Skip to main content
SpringerLink
Log in

Bending and Vibration of a Bio-Inspired Bouligand Composite Plate Using the Finite-Element Method

  • Published:
Mechanics of Composite Materials Aims and scope

Biological structures, such as mantis shrimp crustacean, provide a rich source of inspiration for constructing high-performance materials with an excellent mechanical strength and impact resistance. Therefore, helicoidal structures inspired by mantis shrimp were investigated to explore the static and dynamic properties. The firstorder shear deformation theory of plates was used to describe the displacement field of laminated helicoidal composite plates. By the finite-element analysis (FEA), the bending and vibrations of bio-inspired composite plates were studied numerically using the ANSYS mechanical analysis software and the parametric design language APDL. Three classical orientations (unidirectional, cross-ply, and quasi-isotropic) and two helicoidal (linear and Fibonacci) orientations were considered. The “SHELL281” finite element of the APDL tool was exploited to solve the problem numerically with three integration points in each direction. The model proposed was verified, and its parametric studies were performed to clear up the effects of fiber orientation, slenderness ratio, and elasticity ratio on the static and free vibrations of a Bouligand composite plate. Results showed that the composite material had extraordinary mechanical properties, which is highly important for their unlimited applications in military industry and civil engineering.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. A. Shahbaztabar and A. R. Ranji, “Effects of in-plane loads on free vibration of symmetrically cross-ply laminated plates resting on Pasternak foundation and coupled with fluid,” Ocean Eng., 115, 196-209 (2016). https://doi.org/https://doi.org/10.1016/j.oceaneng.2016.02.014

    Article  Google Scholar 

  2. A. Melaibari, A. Wagih, M. Basha, A. M. Kabeel, G. Lubineau, and M. A. Eltaher, “Bio-inspired composite laminate design with improved out-of-plane strength and ductility,” Compos., Part A, 144, 106362 (2021). https://doi.org/10.1016/j.compositesa.2021.106362

  3. B. Bar-On, B. Bayerlein, H. Blumtritt, and I. Zlotnikov, “Dynamic response of a single interface in a biocomposite structure,” Physical Review Letters, 115, No. 23, 238001 (2015).

    Google Scholar 

  4. L. K Grunenfelder, N. Suksangpanya, C. Salinas, G. Milliron, N. Yaraghi, S. Herrera, and D. Kisailus, “Bio-inspired impact-resistant composites,” Acta biomaterialia, 10, No. 9, 3997-4008 (2014). https://doi.org/https://doi.org/10.1016/j.actbio.2014.03.022

    Article  CAS  Google Scholar 

  5. S. Haldar and H. A. Bruck, “Mechanics of composite sandwich structures with bio-inspired core,” Compos. Sci. and Technol., 95, 67-74 (2014). https://doi.org/https://doi.org/10.1016/j.compscitech.2014.02.011

    Article  CAS  Google Scholar 

  6. T. Apichattrabrut and K. Ravi-Chandar, “Helicoidal composites,” Mech. Adv. Mater. and Struct., 13, No. 1, 61-76 (2006). https://doi.org/https://doi.org/10.1080/15376490500343808

    Article  CAS  Google Scholar 

  7. L. Cheng, A. Thomas, J. L. Glancey, and A. M. Karlsson, “Mechanical behavior of bio-inspired laminated composites,” Compos., Part A, 42, No. 2, 211-220 (2011). https://doi.org/https://doi.org/10.1016/j.compositesa.2010.11.009

    Article  CAS  Google Scholar 

  8. Garg Aman, M. O. Belarbi, H. D. Chalak, L. Li, Anshu Sharma, Mehmet Avcar, Neha Sharma, Sagar Paruthi, and Reeta Gulia, “Buckling and free vibration analysis of bio-inspired laminated sandwich plates with helicoidal/Bouligand face sheets containing softcore.” Ocean Eng. 270, 113684 (2023). https://doi.org/10.1016/j.oceaneng.2023.113684

  9. Garg, Aman, Mohamed-Ouejdi Belarbi, Li Li, Neha Sharma, Ayushi Gupta, and Hanuman Devidas Chalak, “Free vibration analysis of bio-inspired helicoid laminated composite plates,” J. Strain Analysis for Eng. Design, 030932472311604 (2023). https://doi.org/10.1177/03093247231160414

  10. A. Bahmani, G. Li, L. T. Willett, and J. Montesano, “Three-dimensional micromechanical assessment of bio-inspired composites with non-uniformly dispersed inclusions”, Compos. Struct., 212, 484-499 (2019). https://doi.org/https://doi.org/10.1016/j.compstruct.2 019.01.056

    Article  Google Scholar 

  11. K. Karthikeyan, S. Kazemahvazi, and B. P. Russell, “Optimal fibre architecture of soft-matrix ballistic laminates,” Int. J. Impact Eng., 88, 227-237 (2016). https://doi.org/https://doi.org/10.1016/j.ijimpeng.2015.10.012

