DOI QR코드

DOI QR Code

Mechanical behaviour of advanced composite beams via a simple quasi-3D integral higher-order beam theory

  • Khaled Bouakkaz (Laboratoire Materiaux et Structures (LMS), University of Tiaret) ;
  • Ibrahim Klouche Djedid (Laboratoire Materiaux et Structures (LMS), University of Tiaret) ;
  • Kada Draiche (Department of Civil Engineering, University of Tiaret) ;
  • Abdelouahed Tounsi (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Muzamal Hussain (Department of Mathematics, Govt. College University Faisalabad)
  • 투고 : 2022.08.26
  • 심사 : 2024.02.13
  • 발행 : 2024.10.25

초록

In the present paper, a simple quasi-3D integral higher-order beam theory (HBT) is presented, in which both shear deformation and thickness stretching effects are included for mechanical analysis of advanced composite beams with simply supported boundary conditions, handling mainly bending, buckling, and free vibration problems. The kinematics is based on a novel displacement field which includes the undetermined integral terms and the parabolic function is used in terms of thickness coordinate to represent the effect of transverse shear deformation. The governing equilibrium equations are drawn from the dynamic version of the principle of virtual work; whereas the solution of the problem is obtained by assuming a Navier technique for simply supported advanced composite beams subjected to sinusoidally and uniformly distributed loads. The correctness of the present computational method is checked by comparing the obtained numerical results with quasi-3D solutions found in the literature and with those provided by other shear deformation beam theories. It can be confirmed that the proposed model, which does not involve any shear correction factor, is not only accurate but also simple and useful in solving the static and dynamic response of advanced composite beams.

