Steel and Composite Structures

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Study on stability and free vibration behavior of porous FGM beams

  • Bennai, Riadh (Department of Civil Engineering, Faculty of Civil Engineering and Architecture, University Hassiba Benbouali of Chlef) ;
  • Atmane, Redhwane Ait (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Bernard, Fabrice (LGCGM, IINSA RENNES France) ;
  • Nebab, Mokhtar (Laboratory of Structures, Geotechnics and Risks, Department of Civil Engineering, Hassiba Benbouali University of Chlef) ;
  • Mahmoudi, Noureddine (Department of mechanical engineering, university of Saida) ;
  • Atmane, Hassen Ait (Department of Civil Engineering, Faculty of Civil Engineering and Architecture, University Hassiba Benbouali of Chlef) ;
  • Aldosari, Salem Mohammed (Enhanced Composite and Structures Centre, School of Aerospace, Transport, and Manufacturing, Cranfield University) ;
  • Tounsi, Abdelouahed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
  • Received : 2020.09.05
  • Accepted : 2022.10.12
  • Published : 2022.10.10
⟨ Previous Next ⟩

Abstract

In this paper, buckling and free vibration of imperfect, functionally graded beams, including porosities, are investigated, using a higher order shear strain theory. Due to defects during the manufacturing process, micro porosities may appear in the material, hence the appearance of this imperfection in the structure. The material properties of the beams are assumed to vary regularly, with power and sigmoid law, in the direction of thickness. A novel porosity distribution affecting the functionally graded volume fraction is presented. For the compact formulation used for cementite-based materials and already used in P-FGM, we have adapted it for the distribution of S-FGM. The equations of motion in the FG beam are derived using Hamilton's principle. The boundary conditions for beam FG are assumed to be simply supported. Navier's solution is used to obtain the closed form solutions of the FG beam. The numerical results of this work are compared with those of other published research to verify accuracy and reliability. The comparisons of different shear shape functions, the influence of porosity, thickness and inhomogeneity parameters on buckling and free vibration of the FG beam are all discussed. It is established that the present work is more precise than certain theories developed previously.

Keywords

References

  1. Abdulrazzaq, M.A., Fenjan, R.M., Ahmed, R.A. and Faleh, N.M. (2020), "Thermal buckling of nonlocal clamped exponentially graded plate according to a secant function based refined theory", Steel Compos. Struct., 35(1), 147-157. https://doi.org/10.12989/scs.2020.35.1.147.
  2. Akgoz, B. and Civalek, O. (2013), "Buckling analysis of functionally graded microbeams based on the strain gradient theory", Acta Mechanica, 224(9), 2185-2201. https://doi.org/10.1007/s00707-013-0883-5.
  3. Akavci, S.S. (2016), "Mechanical behavior of functionally graded sandwich plates on elastic foundation", Compos. Part B, 96, 136-152. https://doi.org/10.1016/j.compositesb.2016.04.035.
  4. Akbas, S.D. (2017), "Thermal effects on the vibration of functionally graded deep beams with porosity", Int. J. Appl. Mech., 9(5), 1750076. https://doi.org/10.1142/S1758825117500764.
  5. Akbas, S.D. (2017), "Vibration and static analysis of functionally graded porous plates", J. Appl. Comput. Mech., 3(3), 199-207. https://doi.org/10.22055/JACM.2017.21540.1107.
  6. Akbas, S.D. (2015), "Wave propagation of a functionally graded beam in thermal environments", Steel Compos. Struct., 19(6), 1421-1447. https://doi.org/10.12989/scs.2015.19.6.1421.
  7. Attia, M.A. (2017), "On the mechanics of functionally graded nanobeams with the account of surface elasticity", Int. J. Eng. Sci., 115, 73-101. https://doi.org/10.1016/j.ijengsci.2017.03.011.
  8. Avcar, M. and Mohammed, W.K.M. (2018), "Free vibration of functionally graded beams resting on Winkler-Pasternak foundation", Arab. J. Geosci., 11(10), 232. https://doi.org/10.1007/s12517-018-3579-2.
  9. 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.
  10. 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. https://doi.org/10.12989/eas.2018.15.4.369.
