Advertisement

Active Origami pp 331-409 | Cite as

Structural Mechanics and Design of Active Origami Structures

  • Edwin A. Peraza Hernandez
  • Darren J. Hartl
  • Dimitris C. Lagoudas
Chapter

Abstract

A model for the mechanics of active origami structures with smooth folds is presented in this chapter. The model entails the integration of the surface kinematics model for origami with smooth folds developed in Chap.  5 and existing plate theories to obtain a structural representation for folds of non-zero thickness. The implementation of the model in a computational environment is also addressed. We provide examples including origami structures comprised of both elastic materials and active materials. Afterwards, the unfolding polyhedra and tuck-folding methods studied in Chaps.  6 and  7 are extended to develop frameworks for the design of active origami structures. The extensions account for the folding deformation achievable by smooth folds of specified thickness and constituent materials, which is not considered in the purely kinematic formulations of Chaps.  6 and  7.

References

  1. 1.
    M. Schenk, S.D. Guest, Origami folding: a structural engineering approach, in Origami 5: Fifth International Meeting of Origami Science, Mathematics, and Education (2011), pp. 291–304Google Scholar
  2. 2.
    A.A. Evans, J.L. Silverberg, C.D. Santangelo, Lattice mechanics of origami tessellations. Phys. Rev. E 92 (1), 013205 (2015)Google Scholar
  3. 3.
    G.V. Rodrigues, L.M. Fonseca, M.A. Savi, A. Paiva, Nonlinear dynamics of an adaptive origami-stent system. Int. J. Mech. Sci. 133 , 303–318 (2017)Google Scholar
  4. 4.
    C.M. Wheeler, M.L. Culpepper, Soft origami: classification, constraint, and actuation of highly compliant origami structures. J. Mech. Robot. 8(5), 051012 (2016)Google Scholar
  5. 5.
    E.A. Peraza Hernandez, D.J. Hartl, R.J. Malak Jr., D.C. Lagoudas, Origami-inspired active structures: a synthesis and review. Smart Mater. Struct. 23 (9), 094001 (2014)Google Scholar
  6. 6.
    E.A. Peraza Hernandez, D.J. Hartl, D.C. Lagoudas, Kinematics of origami structures with smooth folds. J. Mech. Robot. 8 (6), 061019 (2016)Google Scholar
  7. 7.
    H. Yasuda, Z. Chen, J. Yang, Multitransformable leaf-out origami with bistable behavior. J. Mech. Robot. 8 (3), 031013 (2016)Google Scholar
  8. 8.
    J. Ma, Z. You, The origami crash box, in Origami 5: Fifth International Meeting of Origami Science, Mathematics, and Education (2011), pp. 277–290Google Scholar
  9. 9.
    J. Ma, Z. You, A novel origami crash box with varying profiles, in Proceedings of the ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference IDETC/CIE, No. DETC2013–13495 (American Society of Mechanical Engineers, New York, 2013), pp. V06BT07A048.Google Scholar
  10. 10.
    J. Ma, D. Hou, Y. Chen, Z. You, Quasi-static axial crushing of thin-walled tubes with a kite-shape rigid origami pattern: numerical simulation. Thin-Walled Struct. 100, 38–47 (2016)Google Scholar
  11. 11.
    J. Ma, Z. You, Energy absorption of thin-walled beams with a pre-folded origami pattern. Thin-Walled Struct. 73, 198–206 (2013)Google Scholar
  12. 12.
    Y. Li, Z. You, Thin-walled open-section origami beams for energy absorption, in Proceedings of the ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference IDETC/CIE, No. DETC2014–35204 (American Society of Mechanical Engineers, New York, 2014), pp. V003T01A014Google Scholar
  13. 13.
    D. Hou, Y. Chen, J. Ma, Z. You, Axial crushing of thin-walled tubes with kite-shape pattern, in Proceedings of the ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference IDETC/CIE, No. DETC2015–46671 (American Society of Mechanical Engineers, New York, 2015), pp. V05BT08A037Google Scholar
  14. 14.
    K. Yang, S. Xu, J. Shen, S. Zhou, Y.M. Xie, Energy absorption of thin-walled tubes with pre-folded origami patterns: numerical simulation and experimental verification. Thin-Walled Struct. 103, 33–44 (2016)Google Scholar
  15. 15.