키워드

참고문헌

  1. Akbas, S.D. (2018), "Thermal post-buckling analysis of a laminated composite beam", Struct. Eng. Mech., 67(4), 337-346. https://doi.org/10.12989/sem.2018.67.4.337.
  2. Avcar, M. (2019), "Free vibration of imperfect sigmoid and power law functionally graded beams", Steel Compos. Struct., 30(6), 603-615. https://doi.org/10.12989/scs.2019.30.6.603.
  3. Ayache, B., Bennai, R., Fahsi, B., Fourn, H., Ait Atmane, H. and Tounsi, A. (2018), "Analysis of wave propagation and free vibration of functionally graded porous material beam with a novel four variable refined theory", Earthq. Struct., 15(4), 369-382. http://doi.org/10.12989/eas.2018.15.4.369.
  4. Ait Atmane, H., Tounsi, A. and Bernard, F. (2017), "Effect of thickness stretching and porosity on mechanical response of a functionally graded beams resting on elastic foundations", Int. J. Mech. Mater. Des., 13(1), 71-84. https://doi.org/10.1007/s10999 -015-9318-x.
  5. Bensaid, I., Cheikh, A., Mangouchi, A. and Kerboua, B. (2017), "Static deflection and dynamic behavior of higher-order hyperbolic shear deformable compositionally graded beams", Adv. Mater. Res., 6(1), 13-26. https://doi.org/10.12989/amr. 2017.6.1.013.
  6. Chan, S.H. (2001), "Performance and emissions characteristics of a partially insulated gasoline engine", Int. J. Therm. Sci., 40, 255-261. https://doi.org/10.1016/S1290-0729(00)01215-1.
  7. Chen, C.D. and Su, P.W. (2021), "An analytical solution for vibration in a functionally graded sandwich beam by using the refined zigzag theory", Acta Mech., 232, 4645-4668. https://doi.org/10.1007/s00707-021-03063-9.
  8. Ebrahimi, F., Mahmoodi, F. and Barati, M.R. (2017), "Thermo-mechanical vibration analysis of functionally graded micro/nanoscale beams with porosities based on modified couple stress theory", Adv. Mater. Res., 6(3), 279-301. https://doi.org/10.12989/amr.2017.6.3.279.
  9. Ebrahimi, F. and Hosseini, S.H.S. (2021), "Nonlinear vibration and dynamic instability analysis nanobeams under thermo-magneto-mechanical loads: A parametric excitation study", Eng. Comput., 37, 395-408. https://doi.org/10.1007/s00366-019-00830-0.
  10. Eltaher, M.A., Fouda, N., El-midany, T. and Sadoun, A.M. (2018), "Modified porosity model in analysis of functionally graded porous nanobeams", J. Braz. Soc. Mech. Sci. Eng., 40, 141. https://doi.org/10.1007/s40430-018-1065-0.
  11. Euler, L. (1744), Methodus Inveniendi Lineas Curvas Maximi Minimive Proprietate Gaudentes, Apud Marcum-Michaelem Bousquet & Socio, Lausanne and Geneva, Switzerland.
  12. Ghumare, S.M. and Sayyad, A.S. (2017), "A new fifth-order shear and normal deformation theory for static bending and elastic buckling of P-FGM beams", Lat. Am. J. Solids Struct., 14(11), 1-19. https://doi.org/10.1590/1679-78253972.
  13. Ghumare, S.M. and Sayyad, A.S. (2020), "Analytical solutions for the hygro-thermo-mechanical bending of FG beams using a new fifth order shear and normal deformation theory", J. Appl. Comput. Mech., 14(1), 5-30. https://doi.org/10.24132/acm.2020.580.
  14. Guerroudj, H.Z., Yeghnem, R., Kaci, A. Zaoui, F.Z., Benyoucef, S. and Tounsi, A. (2018), "Eigen frequencies of advanced composite plates using an efficient hybrid quasi-3D shear deformation theory", Smart Struct. Syst., 22(1), 121-132. https://doi.org/10.12989/sss.2018.22.1.121.
  15. Gupta, A. and Talha, M. (2015), "Recent development in modeling and analysis of functionally graded materials and structures", Prog. Aerosp. Sci., 79, 1-14. https://doi.org/10.1016/j.paerosci.2015.07.001.
  16. Jha, D.K., Kant, T. and Singh, R.K. (2013), "A critical review of recent research on functionally graded plates", Compos. Struct., 96, 833-849. https://doi.org/10.1016/j.compstruct.2012.09.001.
  17. Kahya, V. and Turan, M. (2017), "Finite element model for vibration and buckling of functionally graded beams based on the first-order shear deformation theory", Compos. Part B: Eng., 109, 108-115. https://doi.org/10.1016/j.compositesb.2016.10.039.
