Wind and Structures

  • 제27권1호
  • /
  • Pages.59-70
  • /
  • 2018
  • /
  • 1226-6116(pISSN)
  • /
  • 1598-6225(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Geometrically nonlinear analysis of functionally graded porous beams

  • Akbas, Seref D. (Department of Civil Engineering, Bursa Technical University, Yildirim Campus)
  • 투고 : 2017.03.21
  • 심사 : 2018.04.20
  • 발행 : 2018.07.25
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, geometrically non-linear analysis of a functionally graded simple supported beam is investigated with porosity effect. The material properties of the beam are assumed to vary though height direction according to a prescribed power-law distributions with different porosity models. In the nonlinear kinematic model of the beam, the total Lagrangian approach is used within Timoshenko beam theory. In the solution of the nonlinear problem, the finite element method is used in conjunction with the Newton-Raphson method. In the study, the effects of material distribution such as power-law exponents, porosity coefficients, nonlinear effects on the static behavior of functionally graded beams are examined and discussed with porosity effects. The difference between the geometrically linear and nonlinear analysis of functionally graded porous beam is investigated in detail. Also, the effects of the different porosity models on the functionally graded beams are investigated both linear and nonlinear cases.

키워드

참고문헌

  1. Agarwal, S., Chakraborty, A. and Gopalakrishnan, S. (2006), "Large deformation analysis for anisotropic and inhomogeneous beams using exact linear static solutions", Compos. Struct., 72(1), 91-104. https://doi.org/10.1016/j.compstruct.2004.10.019
  2. Akbarzadeh Khorshidi, M., Shariati, M. and Emam, S.A. (2016), "Postbuckling of functionally graded nanobeams based on modified couple stress theory under general beam theory", Int. J. Mech. Sci., 110(1), 160-169. https://doi.org/10.1016/j.ijmecsci.2016.03.006
  3. Akbas, S.D. and Kocaturk, T. (2012), "Post-buckling analysis of Timoshenko beams with temperature-dependent physical properties under uniform thermal loading", Struct. Eng. Mech., 44(1), 109-125. https://doi.org/10.12989/sem.2012.44.1.109
  4. Akbas, S.D. and Kocaturk, T. (2013), "Post-buckling analysis of functionally graded three-dimensional beams under the influence of temperature", J. Therm. Stresses, 36(12), 1235-1254.
  5. Akbas, S.D. (2013a), "Geometrically nonlinear static analysis of edge cracked Timoshenko beams composed of functionally graded material", Math. Probl. Eng., 2013, 14.
  6. Akbas, S.D. (2013b), "Free vibration characteristics of edge cracked functionally graded beams by using finite element method", Int. J. Eng. Trends Technol., 4(10), 4590-4597.
  7. Akbas, S.D. (2014a), "Large post-buckling behavior of Timoshenko beams under axial compression loads", Struct. Eng. Mech., 51(6), 955-971. https://doi.org/10.12989/sem.2014.51.6.955
  8. Akbas, S.D. (2014b), "Free vibration of axially functionally graded beams in thermal environment", Int. J. Eng. Appl. Sci., 6(3), 37-51.
  9. Akbas, S.D. (2015a), "On post-buckling behavior of edge cracked functionally graded beams under axial loads", Int. J. Struct. Stab. Dynam., 15(4), 1450065. https://doi.org/10.1142/S0219455414500655
  10. Akbas, S.D. (2015b), "Post-buckling analysis of axially functionally graded three dimensional beams", Int. J. Appl. Mech., 7(3), 1550047. https://doi.org/10.1142/S1758825115500477
  11. Akbas, S.D. (2015a), "Free vibration and bending of functionally graded beams resting on elastic foundation", Res. Eng. Struct. Mater., 1(1).
  12. Akbas, S.D. (2015b), "Large deflection analysis of edge cracked simple supported beams", Struct. Eng. Mech., 54(3), 433-451. https://doi.org/10.12989/sem.2015.54.3.433
  13. Akbas, S.D. (2015c), "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
  14. Akbas, S.D. (2015d), "Free vibration and bending of functionally graded beams resting on elastic foundation", Res. Eng. Struct. Mater., 1(1).