    E.A. Peraza Hernandez, D.J. Hartl, R.J. Malak Jr., Design and numerical analysis of an SMA mesh-based self-folding sheet. Smart Mater. Struct. 22(9), 094008 (2013)Google Scholar
  16. 16.
    E. Peraza Hernandez, D. Hartl, E. Galvan, R. Malak, Design and optimization of a shape memory alloy-based self-folding sheet. J. Mech. Des. 135(11), 111007 (2013)Google Scholar
  17. 17.
    R.W. Mailen, M.D. Dickey, J. Genzer, M.A. Zikry, A fully coupled thermo-viscoelastic finite element model for self-folding shape memory polymer sheets. J. Polym. Sci. B Polym. Phys. 55(16), 1207–1219 (2017)Google Scholar
  18. 18.
    S. Ahmed, C. Lauff, A. Crivaro, K. McGough, R. Sheridan, M. Frecker, P. von Lockette, Z. Ounaies, T. Simpson, J.-M. Lien, R. Strzelec, Multi-field responsive origami structures: preliminary modeling and experiments, in Proceedings of the ASME 2013 International Design Engineering Technical Conference and Computers and Information in Engineering Conference IDETC/CIE, No. DETC2013–12405, Portland (2013), pp. V06BT07A028Google Scholar
  19. 19.
    T. Hull, Project Origami: Activities for Exploring Mathematics (CRC Press, Boca Raton, 2012)Google Scholar
  20. 20.
    W.S. Slaughter, The Linearized Theory of Elasticity (Birkhäuser, Boston, 2002)Google Scholar
  21. 21.
    J.N. Reddy, Mechanics of Laminated Composite Plates: Theory and Analysis (CRC Press, Boca Raton, 1997)Google Scholar
  22. 22.
    N.J. Pagano, Exact solutions for composite laminates in cylindrical bending. J. Compos. Mater. 3(3), 398–411 (1969)Google Scholar
  23. 23.
    P. Heyliger, S. Brooks, Exact solutions for laminated piezoelectric plates in cylindrical bending. J. Appl. Mech. 63(4), 903–910 (1996)Google Scholar
  24. 24.
    P.V. Nimbolkar, I.M. Jain, Cylindrical bending of elastic plates. Proc. Math. Sci. 10, 793–802 (2015)Google Scholar
  25. 25.
    K. Fuchi, T.H. Ware, P.R. Buskohl, G.W. Reich, R.A. Vaia, T.J. White, J.J. Joo, Topology optimization for the design of folding liquid crystal elastomer actuators. Soft Matter 11(37), 7288–7295 (2015)Google Scholar
  26. 26.
    G.A. Holzapfel, Nonlinear Solid Mechanics: A Continuum Approach for Engineering (Wiley, Chichester, 2000)Google Scholar
  27. 27.
    J.N. Reddy, Energy Principles and Variational Methods in Applied Mechanics (Wiley, Hoboken, 2002)Google Scholar
  28. 28.
    J.N. Reddy, An Introduction to Nonlinear Finite Element Analysis: With Applications to Heat Transfer, Fluid Mechanics, and Solid Mechanics (Oxford University Press, Oxford, 2014)Google Scholar
  29. 29.
    D.C. Lagoudas (ed.), Shape Memory Alloys: Modeling and Engineering Applications (Springer Science +  Business Media, LLC, New York, 2008)Google Scholar
  30. 30.
    M. Budimir, Piezoelectric anisotropy and free energy instability in classic perovskites. Technical report, Materiaux, Ecole Polytechnique Fédérale de Lausane, 2006Google Scholar
  31. 31.
    J. Lee, J.G. Boyd IV, D.C. Lagoudas, Effective properties of three-phase electro-magneto-elastic composites. Int. J. Eng. Sci. 43(10), 790–825 (2005)Google Scholar
  32. 32.
    P. Tan, L. Tong, Modeling for the electro-magneto-thermo-elastic properties of piezoelectric-magnetic fiber reinforced composites. Compos. A: Appl. Sci. Manuf. 33(5), 631–645 (2002)Google Scholar
  33. 33.
