Login | Register

GDFE: Geometry-Driven Finite Element for Four-Dimensional Printing


GDFE: Geometry-Driven Finite Element for Four-Dimensional Printing

Kwok, Tsz Ho ORCID: https://orcid.org/0000-0001-7240-1426 and Chen, Yong (2017) GDFE: Geometry-Driven Finite Element for Four-Dimensional Printing. Journal Of Manufacturing Science And Engineering, 139 (11). p. 111006.

Text (application/pdf)
JMSE17_GDFE.pdf - Accepted Version
Available under License Spectrum Terms of Access.

Official URL: http://dx.doi.org/10.1115/1.4037429


Four-dimensional (4D) printing is a new category of printing that expands the fabrication process to include time as the forth dimension, and its process planning and simulation have to take time into consideration as well. The common tool to estimating the behavior of a deformable object is the finite element method (FEM). Although FEM is powerful, there are various sources of deformation from hardware, environment, and process, just to name a few, which are too complex to model by FEM. This paper introduces Geometry-Driven Finite Element (GDFE) as a solution to this problem. Based on the study on geometry changes, the deformation principles can be drawn to predict the relationship between the 4D-printing process and the shape transformation. Similar to FEM, the design domain is subdivided into a set of GDFEs, and the principles are applied on each GDFE, which are then assembled to a larger system that describes the overall shape. The proposed method converts the complex sources of deformation to a geometric optimization problem, which is intuitive and effective. The usages and applications of the GDFE framework have also been presented in this paper, including freeform design, reserve design, and design validation.

Divisions:Concordia University > Gina Cody School of Engineering and Computer Science > Mechanical, Industrial and Aerospace Engineering
Item Type:Article
Authors:Kwok, Tsz Ho and Chen, Yong
Journal or Publication:Journal Of Manufacturing Science And Engineering
Date:13 September 2017
  • Natural Sciences & Engineering Research Council of Canada
Digital Object Identifier (DOI):10.1115/1.4037429
ID Code:983466
Deposited By: TSZ HO KWOK
Deposited On:05 Feb 2018 14:17
Last Modified:12 Sep 2018 00:00