    Article  Google Scholar 

  12. J. L. Liu, H. P. Lee, and V. B. C. Tan, “Effects of inter-ply angles on the failure mechanisms in bio-inspired helicoidal laminates,” Compos. Sci. and Technol., 165, 282-289 (2018). https://doi.org/https://doi.org/10.1016/j.compscitech.2018.07.017

    Article  CAS  Google Scholar 

  13. S. Askarinejad and N. Rahbar, “Mechanics of bio-inspired lamellar structured ceramic/polymer composites: Experiments and models,” Int. J. Plasticity, 107, 122-149 (2018). https://doi.org/https://doi.org/10.1016/j.ijplas.2018.04.001

    Article  CAS  Google Scholar 

  14. M. R. Abir, T. E Tay, and H. P. Lee, “On the improved ballistic performance of bio-inspired composite,” Compos., Part A, 123, 59-70 (2019). https://doi.org/https://doi.org/10.1016/j.compositesa.2019.04.021

    Article  CAS  Google Scholar 

  15. A. T. Garg, Mukhopadhyay, M. O. Belarbi, and L. Li. “Random forest-based surrogates for transforming the behavioral predictions of laminated composite plates and shells from FSDT to elasticity solutions,” Compos. Struct., 309, 116756 (2023). https://doi.org/10.1016/j.compstruct.2023.116756

  16. F. Yang, W. Xie, and S. Meng, “Global sensitivity analysis of low-velocity impact response of bio-inspired helicoidal laminates,” Int. J. Mech. Sci., 187, 106110 (2020). https://doi.org/https://doi.org/10.1016/j.ijmecsci.2020.106110

    Article  Google Scholar 

  17. A. Ghazlan, T. Ngo, P. Tan, Y.M. Xie, P. Tran, and M. Donough, “Inspiration from Nature’s body armours — A review of biological and bio-inspired composites,” Compos., Part B, 205, 108513 (2021). https://doi.org/10.1016/j.compositesb.2020.108513

  18. L. Amorim, A. Santos, J. P. Nunes, and J. C. Viana, “Bio-inspired approaches for toughening of fibre reinforced polymer composites,” Mater. & Design, 199, 109336 (2021). https://doi.org/https://doi.org/10.1016/j.matdes.2020.109336

    Article  CAS  Google Scholar 

  19. K. H. Almitani, N. Mohamed, M. A. Alazwari, S. A. Mohamed, and M. A. Eltaher, “Exact solution of nonlinear behaviors of imperfect bio-inspired helicoidal composite beams resting on elastic foundations,” Mathematics, 10, No. 6, 887 (2022). https://doi.org/https://doi.org/10.3390/math10060887

    Article  Google Scholar 

  20. F. Yang and W. Xie, “Thermal buckling behavior of Bouligand inspired laminated composite plates,” J. Compos. Mater., 56, No. 26, 3939-3947 (2022). https://doi.org/https://doi.org/10.1177/00219983221125905

    Article  Google Scholar 

  21. S. Lee, D. D. Lim, E. Pegg, and G. X. Gu, “The origin of high-velocity impact response and damage mechanisms for bioinspired composites,” Cell Reports Physical Sci., 3, No. 12, 101152 (2022). https://doi.org/10.1016/j.xcrp.2022.101152

  22. Y. Li, H. He, Q. Wang, L. Zhang, Y. Yu, and D. He, “Bio-inspired diamond composites and their dynamic shock performance,” Mech. Mater., 164, 104105 (2022). https://doi.org/https://doi.org/10.1016/j.mechmat.2021.104105

    Article  Google Scholar 

  23. T. Magrini, A. Senol, R. Style, F. Bouville, and A. R. Studart, “Fracture of hierarchical multi-layered bio-inspired composites”, J. Mech. and Physics of Solids, 159, 104750 (2022). https://doi.org/https://doi.org/10.1016/j.jmps.2021.104750

    Article  CAS  Google Scholar 

  24. N. Mohamed, S. A. Mohamed, and M. A. Eltaher, “Nonlinear static stability of imperfect bio-inspired helicoidal composite beams,” Mathematics, 10, No. 7, 1084 (2022a). https://doi.org/https://doi.org/10.3390/math10071084

    Article  Google Scholar 

  25. S. A. Mohamed, N. Mohamed, and M. A. N. Eltaher, “Bending, buckling and linear vibration of bio-inspired composite plates,” Ocean Eng., 259, 111851 (2022b). https://doi.org/https://doi.org/10.1016/j.oceaneng.2022.111851