    C.Y.K. Chee, L. Tong, G.P. Steven, A review on the modelling of piezoelectric sensors and actuators incorporated in intelligent structures. J. Intell. Mater. Syst. Struct. 9(1), 3–19 (1998)Google Scholar
  34. 34.
    C.M. Wayman, H.K.D.H. Bhadeshia, Phase transformations, nondiffusive. Phys. Metall. 2, 1507–1554 (1983)Google Scholar
  35. 35.
    D.A. Porter, K.E. Easterling, M. Sherif, Phase Transformations in Metals and Alloys (Third Edition) (CRC Press, Boca Raton, 2009)Google Scholar
  36. 36.
    R. Kainuma, Y. Imano, W. Ito, Y. Sutou, H. Morito, S. Okamoto, O. Kitakami, K. Oikawa, A. Fujita, T. Kanomata, K. Ishida, Magnetic-field-induced shape recovery by reverse phase transformation. Nature 439(7079), 957–960 (2006)Google Scholar
  37. 37.
    B. Kiefer, D.C. Lagoudas, Magnetic field-induced martensitic variant reorientation in magnetic shape memory alloys. Philos. Mag. 85(33–35), 4289–4329 (2005)Google Scholar
  38. 38.
    I. Karaman, B. Basaran, H.E. Karaca, A.I. Karsilayan, Y.I. Chumlyakov, Energy harvesting using martensite variant reorientation mechanism in a NiMnGa magnetic shape memory alloy. Appl. Phys. Lett. 90(17), 172505 (2007)Google Scholar
  39. 39.
    A. Lendlein, S. Kelch, Shape-memory polymers. Angew. Chem. Int. Ed. 41(12), 2034–2057 (2002)Google Scholar
  40. 40.
    P.T. Mather, X. Luo, I.A. Rousseau, Shape memory polymer research. Annu. Rev. Mater. Res. 39, 445–471 (2009)Google Scholar
  41. 41.
    Y. Liu, H. Du, L. Liu, J. Leng, Shape memory polymers and their composites in aerospace applications: a review. Smart Mater. Struct. 23(2), 023001 (2014)Google Scholar
  42. 42.
    M.D. Hager, S. Bode, C. Weber, U.S. Schubert, Shape memory polymers: past, present and future developments. Prog. Polym. Sci. 49–50, 3–33 (2015)Google Scholar
  43. 43.
    J.N. Reddy, An Introduction to the Finite Element Method, vol. 2 (McGraw-Hill, New York, 1993)Google Scholar
  44. 44.
    W. Cheney, D. Kincaid, Numerical Analysis. Mathematics of Scientific Computing (Brooks & Cole Publishing Company, Pacific Grove, 1996)Google Scholar
  45. 45.
    J. Solomon, Numerical Algorithms: Methods for Computer Vision, Machine Learning, and Graphics (CRC Press, Boca Raton, 2015)Google Scholar
  46. 46.
    E.A. Peraza Hernandez, B. Kiefer, D.J. Hartl, A. Menzel, D.C. Lagoudas, Analytical investigation of structurally stable configurations in shape memory alloy-actuated plates. Int. J. Solids Struct. 69, 442–458 (2015)Google Scholar
  47. 47.
    D.J. Hartl, D.C. Lagoudas, Constitutive modeling and structural analysis considering simultaneous phase transformation and plastic yield in shape memory alloys. Smart Mater. Struct. 18(10), 104017 (2009)Google Scholar
  48. 48.
    E. Peraza Hernandez, D. Hartl, E. Akleman, D. Lagoudas, Modeling and analysis of origami structures with smooth folds. Comput. Aided Des. 78, 93–106 (2016)Google Scholar
  49. 49.
    E.A. Peraza Hernandez, D.J. Hartl, A. Kotz, R.J. Malak, Design and optimization of an SMA-based self-folding structural sheet with sparse insulating layers, in Proceedings of the ASME 2014 Conference on Smart Materials, Adaptive Structures and Intelligent Systems SMASIS, SMASIS2014–7540 (American Society of Mechanical Engineers, New York, 2014)Google Scholar
  50. 50.