  15. Akbas, S.D. (2017a), "Free vibration of edge cracked functionally graded microscale beams based on the modified couple stress theory", Int. J. Struct. Stab. Dynam., 17(3), 1750033. https://doi.org/10.1142/S021945541750033X
  16. Akbas, S.D. (2017b), "Forced vibration analysis of functionally graded nanobeams", Int. J. Appl. Mech., 9(7), 1750100. https://doi.org/10.1142/S1758825117501009
  17. Akbas, S.D. (2017c), "Post-buckling responses of functionally graded beams with porosities", Steel Compos. Struct., 24(5), 579-589. https://doi.org/10.12989/SCS.2017.24.5.579
  18. Akbas, S.D. (2017d), "Vibration and static analysis of functionally graded porous plates", J. Appl. Comput. Mech., 3(3), 199-207.
  19. Akbas, S.D. (2017e), "Nonlinear static analysis of functionally graded porous beams under thermal effect", Coupled Syst. Mech., 6(4), 399-415. https://doi.org/10.12989/CSM.2017.6.4.399
  20. Akbas, S.D. (2017f), "Stability of a non-homogenous porous plate by using generalized differantial quadrature method", Int. J. Eng. Appl. Sci., 9(2), 147-155.
  21. Akbas, S.D. (2017g), "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
  22. Akbas, S.D. (2018a), "Forced vibration analysis of functionally graded porous deep beams", Compos. Struct., 186, 293-302. https://doi.org/10.1016/j.compstruct.2017.12.013
  23. Akbas, S.D. (2018b), "Geometrically nonlinear analysis of a laminated composite beam", Struct. Eng. Mech., 66(1), 27-36. https://doi.org/10.12989/SEM.2018.66.1.027
  24. Akbas, S.D. (2018c), "Post-buckling responses of a laminated composite beam", Steel Compos. Struct., 26(6), 733-743. https://doi.org/10.12989/SCS.2018.26.6.733
  25. Al Jahwari, F. and Naguib, H.E. (2016), "Analysis and homogenization of functionally graded viscoelastic porous structures with a higher order plate theory and statistical based model of cellular distribution", Appl. Math. Model., 40(3), 2190-2205. https://doi.org/10.1016/j.apm.2015.09.038
  26. Almeida, C.A., Albino, J.C.R., Menezes, I.F.M. and Paulino, G.H. (2011), "Geometric nonlinear analyses of functionally graded beams using a tailored Lagrangian formulation", Mech. Res. Commun., 38(8), 553-559. https://doi.org/10.1016/j.mechrescom.2011.07.006
  27. Amara, K., Bouazza, M. and Fouad, B. (2016), "Postbuckling analysis of functionally graded beams using nonlinear model", Periodica Polytechnica. Eng., Mech. Eng., 60(2), 121-128. https://doi.org/10.3311/PPme.8854
  28. Anandrao, K.S., Gupta, R.K., Ramchandran, P. and Rao, V. (2010), "Thermal post-buckling analysis of uniform slender functionally graded material beams", Struct. Eng. Mech., 36(5), 545-560. https://doi.org/10.12989/sem.2010.36.5.545
  29. Atmane, H.A., Tounsi, A., Bernard, F. and Mahmoud, S.R. (2015a), "A computational shear displacement model for vibrational analysis of functionally graded beams with porosities", Steel Compos. Struct., 19(2), 369-384. https://doi.org/10.12989/scs.2015.19.2.369
  30. Atmane, H.A., Tounsi, A. and Bernard, F. (2015b), "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.
  31. Babilio, E. (2014), "Dynamics of functionally graded beams on viscoelastic foundation", Int. J. Struct. Stab. Dynam., 14(8), 1440014, Doi: 10.1142/S0219455414400148.
  32. Bellifa, H., Benrahou, K.H., Hadji, L., Houari, M.S.A. and Tounsi, A. (2016), "Bending and free vibration analysis of functionally graded plates using a simple shear deformation theory and the concept the neutral surface position", J. Braz. Soc. Mech. Sci. Eng., 38, 265-275. https://doi.org/10.1007/s40430-015-0354-0
  33. Benferhat, R., Daouadji, T.H., Mansour, M.S. and Hadji, L. (2016a), "Effect of porosity on the bending and free vibration response of functionally graded plates resting on Winkler-Pasternak foundations", Earthq. Struct., 10(6), 1429-1449. https://doi.org/10.12989/eas.2016.10.6.1429
  34. Benferhat, R., Hassaine, D., Hadji, L. and Said, M. (2016b), "Static analysis of the FGM plate with porosities", Steel Compos. Struct., 21(1), 123-136. https://doi.org/10.12989/scs.2016.21.1.123
  35. Ebrahimi, F., Salari, E. and Hosseini, S.A.H. (2015), "Thermomechanical vibration behavior of FG nanobeams subjected to linear and non-linear temperature distributions", J. Therm. Stresses, 38(12), 1360-1386. https://doi.org/10.1080/01495739.2015.1073980
  36. Ebrahimi, F. and Salari, E. (2015a), "Effect of various thermal loadings on buckling and vibrational characteristics of nonlocal temperature-dependent FG nanobeams", Mech. Adv. Mater. Struct., 1-58.
