Steel and Composite Structures

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Nonlinear stability of bio-inspired composite beams with higher order shear theory

  • Nazira Mohamed (Department of Engineering Mathematics, Faculty of Engineering, Zagazig University) ;
  • Salwa A. Mohamed (Department of Engineering Mathematics, Faculty of Engineering, Zagazig University) ;
  • Alaa A. Abdelrhmaan (Mechanical Design and Production Dept., Faculty of Engineering, Zagazig University) ;
  • Mohamed A. Eltaher (Mechanical Engineering Dept., Faculty of Engineering, King Abdulaziz University)
  • Received : 2021.09.25
  • Accepted : 2023.03.13
  • Published : 2023.03.25
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Abstract

This manuscript presents a comprehensive mathematical model to investigate buckling stability and postbuckling response of bio-inspired composite beams with helicoidal orientations. The higher order shear deformation theory as well as the Timoshenko beam theories are exploited to include the shear influence. The equilibrium nonlinear integro-differential equations of helicoidal composite beams are derived in detail using the energy conservation principle. Differential integral quadrature method (DIQM) is employed to discretize the nonlinear system of differential equations and solve them via the Newton iterative method then obtain the response of helicoidal composite beam. Numerical calculations are carried out to check the validity of the present solution methodology and to quantify the effects of helicoidal rotation angle, elastic foundation constants, beam theories, geometric and material properties on buckling, postbuckling of bio-inspired helicoidal composite beams. The developed model can be employed in design and analysis of curved helicoidal composite beam used in aerospace and naval structures.

Keywords

References

  1. Greco, F., Leonetti, L., Pranno, A. and Rudykh, S. (2020), "Mechanical behavior of bio-inspired nacre-like composites: A hybrid multiscale modeling approach", Compos. Struct., 233, 111625. https://doi.org/10.1016/j.compstruct.2019.111625.
  2. Polit, O., Pradyumna, B. and Ganapathi, M. (2019), "Large amplitude free flexural vibrations of functionally graded graphene platelets reinforced porous composite curved beams using finite element based on trigonometric shear deformation theory", Int. J. Nonlinear Mech., 116, 302-317. https://doi.org/10.1016/j.ijnonlinmec.2019.07.010.
  3. Abdelrahman, A.A. and El-Shafei, A.G. (2021), "Modeling and analysis of the transient response of viscoelastic solids", Wave. Random Complex Med., 31(6), 1990-2020. https://doi.org/10.1080/17455030.2020.1714790.
  4. Zhao, H., Yang, Z. and Guo, L. (2018), "Nacre-inspired composites with different macroscopic dimensions: strategies for improved mechanical performance and applications", NPG Asia Mater., 10(4), 1-22. https://doi.org/10.1038/s41427-018-0009-6.
  5. Melaibari, A., Abdelrahman, A.A., Hamed, M.A., Abdalla, A.W. and Eltaher, M.A. (2022a), "Dynamic analysis of a piezoelectrically layered perforated nonlocal strain gradient nanobeam with flexoelectricity", Mathematics, 10(15), 2614. https://doi.org/10.3390/math10152614.
  6. Melaibari, A., Daikh, A.A., Basha, M., Abdalla, A.W., Othman, R., Almitani, K.H. and Eltaher, M.A. (2022b), "Free vibration of fg-cntrcs nano-plates/shells with temperature-dependent properties", Mathematics, 10(4), 583. https://doi.org/10.3390/math10040583.
  7. Melaibari, A., Daikh, A.A., Basha, M., Wagih, A., Othman, R., Almitani, K.H. and Eltaher, M.A. (2022c), "A dynamic analysis of randomly oriented functionally graded carbon nanotubes/fiber-reinforced composite laminated shells with different geometries", Mathematics, 10(3), 408. https://doi.org/10.3390/math10030408.
  8. Mohamed, S.A., Mohamed, N. and Eltaher, M.A. (2022), "Bending, buckling and linear vibration of bio-inspired composite plates", Ocean Eng., 259, 111851. https://doi.org/10.1016/j.oceaneng.2022.111851.
  9. Cheng, L., Thomas, A., Glancey, J.L. and Karlsson, A.M. (2011), "Mechanical behavior of bio-inspired laminated composites", Compos. Part A Appl. Sci. Manuf., 42(2), 211-220. https://doi.org/10.1016/j.compositesa.2010.11.009.