    E. Peraza Hernandez, D. Hartl, R. Malak, D. Lagoudas, Analysis and optimization of a shape memory alloy-based self-folding sheet considering material uncertainties, in Proceedings of the ASME 2015 Conference on Smart Materials, Adaptive Structures and Intelligent Systems SMASIS, No. SMASIS2015–9001 (American Society of Mechanical Engineers, New York, 2015), pp. V001T01A013Google Scholar
  51. 51.
  52. 52.
    E.A. Peraza Hernandez, D.J. Hartl, D.C. Lagoudas, Design and simulation of origami structures with smooth folds. Proc. R. Soc. A 473(2200), 20160716 (2017)Google Scholar
  53. 53.
    E.A. Peraza Hernandez, D.J. Hartl, D.C. Lagoudas, Analysis and design of an active self-folding antenna, in ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, page V05BT08A049 (American Society of Mechanical Engineers, New York, 2017)Google Scholar
  54. 54.
    S. Yao, X. Liu, S.V. Georgakopoulos, M.M. Tentzeris, A novel reconfigurable origami spring antenna, in Proceedings of the 2014 IEEE Antennas and Propagation Society International Symposium (APSURSI) (IEEE, Piscataway, 2014), pp. 374–375Google Scholar
  55. 55.
    X. Liu, S. Yao, S.V. Georgakopoulos, B.S. Cook, M.M. Tentzeris, Reconfigurable helical antenna based on an origami structure for wireless communication system, in Proceedings of the 2014 IEEE MTT-S International Microwave Symposium (IMS) (IEEE, Piscataway, 2014), pp. 1–4Google Scholar
  56. 56.
    X. Liu, S. Yao, B.S. Cook, M.M. Tentzeris, S.V. Georgakopoulos, An origami reconfigurable axial-mode bifilar helical antenna. IEEE Trans. Antennas Propag. 63(12), 5897–5903 (2015)Google Scholar
  57. 57.
    X. Liu, S.V. Georgakopoulos, M. Tentzeris, A novel mode and frequency reconfigurable origami quadrifilar helical antenna, in 2015 IEEE 16th Annual Wireless and Microwave Technology Conference (WAMICON) (IEEE, Piscataway, 2015), pp. 1–3Google Scholar
  58. 58.
    X. Liu, S. Yao, S. V. Georgakopoulos, M. Tentzeris, Origami quadrifilar helix antenna in UHF band, in Proceedings of the 2014 IEEE Antennas and Propagation Society International Symposium (APSURSI) (IEEE, Piscataway, 2014), pp. 372–373Google Scholar
  59. 59.
    X. Liu, S. Yao, S.V. Georgakopoulos, A frequency tunable origami spherical helical antenna, in 2017 IEEE International Symposium on Antennas and Propagation & USNC/URSI National Radio Science Meeting (IEEE, Piscataway, 2017), pp. 1361–1362Google Scholar
  60. 60.
    S. Yao, S.V. Georgakopoulos, B. Cook, M. Tentzeris, A novel reconfigurable origami accordion antenna, in Proceedings of the 2014 IEEE MTT-S International Microwave Symposium (IMS) (IEEE, Piscataway, 2014), pp. 1–4Google Scholar
  61. 61.
    S. Yao, X. Liu, S.V. Georgakopoulos, M.M. Tentzeris, A novel tunable origami accordion antenna, in Proceedings of the 2014 IEEE Antennas and Propagation Society International Symposium (APSURSI) (IEEE, Piscataway, 2014), pp. 370–371Google Scholar
  62. 62.
    K. Fuchi, A.R. Diaz, E.J. Rothwell, R.O. Ouedraogo, J. Tang, An origami tunable metamaterial. J. Appl. Physiol. 111(8), 084905 (2012)Google Scholar
  63. 63.
    K. Fuchi, J. Tang, B. Crowgey, A.R. Diaz, E.J. Rothwell, R.O. Ouedraogo, Origami tunable frequency selective surfaces. IEEE Antennas Wirel. Propag. Lett. 11, 473–475 (2012)Google Scholar
  64. 64.
    S.R. Seiler, G. Bazzan, K. Fuchi, E.J. Alanyak, A.S. Gillman, G.W. Reich, P.R. Buskohl, S. Pallampati, D. Sessions, D. Grayson, G.H. Huff, Physical reconfiguration of an origami-inspired deployable microstrip patch antenna array, in 2017 IEEE International Symposium on Antennas and Propagation & USNC/URSI National Radio Science Meeting (IEEE, Piscataway, 2017), pp. 2359–2360Google Scholar
  65. 65.