  37. Ebrahimi, F. and Salari, E. (2015b), "Size-dependent thermoelectrical buckling analysis of functionally graded piezoelectric nanobeams", Smart Mater. Struct., 24(12), 125007. https://doi.org/10.1088/0964-1726/24/12/125007
  38. Ebrahimi, F. and Salari, E. (2015), "A semi-analytical method for vibrational and buckling analysis of functionally graded nanobeams considering the physical neutral axis position", CMES Comput Model Eng Sci, 105(2), 151-181
  39. Ebrahimi, F. and Jafari, A. (2016a), "A higher-order thermomechanical vibration analysis of temperature-dependent FGM beams with porosities", J. Eng., 2016, 20.
  40. Ebrahimi, F. and Jafari, A. (2016b), "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
  41. Ebrahimi, F. Ghasemi, F. and Salari, E. (2016), "Investigating thermal effects on vibration behavior of temperature-dependent compositionally graded Euler beams with porosities", Meccanica, 51(1), 223-249. https://doi.org/10.1007/s11012-015-0208-y
  42. Ebrahimi, F. and Habibi, S. (2016), "Deflection and vibration analysis of higher-order shear deformable compositionally graded porous plate", Steel Compos. Struct., 20(1), 205-225. https://doi.org/10.12989/scs.2016.20.1.205
  43. Ebrahimi, F. and Farzamandnia, N. (2016), "Thermo-mechanical vibration analysis of sandwich beams with functionally graded carbon nanotube-reinforced composite face sheets based on a higher-order shear deformation beam theory", Mech. Adv. Mater. Struct., 1-37
  44. Ebrahimi, F. and Barati, M.R. (2016a), "Dynamic modeling of a thermo-piezo-electrically actuated nanosize beam subjected to a magnetic field", Appl. Phys. A, 122(4), 1-18.
  45. Ebrahimi, F. and Barati, M.R. (2016b), "Vibration analysis of smart piezoelectrically actuated nanobeams subjected to magneto-electrical field in thermal environment", J. Vib. Control, 1077546316646239.
  46. Ebrahimi, F. and Barati, M.R. (2016c), "Small scale effects on hygro-thermo-mechanical vibration of temperature dependent nonhomogeneous nanoscale beams", Mech. Adv. Mater. Struct., 24(11), 924-936.
  47. Ebrahimi, F. and Hosseini, S.H.S. (2016), "Thermal effects on nonlinear vibration behavior of viscoelastic nanosize plates", J. Therm. Stresses, 39(5), 606-625. https://doi.org/10.1080/01495739.2016.1160684
  48. Elmaguiri, M., Haterbouch, M., Bouayad, A. and Oussouaddi, O. (2015), "Geometrically nonlinear free vibration of functionally graded beams", J. Mater. Environ. Sci., 6(12), 3620-3633.
  49. Fallah, A. and Aghdam, M.M. (2011), "Nonlinear free vibration and post-buckling analysis of functionally graded beams on nonlinear elastic foundation", Eur. J. Mech.-A/Solids, 30(4), 571-583. https://doi.org/10.1016/j.euromechsol.2011.01.005
  50. Felippa, C.A. (2017), "Notes on nonlinear finite element methods",url:http://www.colorado.edu/engineering/cas/courses.d/NFEM.d/NFEM.Ch11.d/NFEM.Ch11.pdf.
