Earthquakes and Structures

  • 제19권2호
  • /
  • Pages.91-101
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  • 2020
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  • 2092-7614(pISSN)
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  • 2092-7622(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Analytical modeling of bending and free vibration of thick advanced composite beams resting on Winkler-Pasternak elastic foundation

  • Chami, Khaldoune (Laboratory of Mechanical of Solids and Systems, M'hamed Bougara University) ;
  • Messafer, Tahar (Research Unit of Materials, Processes and Environment, M'Hamed Bougara University of Boumerdes) ;
  • Hadji, Lazreg (Laboratory of Geomatics and Sustainable Development, University of Tiaret)
  • 투고 : 2019.12.08
  • 심사 : 2020.08.06
  • 발행 : 2020.08.25
⟨ 이전 논문 다음 논문 ⟩

초록

This work presents an efficient and original hyperbolic shear deformation theory for the bending and dynamic behavior of functionally graded (FG) beams resting on Winkler - Pasternak foundations. The theory accounts for hyperbolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. Based on the present theory, the equations of motion are derived from Hamilton's principle. Navier type analytical solutions are obtained for the bending and vibration problems. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions. It can be concluded that the present theory is not only accurate but also simple in predicting the bending and vibration behavior of functionally graded beams.

키워드

참고문헌

  1. Abualnour, M., Chikh, A., Hebali, H., Kaci, A., Tounsi, A., Bousahla, A.A. and Tounsi, A., (2019), "Thermomechanical analysis of antisymmetric laminated reinforced composite plates using a new four variable trigonometric refined plate theory", Comput. Concrete, 24(6). 489-498. https://doi.org/10.12989/cac.2019.24.6.489.
  2. Adda Bedia, W., Houari, M.S.A., Bessaim, A., Bousahla, A.A., Tounsi, A., Saeed, T. and Alhodaly, M.S. (2019), "A New Hyperbolic Two-Unknown Beam Model for Bending and Buckling Analysis of a Nonlocal Strain Gradient Nanobeams", J. Nano Res., 57, 175-191. https://doi.org/10.4028/www.scientific.net/JNanoR.57.175.
  3. Addou, F.Y., Meradjah, M., Bousahla, A.A., Benachour, A., Bourada, F., Tounsi, A. and Mahmoud, S.R. (2019), "Influences of porosity on dynamic response of FG plates resting on Winkler/Pasternak/Kerr foundation using quasi 3D HSDT", Comput. Concrete, 24(4), 347-367. https://doi.org/10.12989/cac.2019.24.4.347.
  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. Akbas, S.D. (2014), "Wave propagation analysis of edge cracked beams resting on elastic foundation", Int. J. Eng. Appl. Sci., 6(1), 40-52.
  6. Akbas, S.D. (2015), "Free vibration analysis of edge cracked functionally graded beams resting on WinklerPasternak foundation", Int. J. Eng. Appl. Sci., 7(3), 1-15.
  7. Alimirzaei, S., Mohammadimehr, M. and Tounsi, A., (2019), "Nonlinear analysis of viscoelastic micro-composite beam with geometrical imperfection using FEM: MSGT electro-magneto-elastic bending, buckling and vibration solutions", Struct. Eng. Mech., 71(5), 485-502. https://doi.org/10.12989/sem.2019.71.5.485.
  8. Batou, B., Nebab, M., Bennai, R., Ait Atmane, H., Tounsi, A. and Bouremana, M. (2019), "Wave dispersion properties in imperfect sigmoid plates using various HSDTs", Steel Compos. Struct., 33(5), 699-716. https://doi.org/10.12989/scs.2019.33.5.699
  9. Belbachir, N., Draiche, K., Bousahla, A.A., Bourada, M., Tounsi, A. and Mahmoud, S.R. (2019), "Bending analysis of anti-symmetric cross-ply laminated plates under nonlinear thermal and mechanical loadings", Steel Compos. Struct., 33(1), 913-924. https://doi.org/10.12989/scs.2019.33.1.081.
  10. Benrahou, K.H., Bakora, A., Algarni, A., Bousahla, A.A., Tounsi, A., Tounsi, A. and Mahmoud, S.R. (2019), "Dynamic Analysis of nanosize FG rectangular plates based on simple nonlocal quasi 3D HSDT", Advan. Nano Res., 7(3), 189-206. http://dx.doi.org/10.12989/anr.2019.7.3.191.