  11. Bahl, S. and Bagha, A.K. (2021), ''Finite element modeling and simulation of the fiber-matrix interface in fiber reinforced metal matrix composites'', Materials Today: Proceedings, 39, 70-76. https://doi.org/10.1016/j.matpr.2020.06.160.
  12. Bagha, A.K. and Bahl, S. (2021), ''Finite element analysis of VGCF/pp reinforced square representative volume element to predict its mechanical properties for different loadings'', Materials Today: Proceedings, 39, 54-59. https://doi.org/10.1016/j.matpr.2020.06.108.
  13. Barati, M.R., Shahverdi, H. and Zenkour, A.M. (2017), "Electromechanical vibration of smart piezoelectric FG plates with porosities according to a refined four-variable theory", Mech. Adv. Mater. Struct., 24(12), 987-998. https://doi.org/10.1080/15376494.2016.1196799.
  14. 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. https://doi.org/10.12989/scs.2019.33.5.699.
  15. Bennai, R., Atmane, H.A. and Tounsi, A. (2015), ''A new higherorder shear and normal deformation theory for functionally graded sandwich beams'', Steel Compos. Struct., 19(3), 521-546. http://dx.doi.org/10.12989/scs.2015.19.3.521.
  16. Bennai, R., Fourn, H., Ait Atmane, H., Tounsi, A. and Bessaim, A. (2019 a), "Dynamic and wave propagation investigation of FGM plates with porosities using a four variable plate theory", Wind Struct., 28(1), 49-62. https://doi.org/10.12989/was.2019.28.1.049.
  17. Bennai, R., Ait Atmane, H., Ayache, B., Tounsi, A., Bedia, E.A. and Al-Osta, M.A. (2019 b), "Free vibration response of functionally graded Porous plates using a higher-order Shear and normal deformation theory", Earthq. Struct., 16(5), 547-561. https://doi.org/10.12989/eas.2019.16.5.547.
  18. Chakraverty, S. and Pradhan, K.K. (2014), "Free vibration of exponential functionally graded rectangular plates in thermal environment with general boundary conditions", Aerosp. Sci. Technol., 36, 132-156. https://doi.org/10.1016/j.ast.2014.04.005.
  19. Chen, D., Yang, J. and Kitipornchai, S. (2015), "Elastic buckling and static bending of shear deformable functionally graded porous beam", Compos. Struct., 133, 54-61. https://doi.org/10.1016/j.compstruct.2015.07.052.
  20. Ebrahimi, F. and Jafari, A. (2016), ''Thermo-mechanical vibration analysis of temperature-dependent porous FG beams based on Timoshenko beam theory'', Struct. Eng. Mech., 59(2), 343-371. https://doi.org/10.12989/sem.2016.59.2.343.
  21. Fenjan, R.M., Hamad, L.B. and Faleh, N.M. (2020), "Mechanicalhygro-thermal vibrations of functionally graded porous plates with nonlocal and strain gradient effects", Adv. Air. Spacecraft Sci., 7(2), 169-186. https://doi.org/10.12989/aas.2020.7.2.169.
  22. Fenjan, N.M., Moustafa, N.M. and Faleh, N.M. (2020), "Scaledependent thermal vibration analysis of FG beams having porosities based on DQM", Adv. Nano Res., 8(4), 283-292. https://doi.org/10.12989/anr.2020.8.4.283.
  23. Frahlia, H., Bennai, R., Nebab, M., Ait Atmane, H. and Tounsi, A. (2022), "Assessing effects of parameters of viscoEF on the dynamic response of functionally graded plates using a novel HSDT theory", Mech. Adv. Mater. Struct., 1-15. https://doi.org/10.1080/15376494.2022.2062632.
  24. Gafour, Y., Hamidi, A., Benahmed, A., Zidour, M. and Bensattalah, T. (2020), "Porosity-dependent free vibration analysis of FG nanobeam using non-local shear deformation and energy principle", Adv. Nano Res., 8(1), 37-47. https://doi.org/10.12989/anr.2020.8.1.049.
  25. Ghandourah, E. and Abdraboh, A.M. (2020), "Dynamic analysis of functionally graded nonlocal nanobeam with different porosity models", Steel Compos. Struct., 36(3), 293-305. http://dx.doi.org/10.12989/scs.2020.36.3.293.