  10. Apichattrabrut, T. and Ravi-Chandar, K. (2006), "Helicoidal composites", Mech. Adv. Mater. Struct., 13(1), 61-76. https://doi.org/10.1080/15376490500343808.
  11. Liu, J.L., Lee, H.P. and Tan, V.B.C. (2018), "Effects of inter-ply angles on the failure mechanisms in bioinspired helicoidal laminates", Compos. Sci. Technol., 165, 282-289. https://doi.org/10.1016/j.compscitech.2018.07.017.
  12. Jiang, H., Ren, Y., Liu, Z., Zhang, S. and Lin, Z. (2019), "Lowvelocity impact resistance behaviors of bio-inspired helicoidal composite laminates with non-linear rotation angle-based layups", Compos. Struct., 214, 463-475. https://doi.org/10.1016/j.compstruct.2019.02.034.
  13. Grunenfelder, L.K., Suksangpanya, N., Salinas, C., Milliron, G., Yaraghi, N., Herrera, S. and Kisailus, D. (2014), "Bio-inspired impact-resistant composites", Acta Biomater., 10(9), 3997-4008. http://dx.doi.org/10.1016/j.actbio.2014.03.022.
  14. Shang, J.S., Ngern, N.H. and Tan, V.B. (2016), "Crustaceaninspired helicoidal laminates", Compos. Sci. Technol., 128, 222-232. https://doi.org/10.1016/j.compscitech.2016.04.007.
  15. Alves, M., Carlstedt, D., Ohlsson, F., Asp, L.E. and Pimenta, S. (2020), "Ultra-strong and stiff randomly-oriented discontinuous composites: Closing the gap to quasi-isotropic continuous-fibre laminates", Compos. Part A Appl. Sci. Manufact., 132, 105826. https://doi.org/10.1016/j.compositesa.2020.105826.
  16. Mencattelli, L. and Pinho, S.T. (2020a), "Ultra-thin-ply CFRP Bouligand bio-inspired structures with enhanced load-bearing capacity, delayed catastrophic failure and high energy dissipation capability", Compos. Part A Appl. Sci. Manuf., 129, 105655. https://doi.org/10.1016/j.compositesa.2019.105655.
  17. Mencattelli, L. and Pinho, S.T. (2020b), "Herringbone-Bouligand CFRP structures: A new tailorable damage-tolerant solution for damage containment and reduced delaminations", Compos. Sci. Technol., 190, 108047. https://doi.org/10.1016/j.compscitech.2020.108047.
  18. Liu, J.L., Singh, A.K., Lee, H.P., Tay, T.E. and Tan, V.B.C. (2020), "The response of bio-inspired helicoidal laminates to small projectile impact", Int. J. Impact Eng., 142, 103608. https://doi.org/10.1016/j.ijimpeng.2020.103608.
  19. Zhang, W., Li, R., Yang, Q., Fu, Y. and Kong, X. (2023), "Impact resistance of a fiber metal laminate skin bio-inspired composite sandwich panel with a rubber and foam dual core", Materials, 16(1), 453. https://doi.org/10.3390/ma16010453.
  20. Sabah, S.A., Kueh, A.B.H. and Bunnori, N.M. (2019), "Failure mode maps of bio-inspired sandwich beams under repeated low-velocity impact", Compos. Sci. Technol., 182, 107785. https://doi.org/10.1016/j.compscitech.2019.107785.
  21. Pei, B., Guo, L., Wu, X., Hu, M., Wu, S. and Wang, Y. (2022), "Impact resistant structure design and optimization inspired by turtle carapace", Materials, 15(8), 2899. https://doi.org/10.3390/ma15082899.
  22. San Ha, N. and Lu, G. (2020), "A review of recent research on bio-inspired structures and materials for energy absorption applications", Compos. Part B Eng., 181, 107496. https://doi.org/10.1016/j.compositesb.2019.107496.
  23. Assie, A., Akbas, S.D., Kabeel, A.M., Abdelrahman, A.A. and Eltaher, M.A. (2022), "Dynamic analysis of porous functionally graded layered deep beams with viscoelastic core", Steel Compos. Struct., 43(1), 79-90. https://doi.org/10.12989/scs.2022.43.1.079.
  24. Abdelrahman, A.A., Shanab, R.A., Esen, I. and Eltaher, M.A. (2022), "Effect of moving load on dynamics of nanoscale Timoshenko CNTs embedded in elastic media based on doublet mechanics theory", Steel Compos. Struct., 44(2), 241-256. https://doi.org/10.12989/scs.2022.44.2.255.