    G.J. Hayes, Y. Liu, J. Genzer, G. Lazzi, M.D. Dickey, Self-folding origami microstrip antennas. IEEE Trans. Antennas Propag. 62(10), 5416–5419 (2014)Google Scholar
  66. 66.
    M. Nogi, N. Komoda, K. Otsuka, K. Suganuma, Foldable nanopaper antennas for origami electronics. Nanoscale 5(10), 4395–4399 (2013)Google Scholar
  67. 67.
    I. Toshiyuki, O. Naokazu, H. Takaya, A folding parabola antenna with flat facets. J. Natl. Inst. Inf. Commun. Technol. 50(3–4), 177–181 (2003)Google Scholar
  68. 68.
    X. Liu, S. Yao, S.V. Georgakopoulos, Mode reconfigurable bistable spiral antenna based on kresling origami, in 2017 IEEE International Symposium on Antennas and Propagation & USNC/URSI National Radio Science Meeting (IEEE, Piscataway, 2017), pp. 413–414Google Scholar
  69. 69.
    W. Su, R. Bahr, S.A. Nauroze, M.M. Tentzeris, Novel 3D-printed “Chinese fan” bow-tie antennas for origami/shape-changing configurations, in 2017 IEEE International Symposium on Antennas and Propagation & USNC/URSI National Radio Science Meeting (IEEE, Piscataway, 2017), pp. 1245–1246Google Scholar
  70. 70.
    K. Fuchi, G. Bazzan, A.S. Gillman, G.H. Huff, P.R. Buskohl, E.J. Alyanak, Frequency tuning through physical reconfiguration of a corrugated origami frequency selective surface, in 2017 IEEE International Symposium on Antennas and Propagation & USNC/URSI National Radio Science Meeting (IEEE, Piscataway, 2017), pp. 411–412Google Scholar
  71. 71.
    T. Tachi, Simulation of rigid origami, in Origami 4, Fourth International Meeting of Origami Science, Mathematics, and Education (2009), pp. 175–187Google Scholar
  72. 72.
    S.-M. Belcastro, T.C. Hull, Modelling the folding of paper into three dimensions using affine transformations. Linear Algebra Appl. 348(1–3), 273–282 (2002)Google Scholar
  73. 73.
    S.-W. Qu, C.-L. Ruan, Effect of round corners on bowtie antennas. Prog. Electromagn. Res. 57, 179–195 (2006)Google Scholar
  74. 74.
    J.F. Sauder, M.W. Thomson, Ka-band parabolic deployable antenna (KaPDA) enabling high speed data communication for CubeSats, in AIAA SPACE 2015 Conference and Exposition (2015), p. 4425Google Scholar
  75. 75.
    J.F. Sauder, N. Chahat, B. Hirsch, R. Hodges, Y. Rahmat-Samii, E. Peral, M.W. Thomson, From prototype to flight: qualifying a Ka-band parabolic deployable antenna (KaPDA) for CubeSats, in 4th AIAA Spacecraft Structures Conference (2017), p. 0620Google Scholar
  76. 76.
    P. Agrawal, M. Anderson, M. Card, Preliminary design of large reflectors with flat facets. IEEE Trans. Antennas Propag. 29(4), 688–694 (1981)Google Scholar
  77. 77.
    E. Peraza Hernandez, D.J. Hartl, D.C. Lagoudas, Modeling and design of shape memory alloy-based origami structures with smooth folds, in 25th AIAA/AHS Adaptive Structures Conference (2017), p. 1875Google Scholar
  78. 78.
    L. Eriksson, E. Johansson, N. Kettaneh-Wold, C. Wikström, S. Wold, Design of Experiments: Principles and Applications (Umetrics Academy, Umeå, 2000)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • Edwin A. Peraza Hernandez
    • 1
  • Darren J. Hartl
    • 1
  • Dimitris C. Lagoudas
    • 1
  1. 1.Department of Aerospace EngineeringTexas A&M UniversityCollege StationUSA

Personalised recommendations