  26. Gupta, A., Talha, M. and Chaudhari, V.K. (2016), "Natural frequency of functionally graded plates resting on elastic foundation using finite element method", Procedia Technology, 23, 163-170. https://doi.org/10.1016/j.protcy.2016.03.013.
  27. Gupta, A. and Talha, M. (2017a), "Nonlinear flexural and vibration response of geometrically imperfect gradient plates using hyperbolic higher-order shear and normal deformation theory", Compos. Part B: Eng., 123, 241-261. https://doi.org/10.1016/j.compositesb.2017.05.010.
  28. Gupta, A. and Talha, M. (2017b), "Influence of porosity on the flexural and free vibration responses of functionally graded plates in thermal environment", Int. J. Struct. Stabil. Dyn., 1850013. https://doi.org/10.1142/S021945541850013X.
  29. Gupta, A. and Talha, M. (2018), "Static and stability characteristics of geometrically imperfect FGM plates resting on pasternak elastic foundation with microstructural defect", Arab. J. Sci. Eng., 43, 4931-4947. https://doi.org/10.1007/s13369-018-3240-0.
  30. Hadji, L., Zouatnia, N. and Bernard, F. (2019), "An analytical solution for bending and free vibration responses of functionally graded beams with porosities: Effect of the micromechanical models", Struct. Eng. Mech., 69(2), 231-241. https://doi.org/10.12989/sem.2019.69.2.231.
  31. Hadji, L. and Bernard, F. (2020), "Bending and free vibration analysis of functionally graded beams on elastic foundations with analytical validation", Adv. Mater. Res., 9(1), 63-98. https://doi.org/10.12989/amr.2020.9.1.063.
  32. Ibnorachid, Z., Boutahar, L., EL Bikri, K. and Benamar, R. (2019), ''Buckling temperature and natural frequencies of thick porous functionally graded beams resting on elastic foundation in a thermal environment'', Adv. Acoust. Vib., https://doi.org/10.1155/2019/7986569.
  33. Jamaludin, S.N.S., Basri, S., Ahmad Hussain., Dheya Shujaa AlOthmany., Mustapha, F. and Nuruzzaman, D.M. (2014), "Three-dimensional finite element modeling of thermomechanical problems in functionally graded hydroxyapatite/titanium plate", Mathem. Prob. Eng., 371462, 1-20. https://doi.org/10.1155/2014/371462.
  34. Kadoli, R., Akhtar, K. and Ganesan, N. (2008), "Static analysis of functionally graded beams using higher order shear deformation theory", Appl. Math. Model., 32(12), 2509-2525. https://doi.org/10.1016/j.apm.2007.09.015.
  35. Karami, B., Shahsavari, D., Nazemosadat, Seyed M.R., Li, L. and Ebrahimi, A. (2018) "Thermal buckling of smart porous functionally graded nanobeam rested on Kerr foundation", Steel Compos. Struct., 29(3), 349-362. https://doi.org/10.12989/scs.2018.29.3.349.
  36. Kar, V.R. and Panda, S.K. (2015), "Large deformation bending analysis of functionally graded spherical shell using FEM", Struct. Eng. Mech., 53(4), 661-679. https://doi.org/10.12989/sem.2015.53.4.661.
  37. Kar, V.R. and Panda, S.K. (2016a), "Post-buckling behaviour of shear deformable functionally graded curved shell panel under edge compression", Int. J. Mech. Sci., 115, 318-324. https://doi.org/10.1016/j.ijmecsci.2016.07.014.
  38. Kar, V.R. and Panda, S.K. (2016b), "Nonlinear thermomechanical behavior of functionally graded material cylindrical/hyperbolic/elliptical shell panel with temperaturedependent and temperature-independent properties", J. Pressure Vessel Technol., 138(6), 061202. https://doi.org/10.1115/1.4033701.
  39. Kar, V.R., Panda, S.K. (2016c), "Geometrical nonlinear free vibration analysis of FGM spherical panel under nonlinear thermal loading with TD and TID properties", J. Thermal Stresses, 39(8), 942-959. https://doi.org/10.1080/01495739.2016.1188623.