[1] Hull, C. W., 1984. Apparatus for production of three-dimensional objects by stereolithography. United States patent US 4,575,330.
[2] Park, J.-R., Slanac, D. A., Leong, T. G., Ye, H., Nelson, D. B., and Gracias, D. H., 2008. “Reconfigurable microfluidics with metallic containers”. Journal of Microelectromechanical Systems, 17(2), April, pp. 265–271.
[3] Azam, A., Laflin, K. E., Jamal, M., Fernandes, R., and Gracias, D. H., 2011. “Self-folding micropatterned
polymeric containers”. Biomedical Microdevices, 13(1), pp. 51–58.
[4] Gao, W., Zhang, Y., Ramanujan, D., Ramani, K., Chen, Y., Williams, C. B., Wang, C. C., Shin, Y. C., Zhang, S., and Zavattieri, P. D., 2015. “The status, challenges, and future of additive manufacturing in engineering”. Comput. Aided Des., 69(C), Dec., pp. 65–89.
[5] Lang, R. J., 2011. Origami Design Secrets: Mathematical Methods for an Ancient Art. CRC Press, Boca Raton, FL.
[6] Zhang, K., Qiu, C., and Dai, J. S., 2015. “Helical kirigami-enabled centimeter-scale worm robot with shape-memory-alloy linear actuators”. Journal of Mechanisms and Robotics, 7(2), p. 021014.
[7] Ge, Q., Qi, H. J., and Dunn, M. L., 2013. “Active materials by four-dimension printing”. Applied Physics Letters, 103(13), p. 131901.
[8] Tibbits, S., 2014. “4D printing: Multi-material shape change”. Architectural Design, 84(1), pp. 116–21.
[9] Deng, D., and Chen, Y., 2015. “Origami-based selffolding structure design and fabrication using projection based stereolithography”. J. Mech. Des., 137(2), p. 021701:12.
[10] Sydney Gladman, A., Matsumoto, E. A., Nuzzo, R. G., Mahadevan, L., and Lewis, J. A., 2016. “Biomimetic 4d printing”. Nature Materials, 15(4), pp. 413 – 418.
[11] Felton, S., Tolley, M., Demaine, E., Rus, D., and Wood, R., 2014. “A method for building self-folding machines”. Science, 345(6197), pp. 644–646.
[12] Na, J.-H., Evans, A. A., Bae, J., Chiappelli, M. C., Santangelo, C. D., Lang, R. J., Hull, T. C., and Hayward, R. C., 2015. “Programming reversibly self-folding origami with micropatterned photo-crosslinkable polymer trilayers”. Advanced Materials, 27(1), pp. 79–85.
[13] Breger, J. C., Yoon, C., Xiao, R., Kwag, H. R., Wang, M. O., Fisher, J. P., Nguyen, T. D., and Gracias, D. H., 2015. “Self-folding thermo-magnetically responsive soft microgrippers”. ACS Applied Materials & Interfaces, 7(5), pp. 3398–3405.
[14] Geryak, R., and Tsukruk, V. V., 2014. “Reconfigurable and actuating structures from soft materials”. Soft Matter, 10, pp. 1246–1263.
[15] Malachowski, K., Breger, J., Kwag, H. R., Wang, M. O., Fisher, J. P., Selaru, F. M., and Gracias, D. H., 2014. “Stimuli-responsive theragrippers for chemomechanical controlled release”. Angewandte Chemie International Edition, 53(31), pp. 8045–8049.
[16] Kwok, T.-H., Wang, C. C. L., Deng, D., Zhang, Y., and Chen, Y., 2015. “Four-dimensional printing for freeform surfaces: Design optimization of origami and kirigami structures”. J. Mech. Des., 131(1), p. 111413:10.
[17] Hernandez, E. A. P., Hartl, D. J., Akleman, E., and Lagoudas, D. C., 2016. “Modeling and analysis of origami structures with smooth folds”. ComputerAided Design, 78, pp. 93 – 106. {SPM} 2016.
[18] Momeni, F., Hassani.N, S. M., Liu, X., and Ni, J., 2017. “A review of 4d printing”. Materials & Design, 122, pp. 42 – 79.
[19] Tibbits, S., 2012. “Design to self-assembly”. Architectural Design, 82(2), pp. 68–73.
[20] Khoo, Z. X., Teoh, J. E. M., Liu, Y., Chua, C. K., Yang, S., An, J., Leong, K. F., and Yeong, W. Y., 2015. “3d printing of smart materials: A review on recent progresses in 4d printing”. Virtual and Physical Prototyping, 10(3), pp. 103–122.
[21] Choi, J., Kwon, O.-C., Jo, W., Lee, H. J., and Moon, M.-W., 2015. “4d printing technology: A review”. 3D Printing and Additive Manufacturing, 2(4), pp. 159–167.
[22] Wang, M.-F., Maleki, T., and Ziaie, B., 2008. “Enhanced 3-D folding of silicon microstructures via thermal shrinkage of a composite organic/inorganic bilayer”. Journal of Microelectromechanical Systems, 17(4), Aug, pp. 882–889.