  18. Karamanli, A. (2017), "Bending behavior of two directional functionally graded sandwich beams by using a quasi-3D shear deformation theory", Compos. Struct., 174, 70-86. https://doi.org/10.1016/j.compstruct.2017.04.046.
  19. Karami, B. and Janghorban, M. (2019), "A new size-dependent shear deformation theory for wave propagation analysis of triclinic nanobeams", Steel Compos. Struct., 32(2), 213-223. http://doi.org/10.12989/scs.2019.32.2.213.
  20. Katariya, P.V. and Panda, S.K. (2016), "Thermal buckling and vibration analysis of laminated composite curved shell panel", Aircr. Eng. Aerosp. Technol., 88(1), 97-107. https://doi.org/10.1108/AEAT-11-2013-0202.
  21. Uemura, S. (2003), "The activities of FGM on new applications", Mater. Sci. Forum, 423-425, 1-10. https://doi.org/10.4028/www.scientific.net/MSF.423-425.1.
  22. Koizumi, M. (1993), "The concept of FGM", Ceramic Transaction: Functionally gradient materials, American Ceramic Society, Westerville, OH, USA.
  23. Le, C.I., Le, N.A.T. and Nguyen, D.K. (2021), "Free vibration and buckling of bidirectional functionally graded sandwich beams using an enriched third-order shear deformation beam element", Compos. Struct., 261, 113309. https://doi.org/10.1016/j.compstruct.2020.113309.
  24. Li, X., Wang, B. and Han, J. (2010), "A higher-order theory for static and dynamic analyses of functionally graded beams", Arch. Appl. Mech., 80(10), 1197-1212. https://doi.org/10.1007/s00419-010-0435-6.
  25. Madenci, E. (2019), "A refined functional and mixed formulation to static analyses of FGM beams", Struct. Eng. Mech., 69(4), 427-437. https://doi.org/10.12989/sem.2019.69.4.427.
  26. Madenci, E. (2021), "Free vibration and static analyses of metal-ceramic FG beams via high-order variational MFEM", Steel Compos. Struct., 39(5), 493-509. https://doi.org/10.12989/scs.2021.39.5.493.
  27. Mahamood, R.M. and Akinlabi, E.T. (2017), Functionally Graded Materials, Springer International Publishing, Cham, Switzerland.
  28. Mahi, A., Bedia, E.A., Tounsi, A. and Mechab, I. (2010), "An analytical method for temperature-dependent free vibration analysis of functionally graded beams with general boundary conditions", Compos. Struct., 92(8), 1877-1887. https://doi.org/10.1016/j.compstruct.2010.01.010.
  29. Mouffoki, A., Adda Bedia, E.A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2017), "Vibration analysis of nonlocal advanced nanobeams in hygro-thermal environment using a new two-unknown trigonometric shear deformation beam theory", Smart Struct. Syst., 20(3), 369-383. https://doi.org/10.12989/sss.2017.20.3.369.
  30. Nguyen, T.K., Vo, T.P. and Thai, H.T. (2013), "Static and free vibration of axially loaded functionally graded beams based on the first-order shear deformation theory", Compos. Part B: Eng., 55, 147-157. https://doi.org/10.1016/j.compositesb.2013.06.011.
  31. Nguyen, T., Nguyen, T.T., Vo, T.P. and Thai, H.T. (2015), "Vibration and buckling analysis of functionally graded sandwich beams by a new higher-order shear deformation theory", Compos. Part B: Eng., 76, 273-285. https://doi.org/10.1016/j.compositesb.2015.02.032.
  32. Osofero, A.I., Vo, T.P., Nguyen, T.K. and Lee, J. (2016), "Analytical solution for vibration and buckling of functionally graded sandwich beams using various quasi-3D theories", J. Sandw. Struct. Mater., 18(1), 3-29. https://doi.org/10.1177/ 1099636215582217.
  33. Qin, B., Zhong, R., Wang, Q. and Zhao, X. (2020), "A Jacobi-Ritz approach for FGP beams with arbitrary boundary conditions based on a higher-order shear deformation theory", Compos. Struct., 247(4), 112435. https://doi.org/10.1016/j.compstruct. 2020.112435.
  34. Razouki, A., Boutahar, L. and El Bikri, K. (2020), "A new method of resolution of the bending of thick FGM beams based on refined higher order shear deformation theory", Univers. J. Mech. Eng., 8(2), 105-113. https://doi.org/10.13189/ujme.2020.080205.
