2019. Reconstruction of a CAD model from the deformed mesh using B-spline surfaces. Int. J. Comput. Integr. Manuf. 32, 669–681. https://doi.org/10.1080/0951192X.2019.1599442CrossRefGoogle Scholar
Bendsøe, M.P., Sigmund, O., 1999. Material interpolation schemes in topology optimization. Arch. Appl. Mech. 69, 635–654. https://doi.org/10.1007/s004190050248Google Scholar
Bénière, R., Subsol, G., Gesquière, G., Le Breton, F., Puech, W., 2013. A comprehensive process of reverse engineering from 3D meshes to CAD models. Comput.-Aided Des. 45, 1382–1393. https://doi.org/10.1016/j.cad.2013.06.004CrossRefGoogle Scholar
Blum, H., 1967. A Transformation for Extracting New Descriptors of Shape. M.I.T. Press.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. https://doi.org/10.1080/08905459108905156CrossRefGoogle Scholar
Couprie, M., Bertrand, G., 2015. A 3D Sequential Thinning Scheme Based on Critical Kernels, in: Benediktsson, J.A., Chanussot, J., Najman, L., Talbot, H. (Eds.), Mathematical Morphology and Its Applications to Signal and Image Processing, Lecture Notes in Computer Science. Springer International Publishing, pp. 549–560.CrossRefGoogle Scholar
Dedè, L., Borden, M.J., Hughes, T.J.R., 2012. Isogeometric Analysis for Topology Optimization with a Phase Field Model. Arch. Comput. Methods Eng. 19, 427–465. https://doi.org/10.1007/s11831-012-9075-zCrossRefGoogle Scholar
Denk, M., Paetzold, K., Rother, K., 2019. Feature line detection of noisy triangulated CSGbased objects using deep learning, in: Proceedings of the 30th Symposium Design for X (DFX 2019), DfX. Presented at the DfX Symposium 2019, The Design Society, Jesteburg, Germany, pp. 239–250. https://doi.org/10.35199/dfx2019.21CrossRefGoogle Scholar
Denk, M., Rother, K., Paetzold, K., 2020a. Fully Automated Subdivision Surface Parametrization for Topology Optimized Structures and Frame Structures using Euclidean Distance Transformation and Homotopic Thinning, in: Proceedings of the Munich Symposium on Lightweight Design 2020. Springer Nature, Munich, Germany. https://doi.org/10.1007/978-3-662-63143-0CrossRefGoogle Scholar
Denk, M., Rother, K., Paetzold, K., 2020b. 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. https://doi.org/10.35199/dfx2020.10CrossRefGoogle Scholar
Dey, T.K., Woo, H., Zhao, W., 2003. Approximate medial axis for CAD models, in: Proceedings of the Eighth ACM Symposium on Solid Modeling and Applications, SM ’03. Association for Computing Machinery, New York, NY, USA, pp. 280–285. https://doi.org/10.1145/781606.781652CrossRefGoogle Scholar
Dierckx, P., 1982. Algorithms for smoothing data with periodic and parametric splines. Comput. Graph. Image Process. 20, 171–184. https://doi.org/10.1016/0146-664X(82)90043-0CrossRefGoogle Scholar
Feng, C., Jalba, A.C., Telea, A.C., 2015. Part-Based Segmentation by Skeleton Cut Space Analysis, in: Benediktsson, J.A., Chanussot, J., Najman, L., Talbot, H. (Eds.), Mathematical Morphology and Its Applications to Signal and Image Processing, Lecture Notes in Computer Science. Springer International Publishing, Cham, pp. 607–618. https://doi.org/10.1007/978-3-319-18720-4_51CrossRefGoogle Scholar
Gao, J., Gao, L., Luo, Z., Li, P., 2019. Isogeometric topology optimization for continuum structures using density distribution function. Int. J. Numer. Methods Eng. 119, 991–1017. https://doi.org/10.1002/nme.6081CrossRefGoogle 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. https://doi.org/10.1016/j.apm.2020.01.006CrossRefGoogle Scholar