  11. Berghouti, H., Adda Bedia, E.A., Benkhedda, A. and Tounsi, A. (2019), "Vibration analysis of nonlocal porous nanobeams made of functionally graded material", Advan. Nano Res., 7(5), 351-364. https://doi.org/10.12989/anr.2019.7.5.351.
  12. Boukhlif, Z., Bouremana, M., Bourada, F., Bousahla, A.A., Bourada, M., Tounsi, A. and Al-Osta, M.A. (2019), "A simple quasi-3D HSDT for the dynamics analysis of FG thick plate on elastic foundation", Steel Compos. Struct., 31(5), 503-516. https://doi.org/10.12989/scs.2019.31.5.503.
  13. Boulefrakh, L., Hebali, H., Abdelbaki, C. and Mahmoud, S.R. (2019), "The effect of parameters of visco-Pasternak foundation on the bending and vibration properties of a thick FG plate", Geomech. Eng., 18(2), 161-178. https://doi.org/10.12989/gae.2019.18.2.161.
  14. Bourada, F., Bousahla, A.A., Bourada, M., Azzaz, A., Zinata, A. and Tounsi, A. (2019), "Dynamic investigation of porous functionally graded beam using a sinusoidal shear deformation theory", Wind Struct., 28(1), 19-30. https://doi.org/10.12989/was.2019.28.1.019.
  15. Boussoula, A., Boucham, B., Bourada, M., Bourada, F., Tounsi, A., Bousahla, A.A. and Tounsi, A. (2020), "A simple nth-order shear deformation theory for thermomechanical bending analysis of different configurations of FG sandwich plates", Smart Struct. Syst., 25(2), 197-218. https://doi.org/10.12989/sss.2020.25.2.197.
  16. Boutaleb, S., Benrahou, K.H., Bakora, A., Algarni, A., Bousahla, A.A., Tounsi, A., Tounsi, A. and Mahmoud, S.R. (2019), "Dynamic Analysis of nanosize FG rectangular plates based on simple nonlocal quasi 3D HSDT", Advan. Nano Res., 7(3), 189-206. http://dx.doi.org/10.12989/anr.2019.7.3.191.
  17. Chaabane, L.A., Bourada, F., Sekkal, M., Zerouati, S., Zaoui, F.Z., Tounsi, A., Derras, A., Bousahla, A.A and Tounsi, A., (2019), "Analytical study of bending and free vibration responses of functionally graded beams resting on elastic foundation", Struct. Eng. Mech., 71(2), 185-196. https://doi.org/10.12989/sem.2019.71.2.185.
  18. Chikr, S.C., Kaci, A., Bousahla, A.A., Bourada, F., Tounsi, A., AddaBedia, E.A., Mahmoud, S.R., Benrahou, S.R. and Tounsi, A. (2020), "A novel four-unknown integral model for buckling response of FG sandwich plates resting on elastic foundations under various boundary conditions using Galerkin's approach", Geomech. Eng., 21(5), 471-487. https://doi.org/10.12989/gae.2020.21.5.471.
  19. Draiche, K., Bousahla, A.A., Tounsi, A., Alwabli, A. S., Tounsi, A. and Mahmoud, S.R. (2019), "Static analysis of laminated reinforced composite plates using a simple first-order shear deformation theory", Comput. Concrete, 24(4), 369-378. https://doi.org/10.12989/cac.2019.24.4.369.
  20. Draoui, A., Zidour, M., Tounsi, A. and Adim, B. (2019), "Static and dynamic behavior of nanotubes-reinforced sandwich plates using (FSDT)", J. Nano Res., 57, 117-135. https://doi.org/10.4028/www.scientific.net/JNanoR.57.117.
  21. Euler, L. (1744), Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes, Lausanne and Geneva: ApudMarcum-Michaelem Bousquet & Socio.
  22. Fazzolari, F.A. (2018), "Generalized exponential, polynomial and trigonometric theories for vibration and stability analysis of porous FG sandwich beams resting on elastic foundations", Compos. Part B Eng, 136, 254-271. https://doi.org/10.1016/j.compositesb.2017.10.022.
  23. Hellal, H., Bourada, M., Hebali, H., Bourda, F., Tounsi, A., Bousahla, A.A. and Mahmour, S.R., (2019), "Dynamic and stability analysis of functionally graded material sandwich plates in hygro-thermal environment using a simple higher shear deformation theory", J. Sandwich Struct. Mater., 1099636219845841. https://doi.org/10.1177%2F1099636219845841.
  24. Hussain, M., Naeem, M.N., Tounsi, A. and Taj, M. (2019), "Nonlocal effect on the vibration of armchair and zigzag SWCNTs with bending rigidity", Advan. Nano Res., 7(6), 431-442. https://doi.org/10.12989/anr.2019.7.6.431.