  25. Esen, I., Alazwari, M.A., Eltaher, M.A. and Abdelrahman, A.A. (2022), "Dynamic response of FG porous nanobeams subjected thermal and magnetic fields under moving load", Steel Compos. Struct., 42(6), 805-826. https://doi.org/10.12989/scs.2022.42.6.805.
  26. Lacarbonara, W., Arafat, H.N. and Nayfeh, A.H. (2005), "Nonlinear interactions in imperfect beams at veering", Int. J. Nonlinear Mech., 40(7), 987-1003. https://doi.org/10.1016/j.ijnonlinmec.2004.10.006.
  27. Ouyang, W., Gong, B., Wang, H., Scarpa, F., Su, B. and Peng, H. X. (2021), "Identifying optimal rotating pitch angles in composites with Bouligand structure", Compos. Commun., 23, 100602. https://doi.org/10.1016/j.coco.2020.100602.
  28. Melaibari, A., Wagih, A., Basha, M., Kabeel, A.M., Lubineau, G. and Eltaher, M.A. (2021), "Bio-inspired composite laminate design with improved out-of-plane strength and ductility", Compos. Part A Appl. Sci. Manuf., 144, 106362. https://doi.org/10.1016/j.compositesa.2021.106362.
  29. Wang, D., Zaheri, A., Russell, B., Espinosa, H. and Zavattieri, P. (2020), "Fiber reorientation in hybrid helicoidal composites", J. Mech. Behav. Biomed. Mater., 110, 103914. https://doi.org/10.1016/j.jmbbm.2020.103914.
  30. Yang, F., Xie, W. and Meng, S. (2020a), "Global sensitivity analysis of low-velocity impact response of bio-inspired helicoidal laminates", Int. J. Mech. Sci., 187, 106110. https://doi.org/10.1016/j.ijmecsci.2020.106110.
  31. Yang, F., Xie, W. and Meng, S. (2021), "Crack-driving force and toughening mechanism in crustacean-inspired helicoidal structures", Int. J. Solids Struct., 208, 107-118. https://doi.org/10.1016/j.ijsolstr.2020.10.016.
  32. Yin, S., Yang, R., Huang, Y., Guo, W., Chen, D., Zhang, W. and Xu, J. (2021), "Toughening mechanism of coelacanth-fishin-spired double-helicoidal composites", Compos. Sci. Technol., 205, 108650. https://doi.org/10.1016/j.compscitech.2021.108650.
  33. Eltaher, M.A., Mohamed, N., Mohamed, S.A. and Seddek, L.F. (2019), "Periodic and nonperiodic modes of postbuckling and nonlinear vibration of beams attached to nonlinear foundations", Appl. Math. Model., 75, 414-445. https://doi.org/10.1016/j.apm.2019.05.026.
  34. Gupta, R.K., Gunda, J.B., Janardhan, G.R. and Rao, G.V. (2010), "Post-buckling analysis of composite beams: simple and accurate closed-form expressions", Compos. Struct., 92(8), 1947-1956. https://doi.org/10.1016/j.compstruct.2009.12.010.
  35. Gunda, J.B., Gupta, R.K., Janardhan, G.R. and Rao, G.V. (2011), "Large amplitude vibration analysis of composite beams: simple closed-form solutions", Compos. Struct., 93(2), 870-879. https://doi.org/10.1016/j.compstruct.2010.07.006.
  36. Alazwari, M.A., Daikh, A.A., Houari, M.S.A., Tounsi, A. and Eltaher, M.A. (2021), "On static buckling of multilayered carbon nanotubes reinforced composite nanobeams supported on non-linear elastic foundations", Steel Compos. Struct., 40(3), 389-404. https://doi.org/10.12989/scs.2021.40.3.389.
  37. Emam, S.A., Eltaher, M.A., Khater, M.E. and Abdalla, W.S. (2018), "Postbuckling and free vibration of multilayer imperfect nanobeams under a pre-stress load", Appl. Sci., 8(11), 2238. https://doi.org/10.3390/app8112238.
  38. Ghuku, S. and Saha, K.N. (2018), "Large deflection analysis of curved beam problem with varying curvature and moving boundaries", Eng. Sci. Technol. Int. J., 21(3), 408-420. https://doi.org/10.1016/j.jestch.2018.04.007.