Gauthier, S., Puech, W., Bénière, R., Subsol, G., 2017. Analysis of digitized 3D mesh curvature histograms for reverse engineering. Comput. Ind. . https://doi.org/10.1016/j.compind.2017.06.008CrossRefGoogle Scholar
Goyal, M., Murugappan, S., Piya, C., Benjamin, W., Fang, Y., Liu, M., Ramani, K., 2012. Towards locally and globally shape-aware reverse 3D modeling. Comput.-Aided Des. 44, 537–553. https://doi.org/10.1016/j.cad.2011.12.004CrossRefGoogle Scholar
Hisada, M., Belyaev, A.G., Kunii, T.L., 2001. A 3D Voronoi-based skeleton and associated surface features, in: Proceedings Ninth Pacific Conference on Computer Graphics and Applications. Pacific Graphics 2001. Presented at the Proceedings Ninth Pacific Conference on Computer Graphics and Applications. Pacific Graphics 2001, pp. 89–96. https://doi.org/10.1109/PCCGA.2001.962861CrossRefGoogle Scholar
Hua Li, Yezzi. A., 2006. Vessels as 4D Curves: Global Minimal 4D Paths to Extract 3D Tubular Surfaces, in: 2006 Conference on Computer Vision and Pattern Recognition Workshop (CVPRW'06). Presented at the 2006 Conference on Computer Vision and Pattern Recognition Workshop (CVPRW'06), pp. 82–82. https://doi.org/10.1109/CVPRW.2006.210CrossRefGoogle Scholar
Koehoorn, J., Feng, C., Kustra, J., Jalba, A., Telea, A., 2017. Unified part-patch segmentation of mesh shapes using surface skeletons, in: Skeletonization. Elsevier, Netherlands, pp. 89–122. https://doi.org/10.1016/B978-0-08-101291-8.00005-5Google Scholar
Kong, T.Y., Rosenfeld, A., 1989. Digital topology: Introduction and survey. Comput. Vis. Graph. Image Process. 48, 357–393. https://doi.org/10.1016/0734-189X(89)90147-3CrossRefGoogle Scholar
Kresslein, J., Haghighi, P., Park, J., Ramnath, S., Sutradhar, A., Shah, J.J., 2018. Automated cross-sectional shape recovery of 3D branching structures from point cloud. J. Comput. Des. Eng. 5, 368–378. https://doi.org/10.1016/j.jcde.2017.11.010Google 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. https://doi.org/10.1006/cgip.1994.1042CrossRefGoogle Scholar
Lian, H., Christiansen, A.N., Tortorelli, D.A., Sigmund, O., Aage, N., 2017. Combined shape and topology optimization for minimization of maximal von Mises stress. Struct. Multidiscip. Optim. 55, 1541–1557. https://doi.org/10.1007/s00158-017-1656-xCrossRefGoogle Scholar
Lidayová, K., Frimmel, H., Wang, C., Bengtsson, E., Smedby, Ö., 2016. Fast vascular skeleton extraction algorithm. Pattern Recognit. Lett., Special Issue on Skeletonization and its Application 76, 67–75. https://doi.org/10.1016/j.patrec.2015.06.024Google Scholar
Louhichi, B., Abenhaim, G.N., Tahan, A.S., 2015. CAD/CAE integration: updating the CAD model after a FEM analysis. Int. J. Adv. Manuf. Technol. 76, 391–400. https://doi.org/10.1007/s00170-014-6248-yCrossRefGoogle 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. https://doi.org/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. https://doi.org/10.1016/j.compstruc.2017.04.018CrossRefGoogle Scholar
Picelli, R., Townsend, S., Brampton, C., Norato, J., Kim, H.A., 2018. Stress-based shape and topology optimization with the level set method. Comput. Methods Appl. Mech. Eng. 329, 1–23. https://doi.org/10.1016/j.cma.2017.09.001CrossRefGoogle Scholar
Ramanathan, M., Gurumoorthy, B., 2010. Interior Medial Axis Transform computation of 3D objects bound by free-form surfaces. Comput.-Aided Des. 42, 1217–1231. https://doi.org/10.1016/j.cad.2010.08.006CrossRefGoogle Scholar
Reniers, D., Telea, A., 2008a. Part-type Segmentation of Articulated Voxel-Shapes using the Junction Rule. Comput. Graph. Forum 27, 1845–1852. https://doi.org/10.1111/j.1467-8659.2008.01331.xCrossRefGoogle Scholar