  25. Jodaei, A. and Yas, M.H. (2012), "Three-dimensional free vibration analysis of functionally graded annular plates on elastic foundations via state-space based differential quadrature method", J Pressure Vessel Technol., 134, 031208-1. https://doi.org/10.1016/j.compositesb.2011.08.052.
  26. Kaddari, M., Kaci, A., Bousahla, A.A., Tounsi, A., Bourada, F., Tounsi, A., Adda Bedia, E.A., and Al-Osta, M.A., (2020), "A study on the structural behaviour of functionally graded porous plates on elastic foundation using a new quasi-3D model: Bending and Free vibration analysis", Comput. Concrete, 25(1), 37-57. https://doi.org/10.12989/cac.2020.25.1.037.
  27. Karami, B., Janghorban, M. and Tounsi, A. (2019b), "Galerkin's approach for buckling analysis of functionally graded anisotropic nanoplates/different boundary conditions", Eng. Comput., 35, 1297-1316. https://doi.org/10.1007/s00366-018-0664-9.
  28. Karami, B., Janghorban, M. and Tounsi, A. (2019d), "On exact wave propagation analysis of triclinic material using three dimensional bi-Helmholtz gradient plate model", Struct. Eng. Mech., 69(5), 487-497. https://doi.org/10.12989/sem.2019.69.5.487.
  29. Karami, B., Janghorban, M. and Tounsi, A. (2019e), "On pre stressed functionally graded anisotropic nanoshell in magnetic field", J. Brazil. Soc. Mech. Sci. Eng., 41(11), 495. https://doi.org/10.1007/s40430-019-1996-0.
  30. Karami, B., Janghorban, M. and Tounsi, A., (2019a), "Wave propagation of functionally graded anisotropic nanoplates resting on Winkler-Pasternak foundation", Struct. Eng. Mech., 70(1), 55-66. https://doi.org/10.12989/sem.2019.70.1.055.
  31. Karami, B., Shahsavari, D., Janghorban, M. and Tounsi, A. (2019c), "Resonance behavior of functionally graded polymer composite nanoplates reinforced with grapheme nanoplatelets", Int. J. Mech. Sci., 156, 94-105. https://doi.org/10.1016/j.ijmecsci.2019.03.036.
  32. Khelifa, Z., Hadji, L., Hassaine Daouadji, T. and Bourada, M. (2018), "Buckling response with stretching effect of carbon nanotube-reinforced composite beams resting on elastic foundation", Struct. Eng. Mech., 67(2), 125-130. https://doi.org/10.12989/sem.2018.67.2.125.
  33. Khiloun, M., Bousahla, A.A., Kaci, A., Bessaim, A., Tounsi, A. and Mahmoud, S.R. (2020), "Analytical modeling of bending and vibration of thick advanced composite plates using a four-variable quasi 3D HSDT", Eng. Comput., 36, 807-821. https://doi.org/10.1007/s00366-019-00732-1.
  34. Mahmoud, S.R. and Tounsi, A. (2019), "On the stability of isotropic and composite thick plates", Steel Compos. Struct., 33(4), 551-568. https://doi.org/10.12989/scs.2019.33.4.551.
  35. Mahmoudi, A., Benyoucef, S., Tounsi, A., Benachour, A. and Adda Bedia, E.A. (2018), "On the effect of the micromechanical models on the free vibration of rectangular FGM plate resting on elastic foundation", Earthq. Struct., 14(2), 117-128. https://doi.org/10.12989/eas.2018.14.2.117.
  36. Mahmoudi, A., Benyoucef, S., Tounsi, A., Benacour, A., Adda Bedia, E.A. and Mahmoud, S.R. (2019), "A refined quasi-3D shear deformation theory for thermo-mechanical behavior of functionally graded sandwich plates on elastic foundations", J. Sandwich Struct. Mater., 21(6), 1906-1926. https://doi.org/10.1177%2F1099636217727577. https://doi.org/10.1177/1099636217727577
  37. Medani, M., Benahmed, A., Zidour, M., Heireche, H., Tounsi, A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2019), "Static and dynamic behavior of (FG-CNT) reinforced porous sandwich plate", Steel Compos. Struct., 32(5), 595-610. https://doi.org/10.12989/scs.2019.32.5.595.
  38. Meksi, R., Benyoucef, S., Mahmoudi, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2019), "An analytical solution for bending, buckling and vibration responses of FGM sandwich plates", J. Sandw. Struct. Mater., 21(2), 727-757. https://doi.org/10.1177%2F1099636217698443. https://doi.org/10.1177/1099636217698443