  39. Mohamed, N., Eltaher, M.A., Mohamed, S.A. and Seddek, L.F. (2018), "Numerical analysis of nonlinear free and forced vibrations of buckled curved beams resting on nonlinear elastic foundations", Int. J. Nonlinear Mech., 101, 157-173. https://doi.org/10.1016/j.ijnonlinmec.2018.02.014.
  40. Guo, J., Shi, D., Wang, Q., Pang, F. and Liang, Q. (2019), "A domain decomposition approach for static and dynamic analysis of composite laminated curved beam with general elastic restrains", Mech. Adv. Mater. Struct., 26(16), 1390-1402. https://doi.org/10.1080/15376494.2018.1432810.
  41. Hamed, M.A., Abo-bakr, R.M., Mohamed, S.A. and Eltaher, M.A. (2020a), "Influence of axial load function and optimization on static stability of sandwich functionally graded beams with porous core", Eng. Comput., 36(4), 1929-1946. https://doi.org/10.1007/s00366-020-01023-w.
  42. Hamed, M.A., Mohamed, S.A. and Eltaher, M.A. (2020b), "Buckling analysis of sandwich beam rested on elastic foundation and subjected to varying axial in-plane loads", Steel Compos. Struct., 34(1), 75-89. https://doi.org/10.12989/scs.2020.34.1.075.
  43. Abo-bakr, H.M., Abo-bakr, R.M., Mohamed, S.A. and Eltaher, M.A. (2021), "Multi-objective shape optimization for axially functionally graded microbeams", Compos. Struct., 258, 113370. https://doi.org/10.1016/j.compstruct.2020.113370.
  44. Emam, S. and Lacarbonara, W. (2021), "Buckling and postbuckling of extensible, shear-deformable beams: Some exact solutions and new insights", Int. J. Nonlinear Mech., 129, 103667. https://doi.org/10.1016/j.ijnonlinmec.2021.103667.
  45. She, G.L., Liu, H.B. and Karami, B. (2020), "On resonance behavior of porous FG curved nanobeams", Steel Compos. Struct., 36(2), 179. http://dx.doi.org/10.12989/scs.2020.36.2.179.
  46. She, G.L. (2020), "Wave propagation of FG polymer composite nanoplates reinforced with GNPs", Steel Compos Struct., 37(1), 27. http://dx.doi.org/10.12989/scs.2020.37.1.027.
  47. Zhang, Y.Y., Wang, Y.X., Zhang, X., Shen, H.M. and She, G.L. (2021b), "On snap-buckling of FG-CNTR curved nanobeams considering surface effects", Steel Compos. Struct., 38(3), 293-304. https://doi.org/10.12989/scs.2021.38.3.293.
  48. Zhang, P., Ma, J., Duan, M., Yuan, Y. and Wang, J. (2021a), "A high-precision curvature constrained Bernoulli-Euler planar beam element for geometrically nonlinear analysis", Appl. Math. Comput., 397, 125986. https://doi.org/10.1016/j.amc.2021.125986.
  49. Emam, S. and Eltaher, M.A. (2016), "Buckling and postbuckling of composite beams in hygrothermal environments", Compos. Struct., 152, 665-675. https://doi.org/10.1016/j.compstruct.2016.05.029.
  50. She, G. L., Jiang, X.Y. and Karami, B. (2019a), "On thermal snap-buckling of FG curved nanobeams", Mater. Res. Express, 6(11), 115008. https://doi.org/10.1088/2053-1591/ab44f1.
  51. She, G.L., Ren, Y.R. and Yuan, F.G. (2019b), "Hygro-thermal wave propagation in functionally graded double-layered nanotubes systems", Steel Compos. Struct., 31(6), 2019. http://dx.doi.org/10.12989/scs.2019.31.6.641.
  52. She, G.L., Yuan, F.G., Karami, B., Ren, Y.R. and Xiao, W.S. (2019c), "On nonlinear bending behavior of FG porous curved nanotubes", Int. J. Eng. Sci., 135, 58-74. https://doi.org/10.1016/j.ijengsci.2018.11.005.
  53. Wang, Y., Feng, C., Santiuste, C., Zhao, Z. and Yang, J. (2019), "Buckling and postbuckling of dielectric composite beam reinforced with Graphene Platelets (GPLs)", Aerosp. Sci. Technol., 91, 208-218. https://doi.org/10.1016/j.ast.2019.05.008.