Reniers, D., Telea, A., 2008b. Patch-type Segmentation of Voxel Shapes using Simplified Surface Skeletons. Comput. Graph. Forum 27, 1837–1844. https://doi.org/10.1111/j.1467-8659.2008.01330.xCrossRefGoogle Scholar
Saha, P.K., Gomberg, B.R., Wehrli, F.W., 2000. Three-dimensional digital topological characterization of cancellous bone architecture. Int. J. Imaging Syst. Technol. 11, 81–90. https://doi.org/10.1002/(SICI)1098-1098(2000)11:1<81::AID-IMA9>3.0.CO;2-13.0.CO;2-1>CrossRefGoogle Scholar
Siddiqi, K., Bouix, S., Tannenbaum, A., Zucker, S.W., 2002. Hamilton-Jacobi Skeletons. Int. J. Comput. Vis. 48, 215–231. https://doi.org/10.1023/A:1016376116653CrossRefGoogle Scholar
Sobiecki, A., Yasan, H.C., Jalba, A.C., Telea, A.C., 2013. Qualitative Comparison of Contraction-Based Curve Skeletonization Methods, in: Hendriks, C.L.L., Borgefors, G., Strand, R. (Eds.), Mathematical Morphology and Its Applications to Signal and Image Processing, Lecture Notes in Computer Science. Springer Berlin Heidelberg, pp. 425–439.CrossRefGoogle Scholar
Stangl, T., Wartzack, S., 2015. Feature based interpretation and reconstruction of structural topology optimization results, in: Weber, M. C.; Husung, S.; Cascini, G.; Cantamessa, M.; Marjanovic, D.; Bordegoni, (Ed.), Proceedings of the 20th International Conference on Engineering Design (ICED15). Design Society, p. Vol. 6, 235-245.Google Scholar
Storti, D.W., Turkiyyah, G.M., Ganter, M.A., Lim, C.T., Stal, D.M., 1997. Skeleton-based modeling operations on solids, in: Proceedings of the Fourth ACM Symposium on Solid Modeling and Applications, SMA ’97. Association for Computing Machinery, New York, NY, USA, pp. 141–154. https://doi.org/10.1145/267734.267771CrossRefGoogle Scholar
Svensson, S., Nyström, I., Sanniti di Baja, G., 2002. Curve skeletonization of surface-like objects in 3D images guided by voxel classification. Pattern Recognit. Lett. 23, 1419–1426. https://doi.org/10.1016/S0167-8655(02)00102-2CrossRefGoogle Scholar
Tagliasacchi, A., Alhashim, I., Olson, M., Zhang, H., 2012. Mean Curvature Skeletons. Comput. Graph. Forum 31, 1735–1744. https://doi.org/10.1111/j.1467-8659.2012.03178.xCrossRefGoogle 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. https://doi.org/10.1111/cgf.12865CrossRefGoogle Scholar
Vidal, V., Wolf, C., Dupont, F., 2014. Mechanical Mesh Segmentation and Global 3D Shape Extraction.Google Scholar
Wang, P., Gan, Y., Shui, P., Yu, F., Zhang, Y., Chen, S., Sun, Z., 2018. 3D shape segmentation via shape fully convolutional networks. Comput. Graph. 76, 182–192. https://doi.org/10.1016/j.cag.2018.07.011CrossRefGoogle Scholar
Weber, S., Montero, J., Bleckmann, M., Paetzold, K., 2020. Parameters on Support Structure Design for Metal Additive Manufacturing. Proc. Des. Soc. Des. Conf. 1, 1145–1154. https://doi.org/10.1017/dsd.2020.14CrossRefGoogle Scholar
Wu, B., Xu, K., Zhou, Y., Xiong, Y., Huang, H., 2016. Skeleton-guided 3D shape distance field metamorphosis. Graph. Models, SI: CVM 2016 selected Papers 85, 37–45. https://doi.org/10.1016/j.gmod.2016.03.003CrossRefGoogle Scholar
Yin, G., Xiao, X., Cirak, F., 2020. Topologically robust CAD model generation for structural optimisation. Comput. Methods Appl. Mech. Eng. 369, 113102. https://doi.org/10.1016/j.cma.2020.113102CrossRefGoogle Scholar
Yoely, Y.M., Amir, O., Hanniel, I., 2018. Topology and shape optimization with explicit geometric constraints using a spline-based representation and a fixed grid. Procedia Manuf., 15th Global Conference on Sustainable Manufacturing 21, 189–196. https://doi.org/10.1016/j.promfg.2018.02.110CrossRefGoogle Scholar