    Article  Google Scholar 

  26. A. O. Sojobi and K. M. Liew, “Multi-objective optimization of high performance bio-inspired prefabricated composites for sustainable and resilient construction,” Compos. Struct., 279, 114732 (2022). https://doi.org/https://doi.org/10.1016/j.compstruct.2021.114732

    Article  Google Scholar 

  27. S. A. Mohamed, N. Mohamed, and M. A. Eltaher, “Snap-through instability of helicoidal composite imperfect beams surrounded by nonlinear elastic foundation,” Ocean Eng., 263, 112171 (2022c). https://doi.org/https://doi.org/10.1016/j.oceaneng.2022.112171

    Article  Google Scholar 

  28. Z. Xu, W. Gao, and H. Bai, “Silk-based bio-inspired structural and functional materials,” Iscience, 103940 (2022). https://doi.org/10.1016/j.isci.2022.103940

  29. S. A. Kumar, S. Gundu, P. Kumari, T. Klepka, and A. Sionkowska, “Silk-based biomaterials for designing bio-inspired microarchitecture for various biomedical applications”, Biomimetics, 8, No. 1, 55 (2023). https://doi.org/https://doi.org/10.3390/biomimetics8010055

    Article  CAS  Google Scholar 

  30. M. Ö. Yayli, ‘‘Free vibration behavior of a gradient elastic beam with varying cross section,” Shock and Vibration, 2014, 1-11 (2014). https://doi.org/https://doi.org/10.1155/2014/801696

    Article  Google Scholar 

  31. M. Ö. Yayli, “Free longitudinal vibration of a nanorod with elastic spring boundary conditions made of functionally graded material,” Micro & Nano Letters, 13, No. 7, 1031-1035 (2018a). https://doi.org/https://doi.org/10.1049/mnl.2018.0181

    Article  CAS  Google Scholar 

  32. M. Ö. Yayli, “Free vibration analysis of a single‐walled carbon nanotube embedded in an elastic matrix under rotational restraints,” Micro & Nano Letters, 13, No. 2, 202-206 (2018b). https://doi.org/https://doi.org/10.1049/mnl.2017.0463

    Article  CAS  Google Scholar 

  33. M. Ö. Yayli, “Free vibration analysis of a rotationally restrained (FG) nanotube,” Microsystem Technol., 25, No. 10, 3723-3734 (2019). https://doi.org/https://doi.org/10.1007/s00542-019-04307-4

    Article  Google Scholar 

  34. M. Ö. Yayli, “Axial vibration analysis of a Rayleigh nanorod with deformable boundaries,” Microsystem Technol., 26, 2661-2671 (2020). https://doi.org/https://doi.org/10.1007/s00542-020-04808-7

    Article  Google Scholar 

  35. M. Ö. Yayli, “Torsional vibration analysis of nanorods with elastic torsional restraints using non‐local elasticity theory,” Micro & Nano Letters, 13, No. 5, 595-599 (2018). https://doi.org/https://doi.org/10.1049/mnl.2017.0751

    Article  CAS  Google Scholar 

  36. M. Ö. Yayli, “Buckling analysis of a microbeam embedded in an elastic medium with deformable boundary conditions,” Micro & Nano Letters, 11, No. 11, 741-745 (2016). https://doi.org/https://doi.org/10.1049/mnl.2016.0257

    Article  Google Scholar 

  37. M. Ö. Yayli, “Buckling analysis of a cantilever single‐walled carbon nanotube embedded in an elastic medium with an attached spring,” Micro & Nano Letters, 12, No. 4, 255-259 (2017). https://doi.org/https://doi.org/10.1049/mnl.2016.0662

    Article  CAS  Google Scholar 

  38. M. Ö. Yayli, “Effects of rotational restraints on the thermal buckling of carbon nanotube,” Micro & Nano Letters, 14, No. 2, 158-162 (2019). https://doi.org/https://doi.org/10.1049/mnl.2018.5428

    Article  CAS  Google Scholar 

  39. J. N. Reddy, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis. CRC press. (2003).

  40. A. Karamanli, M. A. Eltaher, S. Thai, and T. P. Vo, “Transient dynamics of 2D-FG porous microplates under moving loads using higher order finite element model,” Eng. Struct., 278, 115566 (2023). https://doi.org/https://doi.org/10.1016/j.engstruct.2022.115566

    Article  Google Scholar 

  41. A. E. Assie, S. M. Mohamed, R. A. Shanab, R. M. Abo-bakr, and M. A. Eltaher, “Static buckling of 2D FG porous plates resting on elastic foundation based on unified shear theories,” J. Appl. and Comput. Mech., 9, No. 1, 239-258 (2023).