  35. Reddy, J.N. (1984), "Simple higher order theory for laminated composite plates", J. Appl. Mech., 51, 745-752. https://doi.org/10.1115/1.3167719.
  36. Safa, A., Hadji, L., Bourada, M. and Zouatnia, N. (2019), "Thermal vibration analysis of FGM beams using an efficient shear deformation beam theory", Earthq. Struct., 17(3), 329-336. http://doi.org/10.12989/eas.2019.17.3.329.
  37. Sallai, B.O., Tounsi, A., Mechab, I., Bachir Bouiadjra, M., Meradjah, M. and Adda Bedia, E.A. (2009), "A theoretical analysis of flexional bending of Al/Al2O3 S-FGM thick beams", Comput. Mater. Sci., 44(4), 1344-1350. https://doi.org/10.1016/j. commatsci.2008.09.001.
  38. Sayyad, A.S. and Ghugal, Y.M. (2016), "Single variable refined beam theories for the bending, buckling and free vibration of homogenous beams", Appl. Comput. Mech., 10(2), 123-138.
  39. Sayyad, A.S. and Ghugal, Y.M. (2018a), "Analytical solutions for bending, buckling, and vibration analyses of exponential functionally graded higher order beams", Asian J. Civil Eng., 19, 607-623. https://doi.org/10.1007/s42107-018-0046-z.
  40. Sayyad, A.S. and Ghugal, Y.M. (2018b). "Bending, buckling and free vibration responses of hyperbolic shear deformation FGM beams", Mech. Adv. Compos. Struct., 5(1), 13-24. https://doi.org/10.22075/MACS.2018.12214.1117.
  41. Schulz, U., Peters, M., Bach, F.W. and Tegeder, G. (2003), "Graded coatings for thermal, wear and corrosion barriers", Mater. Sci. Eng. A, 362(1), 61-80. https://doi.org/10.1016/S0921-5093(03)00579-3.
  42. Selmi, A. and Bisharat, A. (2018), "Free vibration of functionally graded SWNT reinforced aluminum alloy beam", J. Vibroeng., 20(5), 2151-2164. https://doi.org/10.21595/jve.2018.19445.
  43. Simsek, M. (2010), "Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories", Nuclear Eng. Des., 240, 697-705. https://doi.org/10.1016/j.nucengdes.2009.12.013.
  44. Sina, S.A., Navazi, H.M. and Haddadpour, H. (2009), "An analytical method for free vibration analysis of functionally graded beams", Mater. Des., 30, 741-747. https://doi.org/10.1016/j.matdes.2008.05.015.
  45. Soldatos, K.P. (1992), "A transverse shear deformation theory for homogeneous monoclinic plates", Acta Mech., 94, 195-220. https://doi.org/10.1007/BF01176650.
  46. Tarlochan, F. (2012), "Functionally graded material: A new breed of engineered material", J. Appl. Mech. Eng., 1(5), 1-2. https://doi.org/10.4172/2168-9873.1000e115.
  47. Thai, H.T. and Vo, T.P. (2012), "Bending and free vibration of functionally graded beams by using various higher order shear deformation beam theories", Int. J. Mech. Sci., 62, 57-66. https://doi.org/10.1016/j.ijmecsci.2012.05.014.
  48. Timoshenko, S.P. (1921), "On the correction for shear of the differential equation for transverse vibrations of prismatic bars", Philos. Magaz. J. Sci., 41, 742-746. https://doi.org/10.1080/14786442108636264.
  49. Vo, T.P., Thai, H.T., Nguyen, T.K., Maheri, A. and Lee, J. (2014), "Finite element model for vibration and buckling of functionally graded sandwich beams based on a refined shear deformation theory", Eng. Struct., 64, 12-22. https://doi.org/10.1016/j.engstruct. 2014.01.029.
  50. Vo, T.P., Thai, H.T., Nguyen, T.K., Inam, F. and Lee, J. (2015), "Static behaviour of functionally graded sandwich beams using a quasi-3D theory", Compos. Part B: Eng., 68, 59-74. https://doi.org/10.1016/j.compositesb.2014. 08.030.
  51. Watanabe, R., Nishida, T. and Hirai, T. (2003), "Present status of research on design and processing of functionally graded materials", Metal. Mater. Int., 9(6), 513-519. https://doi.org/10.1007/bf03027249.
  52. Youcef, A. Bourada, M., Draiche, K., Boucham, B., Bourada, F. and Addou, F.Y. (2020), "Bending behaviour of FGM plates via a simple quasi-3D and 2D shear deformation theories", Coupled Syst. Mech., 9(3), 237-264. http://doi.org/10.12989/csm.2020.9.3.237.