  39. Mirza, S.B., Yaqoob, Y. and Hasan, M.K. (2018), "Analysis of Laminated and FGM Beams using Various Theories", IOP Conf. Series: Mater. Sci. Eng., 404(1), 012030. https://ui.adsabs.harvard.edu/link_gateway/2018MS&E..404a2030S/doi:10.1088/1757-899X/404/1/012030.
  40. Pasternak, P.L. (1954), "On a new method of analysis of an elastic foundation by means of two foundation constants", Gosudarstvennoe Izdatelstvo Literaturi po Stroitelstvu I Arkhitekture, Moscow: USSR, 1, 1-56.
  41. Reddy, J.N. (1984), "A simple higher order theory for laminated composite plates", ASME J. Appl. Mech., 51, 745-752. https://doi.org/10.1115/1.3167719.
  42. Refrafi, S., Bousahla, A.A., Bouhadra, A., Menasria, A., Bourada, F., Tounsi, A., AddaBedia, E.A., Mahmoud, S.R., Benrahou, K.H. and Tounsi, A. (2020), "Effects of hygro-thermo-mechanical conditions on the buckling of FG sandwich plates resting on elastic foundations", Comput. Concrete, 25(4), 311-325. https://doi.org/10.12989/cac.2020.25.4.311.
  43. 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. https://doi.org/10.12989/eas.2019.17.3.329.
  44. Sahla, M., Saidi, H., Draiche, K., Bousahla, A.A., Bourada, F. and Tounsi, A. (2019), "Free vibration analysis of angle-ply laminated composite and soft core sandwich plates", Steel Compos. Struct., 33(5), 663-679. https://doi.org/10.12989/scs.2019.33.5.663.
  45. Sahouane, A., Hadji, L. and Bourada, M. (2019), "Numerical analysis for free vibration of functionally graded beams using an original HSDBT", Earthq. Struct., 17(1), 31-37. https://doi.org/10.12989/eas.2019.17.1.031.
  46. Sayyad, A.S. and Ghugal, Y.M. (2018), "An inverse hyperbolic theory for FG beams resting on Winkler-Pasternak elastic foundation", Advan. Aircraft Spacecraft Sci., 5(6), 671-689. http://dx.doi.org/10.12989/aas.2018.5.6.671.
  47. Semmah, A., Heireche, H., Bousahla, A.A. and Tounsi, A. (2019), "Thermal buckling analysis of SWBNNT on Winkler foundation by non local FSDT", Advan. Nano Res., 7(2), 89-98. http://dx.doi.org/10.12989/anr.2019.7.2.089.
  48. 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.
  49. Thai, H.T. and Choi, D.H. (2012), "A refined shear deformation theory for free vibration of functionally graded plates on elastic foundation", Compos.: Part B Eng., 43(5), 2335-2347. https://doi.org/10.1016/j.compositesb.2011.11.062.
  50. Timoshenko, S.P. (1921), "On the correction for shear of the differential equation for transverse vibrations of prismatic bars", Philos. Mag., 41(245), 742-746. https://doi.org/10.1080/14786442108636264.
  51. Tlidji, Y., Zidour, M., Draiche, K., Safa, A., Bourada, M., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2019), "Vibration analysis of different material distributions of functionally graded microbeam", Struct. Eng. Mech., 69(6), 637-649. https://doi.org/10.12989/sem.2019.69.6.637.
  52. Winkler, E. (1867), "Die Lehre von der Elasticitaet und Festigkeit", Prag Dominicus.
  53. Yas, M.H. and Tahouneh, V. (2012), "3-D free vibration analysis of thick functionally graded annular plates on Pasternak elastic foundation via differential quadrature method (DQM)", Acta Mech., 223(1), 43-62. https://doi.org/10.1007/s00707-011-0543-6.
  54. Zaoui, F.Z., Ouinas, D. and Tounsi, A. (2019), "New 2D and quasi-3D shear deformation theories for free vibration of functionally graded plates on elastic foundations", Compos. Part B: Eng., 159(15), 231-247. https://doi.org/10.1016/j.compositesb.2018.09.051.
  55. Zarga, D., Tounsi, A., Bousahla, A.A., Bourada, F. and Mahmoud, S.R. (2019), "Thermomechanical bending study for functionally graded sandwich plates using a simple quasi-3D shear deformation theory", Steel Compos. Struct., 32(3), 389-410. https://doi.org/10.12989/scs.2019.32.3.389.

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