    Google Scholar 

  42. S. Mohamed, A. E. Assie, and M. A. Eltaher, “Novel incremental procedure in solving nonlinear static response of 2DFG porous plates,” Thin-Walled Struct., 188, 110779 (2023). https://doi.org/https://doi.org/10.1016/j.tws.2023.110779

    Article  Google Scholar 

  43. P. Van Vinh, M. Avcar, M. O. Belarbi, and A. Tounsi, “A new higher-order mixed four-node quadrilateral finite element for static bending analysis of functionally graded plates,” Struct., 47, 1595-1612 (2023). https://doi.org/https://doi.org/10.1016/j.istruc.2022.11.113

    Article  Google Scholar 

  44. M. O. Belarbi, A. M. Zenkour, A. Tati, S. J. Salami, A. Khechai, and M. S. A. Houari, “An efficient eight‐node quadrilateral element for free vibration analysis of multilayer sandwich plates,” Int. J. Numerical Methods in Eng., 122, No. 9, 2360-2387 (2021). https://doi.org/https://doi.org/10.1002/nme.6624

    Article  Google Scholar 

  45. M. O. Belarbi, A. Tati, H., Ounis, and A. Khechai, “On the free vibration analysis of laminated composite and sandwich plates: a layerwise finite element formulation,” Latin American J. Solids and Struct., 14, 2265-2290 (2017). https://doi.org/10.1590/1679-78253222

  46. A. A. Abdelrahman and A. G. El-Shafei, “Modeling and analysis of the transient response of viscoelastic solids”, Waves in Random and Complex Media, 31, No. 6, 1990-2020 (2021). https://doi.org/https://doi.org/10.1080/17455030.2020.1714790

    Article  Google Scholar 

  47. A. A. Abdelrahman, A. G. El-Shafei, and F. F. Mahmoud, “Analysis of steady-state frictional rolling contact problems in Schapery–nonlinear viscoelasticity,” Proc. Institution of Mech. Engineers, Part J: J. Eng. Tribology, 233, No. 6, 911-926 (2019). https://doi.org/10.1177/1350650118806675

  48. V. N. Burlayenko, H. Altenbach, and T. Sadowski, “An evaluation of displacement-based finite element models used for free vibration analysis of homogeneous and composite plates,” J. Sound and Vibration, 358, 152-175 (2015). http://dx.doi.org/https://doi.org/10.1016/j.jsv.2015.08.010

    Article  Google Scholar 

  49. A. A. Daikh, M. O., Belarbi, A. Khechai, L. Li, H. M. Ahmed, and M. A. Eltaher, “Buckling of bi-coated functionally graded porous nanoplates via a nonlocal strain gradient quasi-3D theory,” Acta Mechanica, 1-24 (2023). https://doi.org/10.1007/s00707-023-03548-9

  50. A. A. Daikh, M. S. A. Houari, M. O. Belarbi, S. A. Mohamed, and M. A. Eltaher, “Static and dynamic stability responses of multilayer functionally graded carbon nanotubes reinforced composite nanoplates via quasi 3D nonlocal strain gradient theory,” Defense Technology, 18, No. 10, 1778-1809 (2022). https://doi.org/https://doi.org/10.1016/j.dt.2021.09.011

    Article  Google Scholar 

  51. R. Vaziri, X. Quan, and M. D. Olson, “Impact analysis of laminated composite plates and shells by super finite elements,” Int. J. Impact Eng., 18, Nos. 7-8, 765-782 (1996). https://doi.org/https://doi.org/10.1016/S0734-743X(96)00030-9

    Article  Google Scholar 

  52. H. Wang, C. Wang, P. J. Hazell, A. Wright, Z. Zhang, X. Lan, X., and M. Zhou, “Insights into the high-velocity impact behaviour of bio-inspired composite laminates with helicoidal layups,” Polymer Testing, 103, 107348 (2021). https://doi.org/10.1016/j.polymertesting.2021.107348

  53. S. A. Mohamed, N. Mohamed, R. M. Abo-bakr, and M. A. Eltaher, “Multi-objective optimization of snap-through instability of helicoidal composite imperfect beams using Bernstein polynomials method,” Appl. Math. Modelling, 120, 301-329 (2023). https://doi.org/https://doi.org/10.1016/j.apm.2023.03.034

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia

    M. A. Eltaher, O. A. Aleryani & A. Melaibari

  2. Mechanical Design and Production Department, Faculty of Engineering, Zagazig University, Zagazig, Egypt

    M. A. Eltaher & A. A. Abdelrahman

Authors
  1. M. A. Eltaher
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. O. A. Aleryani
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. Melaibari
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. A. Abdelrahman
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. A. Eltaher.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Eltaher, M.A., Aleryani, O.A., Melaibari, A. et al. Bending and Vibration of a Bio-Inspired Bouligand Composite Plate Using the Finite-Element Method. Mech Compos Mater 59, 1199–1216 (2024). https://doi.org/10.1007/s11029-023-10166-y

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11029-023-10166-y

Keywords

Search

Navigation