  54. Yang, F., Xie, W. and Meng, S. (2020a), "Global sensitivity analysis of low-velocity impact response of bio-inspired helicoidal laminates", Int. J. Mech. Sci., 187, 106110. https://doi.org/10.1016/j.ijmecsci.2020.106110.
  55. Abdelrahman, A.A., Esen, I. and Eltaher, M.A. (2021), "Vibration response of Timoshenko perforated microbeams under accelerating load and thermal environment", Appl. Math. Comput., 407, 126307. https://doi.org/10.1016/j.amc.2021.126307.
  56. Dos Santos, C.R., Pacheco, D.R., Taha, H.E. and Zakaria, M.Y. (2021), "Nonlinear modeling of electro-aeroelastic dynamics of composite beams with piezoelectric coupling", Compos. Struct., 255, 112968. https://doi.org/10.1016/j.compstruct.2020.112968.
  57. Krishnan, K.V. and Ganguli, R. (2021), "Multi-fidelity analysis and uncertainty quantification of beam vibration using cokriging interpolation method", Appl. Math. Comput., 398, 125987. https://doi.org/10.1016/j.amc.2021.125987.
  58. Song, Z., Li, W., He, X. and Xie, D. (2021), "Comparisons of matched interface and boundary (MIB) method and its interpolation formulation for free vibration analysis of stepped beams and plates", Appl. Math. Comput., 394, 125817. https://doi.org/10.1016/j.amc.2020.125817.
  59. Emam, S.A. (2009), "A static and dynamic analysis of the postbuckling of geometrically imperfect composite beams", Compos. Struct., 90(2), 247-253. https://doi.org/10.1016/j.compstruct.2009.03.020.
  60. Emam, S.A. (2011), "Analysis of shear-deformable composite beams in postbuckling", Compos. Struct., 94(1), 24-30. https://doi.org/10.1016/j.compstruct.2011.07.024.
  61. Eltaher, M.A., Mohamed, S.C. and Melaibari, A.A. (2020a), "Static stability of a unified composite beams under varying axial loads", Thin. Wall. Struct., 147, 106488. https://doi.org/10.1016/j.tws.2019.106488.
  62. Melaibari, A., Khoshaim, A.B., Mohamed, S.A. and Eltaher, M.A. (2020), "Static stability and of symmetric and sigmoid functionally graded beam under variable axial load", Steel Compos. Struct., 35(5), 671-685. https://doi.org/10.12989/scs.2020.35.5.671.
  63. Eltaher, M.A. and Mohamed, N. (2020), "Nonlinear stability and vibration of imperfect CNTs by doublet mechanics", Appl. Math. Comput., 382, 125311. https://doi.org/10.1016/j.amc.2020.125311.
  64. Eltaher, M.A., Mohamed, N. and Mohamed, S.A. (2020b), "Nonlinear buckling and free vibration of curved CNTs by doublet mechanics", Smart Struct. Syst., 26(2), 213-226. https://doi.org/10.12989/sss.2020.26.2.213.
  65. Mohamed, N., Eltaher, M.A., Mohamed, S.A. and Seddek, L.F. (2019), "Energy equivalent model in analysis of postbuckling of imperfect carbon nanotubes resting on nonlinear elastic foundation", Struct. Eng. Mech., 70(6), 737-750. https://doi.org/10.12989/sem.2019.70.6.737.
  66. Attia, M.A. and Mohamed, S. (2017), "Nonlinear modeling and analysis of electrically actuated viscoelastic microbeams based on the modified couple stress theory", Appl. Math. Model., 41, 195-222. https://doi.org/10.1016/j.apm.2016.08.036.
  67. Mohamed, N., Eltaher, M.A., Mohamed, S.A. and Seddek, L.F. (2018), "Numerical analysis of nonlinear free and forced vibrations of buckled curved beams resting on nonlinear elastic foundations", Int. J. Nonlinear Mech., 101, 157-173. https://doi.org/10.1016/j.ijnonlinmec.2018.02.014.
  68. Quan, J.R. and Chang, C.T. (1989), "New insights in solving distributed system equations by the quadrature method-I. Analysis", Comput. Chem. Eng., 13(7), 779-788. https://doi.org/10.1016/0098-1354(89)85051-3.
  69. Reddy, J.N. (1997), Mechanics of laminated Composite Plates-Theory and Analysis, Boca Raton, FL: CRC Press.