[23] Yasu, K., and Inami, M., 2012. “Popapy: Instant paper craft made up in a microwave oven”. In Advances in Computer Entertainment, A. Nijholt, T. Romo, and D. Reidsma, eds., Vol. 7624 of Lecture Notes in Computer Science. Springer Berlin Heidelberg, pp. 406–420.
[24] Smela, E., 2003. “Conjugated polymer actuators for biomedical applications”. Advanced Materials, 15(6), pp. 481–494.
[25] Ionov, L., 2012. “Biomimetic 3D self-assembling biomicroconstructs by spontaneous deformation of thin polymer films”. J. Mater. Chem., 22, pp. 19366–19375.
[26] Peraza-Hernandez, E., Hartl, D., Galvan, E., and Malak, R., 2013. “Design and optimization of a shape memory alloy-based self-folding sheet”. Journal of Mechanical Design, 135, p. 111007.
[27] Ionov, L., 2011. “Soft microorigami: self-folding polymer films”. Soft Matter, 7, pp. 6786–6791.
[28] Shim, T. S., Kim, S.-H., Heo, C.-J., Jeon, H. C., and Yang, S.-M., 2012. “Controlled origami folding of hydrogel bilayers with sustained reversibility for robust microcarriers”. Angewandte Chemie International Edition, 51(6), pp. 1420–1423.
[29] Stoychev, G., Turcaud, S., Dunlop, J. W. C., and Ionov, L., 2013. “Hierarchical multi-step folding of polymer bilayers”. Advanced Functional Materials, 23(18), pp. 2295–2300.
[30] Ahmed, S., Lauff, C., Crivaro, A., McGough, K., Sheridan, R., Frecker, M., von Lockette, P., Ounaies, Z., Simpson, T., Lien, J.-M., and Strzelec, R., 2013. “Multi-field responsive origami structures: Preliminary modeling and experiments”. In Proceedings of the ASME IDETC/CIE, August 4-7, Portland, Oregon, USA, p. V06BT07A028.
[31] Liu, Y., Boyles, J. K., Genzer, J., and Dickey, M. D., 2012. “Self-folding of polymer sheets using local light absorption”. Soft Matter, 8, pp. 1764–1769.
[32] Raviv, D., Zhao, W., McKnelly, C., Papadopoulou, A., Kadambi, A., Shi, B., Hirsch, S., Dikovsky, D., Zyracki, M., Olguin, C., Raskar, R., and Tibbits, S., 14. “Active printed materials for complex self-evolving deformations”. Sci. Rep., 4.
[33] Schenk, M., and Guest, S. D. ., 2011. “Origami folding: A structural engineering approach”. In Origami 5: Fifth International Meeting of Origami Science, Mathematics, and Education, p. 291303.
[34] Tachi, T., 2013. “Interactive form-finding of elastic origami”. In the International Association for Shell and Spatial Structures (IASS) Symposium.
[35] Zhu, L., Igarashi, T., and Mitani, J., 2013. “Soft folding”. Computer Graphics Forum, 32(7), pp. 167–176.
[36] Belcastro, S.-M., and Hull, T. C., 2002. “Modelling the folding of paper into three dimensions using affine transformations”. Linear Algebra and its Applications, 348(13), pp. 273 – 282.
[37] Tachi, T., 2010. Advances in Architectural Geometry. Springer Vienna, Vienna, ch. Freeform RigidFoldable Structure using Bidirectionally Flat-Foldable Planar Quadrilateral Mesh, pp. 87–102.
[38] Hwang, H.-D., and Yoon, S.-H., 2015. “Constructing developable surfaces by wrapping cones and cylinders”. Computer-Aided Design, 58, pp. 230 – 235. Solid and Physical Modeling 2014.
[39] Pan, Y., Zhou, C., and Chen, Y., 2012. “A fast mask projection stereolithography process for fabricating digital models in minutes”. Journal of Manufacturing Science and Engineering, 134(5), pp. 051011 – 9.
[40] Zhou, C., Chen, Y., Yang, Z., and Khoshnevis, B., 2013. “Digital material fabrication using maskimageprojectionbased stereolithography”. Rapid Prototyping Journal, 19(3), pp. 153–165.
[41] Bodansky, E., and Gribov, A., 2006. Approximation of a Polyline with a Sequence of Geometric Primitives. Springer Berlin Heidelberg, Berlin, Heidelberg, pp. 468–478.
All items in Spectrum are protected by copyright, with all rights reserved. The use of items is governed by Spectrum's terms of access.

Repository Staff Only: item control page

Downloads per month over past year

Back to top Back to top