  40. Kar, V.R. and Panda, S.K. (2016e), "Nonlinear free vibration of functionally graded doubly curved shear deformable panels using finite element method", J. Vib. Control, 22(7), 1935-1949. https://doi.org/10.1177/1077546314545102.
  41. Kendall, K., Howard, A., Birchall, J., Prat, P., Proctor, A. and Jefferies, S.A. (1983), "The relation between porosity, microstructure and strength, and the approach to advanced cement-based materials", Phil. Trans. Roy. Soc. Lond. A., 310(1511), 139-153. https://doi.org/10.1098/rsta.1983.0073.
  42. Koizumi, M. and Niino, M. (1995), "Overview of FGM research in Japan", MRS Bull., 1995, 19-21. https://doi.org/10.1557/S0883769400048867
  43. Kumar Saini, M., Kumar Bagha, A., Kumar, S. and Bahl, S. (2021), ''Finite element analysis for predicting the vibration characteristics of natural fiber reinforced epoxy composites'', Materials Today: Proceedings, 41, 223-227. https://doi.org/10.1016/j.matpr.2020.08.717.
  44. Kumar Bagha, A. and Bahl, S. (2021), ''Strain energy and finite element analysis to predict the mechanical properties of vapor grown carbon fiber reinforced polypropylene nanocomposites'', Materials Today: Proceedings, 41, 265-268. https://doi.org/10.1016/j.matpr.2020.09.034.
  45. 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.
  46. Melaibari, A., Abo-bakr, R.M., Mohamed, S.A. and Eltaher, M.A. (2020), "Static stability of higher order functionally graded beam under variable axial load", Alexandria Eng. J., 59(3), 1661-1675. https://doi.org/10.1016/j.aej.2020.04.012.
  47. Mellal, F., Bennai, R., Nebab, M., Atmane, H.A., Bourada, F., Hussain, M. and Tounsi, A. (2021), "Investigation on the effect of porosity on wave propagation in FGM plates resting on EFs via a quasi-3D HSDT", Waves Random Complex Media, 1-27. https://doi.org/10.1080/17455030.2021.1983235.
  48. Mantari, J.L. and Guedes Soares, C. (2013), ''A novel higher-order shear deformation theory with stretching effect for functionally graded plates'', Compos. Part B: Eng., 45(1), 268-281. https://doi.org/10.1016/j.compositesb.2012.05.036.
  49. Nebab, M., Ait Atmane, H., Bennai, R. and Tounsi, A. (2019a), ''Effect of variable elastic foundations on static behavior of functionally graded plates using sinusoidal shear deformation'', Arab. J. Geosci.. 12(24), 809. https://doi.org/10.1007/s12517-019-4871-5.
  50. Nebab, M., Ait Atmane, H., Bennai, R. and Tahar, B. (2019b), ''Effect of nonlinear elastic foundations on dynamic behavior of FG plates using four-unknown plate theory'', Earthq. Struct., 17(5), 447-462.https://doi.org/10.12989/eas.2019.17.5.447.
  51. Nebab, M., Ait Atmane, H., Bennai, R., Tounsi, A. and Bedia, E. (2019c), ''Vibration response and wave propagation in FG plates resting on elastic foundations using HSDT'', Struct. Eng. Mech.. 69(5), 511-525. https://doi.org/10.12989/sem.2019.69.5.511.
  52. Nguyen, T.K., Vo, T.H. and Thai, T.H. (2013), ''Static and free vibration of axially loaded functionally graded beams based on the first-order shear deformation theory", Compos. Part B. 55, 147-157. https://doi.org/10.1016/j.compositesb.2013.06.011.
  53. Rachedi, M.A., Benyoucef, S., Bouhadra, A., Bachir Bouiadjra, R., Sekkal, M. and Benachour, A. (2020), "Impact of the homogenization models on the thermoelastic response of FG plates on variable elastic foundation", Geomech. Eng., 22(1), 65-80. https://doi.org/10.12989/gae.2020.22.1.065.
  54. Reddy, J.N. (2000), "Analysis of functionally graded plates", Int. J. Numer. Meth. Eng., 47, 663-684. https://doi.org/10.1002/(SICI)10970207(20000110/30)47:1/3<6 63::AID-NME787>3.0.CO;2-8.
  55. Reddy, J.N. and Cheng, Z.Q. (2001), "Three-dimensional thermomechanical deformations of functionally graded rectangular plates", Eur. J. Mech. A/Solid., 20, 841-855. https://doi.org/10.1016/S0997-7538(01)01174-3.
  56. Shahsavari, D., Shahsavarib, M., Li, L. and Karami, B. (2018), "A novel quasi-3D hyperbolic theory for free vibration of FG plates with porosities resting on Winkler/Pasternak/Kerr foundation", Aeros. Sci. Technol., 72, 134-149. https://doi.org/10.1016/j.ast.2017.11.004.
  57. Shimpi, R.P. and Patel, H.G. (2006), "Free vibrations of plate using two variable refined plate theory", J. Sound Vib., 296(4-5), 979-999. https://doi.org/10.1016/j.jsv.2006.03.030.
  58. Simsek, M. (2010a), "Non-linear vibration analysis of a functionally graded Timoshenko beam under action of a moving harmonic load", Compos. Struct., 92(10), 2532-2546. https://doi.org/10.1016/j.compstruct.2010.02.008.
  59. Simsek, M. (2010b), ''Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories'', Nuclear Eng. Des., 240(4), 697-705. https://doi.org/10.1016/j.nucengdes.2009.12.013.
  60. Sobhy, M. (2013), "Buckling and free vibration of exponentially graded sandwich plates resting on elastic foundations under various boundary conditions", Compos. Struct., 99, 76-87. https://doi.org/10.1016/j.compstruct.2012.11.018.
  61. Sofiyev, A.H., Alizada, A.N., Akin, O., Valiyev, Avcar, M. and Adiguzel, S. (2011), "On the stability of FGM shells subjected to combined loads with different edge conditions and resting on elastic foundations", Acta Mech., 223(1), 189-204. https://doi.org/10.1007/s00707-011-0548-1.
  62. Tayeb, T.S., Zidour, M., Bensattalah, T., Heireche, H., Benahmed, A. and Bedia, E.A. (2020), "Mechanical buckling of FG-CNTs reinforced composite plate with parabolic distribution using Hamilton's energy principle", Adv. Nano Res., 8(2), 135-148. https://doi.org/10.12989/anr.2020.8.2.135.
  63. 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.
  64. Vo, T.P., Thai, H.T., Nguyen, T.K., Inam, F. and Lee, J. (2015a), "A quasi- 3D theory for vibration and buckling of functionally graded sandwich beams", Compos. Struct. 119, 1-12. https://doi.org/10.1016/j.compstruct.2014.08.006.
  65. Vo, T.P., Thai, H.T., Nguyen, T.K., Inam, F. and Lee, J. (2015b), "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.
  66. Wattanasakulpong, N. and Ungbhakorn, V. (2014), "Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities", Aerosp. Sci. Technol., 32(1), 111-120. https://doi.org/10.1016/j.ast.2013.12.002.
  67. Yaghoobi, H. and Taheri, F. (2020), "Analytical solution and statistical analysis of buckling capacity of sandwich plates with uniform and non-uniform porous core reinforced with graphene nanoplatelets", Compos. Struct., 252, 112700. https://doi.org/10.1016/j.compstruct.2020.112700.
  68. Yaghoobi, H., Valipour, M.S., Fereidoon, A. and Khoshnevisrad, P. (2014), "Analytical study on post-buckling and nonlinear free vibration analysis of FG beams resting on nonlinear elastic foundation under thermo-mechanical loading using VIM", Steel Compos. Struct., 17(5), 753-776. https://doi.org/10.12989/scs.2014.17.5.753.
  69. Yousfi, M., Atmane, H.A., Meradjah, M., Tounsi, A. and Bennai, R. (2018), ''Free vibration of FG beams with porosity by a shearleedeformation theory with four variables'', Struct. Eng. Mech., 66(3), 353-368. https://data.doi.or.kr/cite/10.12989/scs.2018.27.1.109.
  70. Zhu, J., Lai, Z., Yin, Z., Jeon, J. and Lee, S. (2001), "Fabrication of ZrO2-NiCr functionally graded material by powder metallurgy", Mater. Chem. Phys., 68, 130-135. https://doi.org/10.1016/S0254-0584(00)00355-2.