  51. Galeban, M.R., Mojahedin, A., Taghavi, Y. and Jabbari, M. (2016), "Free vibration of functionally graded thin beams made of saturated porous materials", Steel Compos. Struct., 21(5), 999-1016. https://doi.org/10.12989/scs.2016.21.5.999
  52. Hadji, L. and Bedia, E.A.A. (2015), "Influence of the porosities on the free vibration of FGM beams", Wind Struct., 21(3) 273-287. https://doi.org/10.12989/was.2015.21.3.273
  53. Hadji, L., Daouadji, T.H. and Bedia, E.A. (2015), "A refined exponential shear deformation theory for free vibration of FGM beam with porosities", Geomech. Eng., 9(3), 361-372. https://doi.org/10.12989/gae.2015.9.3.361
  54. Hadji, L., Khelifa, Z. and Adda Bedia, E.A. (2016), "A new higher order shear deformation model for functionally graded beams", KSCE J. Civil Eng., 20(5), 1835-1841. https://doi.org/10.1007/s12205-015-0252-0
  55. Hadji, L. (2017), "Analysis of functionally graded plates using a sinusoidal shear deformation theory", Smart Struct. Syst., 19(4), 441-448. https://doi.org/10.12989/sss.2017.19.4.441
  56. Hadji, L., Zouatnia, N. and Kassoul, A. (2017), "Wave propagation in functionally graded beams using various higher-order shear deformation beams theories", Struct. Eng. Mech., 62(2), 143-149. https://doi.org/10.12989/sem.2017.62.2.143
  57. Hosseini, M. and Fazelzadeh, S.A. (2011), "Thermomechanical stability analysis of functionally graded thin-walled cantilever pipe with flowing fluid subjected to axial load", Int. J. Struct. Stab. Dynam., 11(3), 513-534. https://doi.org/10.1142/S0219455411004154
  58. Hui-Shen, S. and Wang, Z.X. (2014), "Nonlinear analysis of shear deformable FGM beams resting on elastic foundations in thermal environments", Int. J. Mech. Sci., 81, 195-206. https://doi.org/10.1016/j.ijmecsci.2014.02.020
  59. Jahwari, F. and Naguib, H.E. (2016), "Analysis and homogenization of functionally graded viscoelastic porous structures with a higher order plate theory and statistical based model of cellular distribution", Appl. Math. Model., 40(3), 2190-2205. https://doi.org/10.1016/j.apm.2015.09.038
  60. Kolakowski, Z. and Teter, A. (2015), "Static interactive buckling of functionally graded columns with closed cross-sections subjected to axial compression", Compos. Struct., 123(1), 257-262. https://doi.org/10.1016/j.compstruct.2014.12.051
  61. Kang, Y.A. and Li, X.F. (2009), "Bending of functionally graded cantilever beam with power-law non-linearity subjected to an end force", Int. J. Nonlinear Mech., 44(6), 696-703. https://doi.org/10.1016/j.ijnonlinmec.2009.02.016
  62. Kang, Y.A. and Li, X.F., (2010), "Large deflections of a non-linear cantilever functionally graded beam", J. Reinf. Plast. Comp., 29(12), 1761-1774. https://doi.org/10.1177/0731684409103340
  63. Ke, L.L., Yang, J. and Kitipornchai, S. (2009), "Postbuckling analysis of edge cracked functionally graded Timoshenko beams under end shortening", Compos. Struct., 90(2), 152-160. https://doi.org/10.1016/j.compstruct.2009.03.003
  64. Kocaturk, T. and Akbas, S.D. (2010), "Geometrically non-linear static analysis of a simply supported beam made of hyperelastic material", Struct. Eng. Mech., 35(6), 677-697. https://doi.org/10.12989/sem.2010.35.6.677
  65. Kocaturk, T. and Akbas, S.D. (2011), "Post-buckling analysis of Timoshenko beams with various boundary conditions under non-uniform thermal loading", Struct. Eng. Mech., 40(3), 347-371. https://doi.org/10.12989/sem.2011.40.3.347
  66. Kocaturk, T., Simsek, M. and Akbas, S.D. (2011), "Large displacement static analysis of a cantilever Timoshenko beam composed of functionally graded material", Sci. Eng. Compos. Mater., 18, 21-34.
  67. Kocaturk, T. and Akbas, S.D. (2012), "Post-buckling analysis of Timoshenko beams made offunctionally graded material under thermal loading". Struct. Eng. Mech., 41(6), 775-789. https://doi.org/10.12989/sem.2012.41.6.775
  68. Kocaturk, T. and Akbas, S.D. (2013), "Thermal post-buckling analysis of functionally graded beams with temperaturedependent physical properties", Steel Compos. Struct., 15(5), 481-505. https://doi.org/10.12989/scs.2013.15.5.481
  69. Li, S.R., Zhang, J.H. and Zhao, Y.G. (2006), "Thermal postbuckling of functionally graded material Timoshenko beams", Appl. Math. Mech., (English Edition), 26(6), 803-810.
  70. Li, Q. and Li, S. (2011), "Post-bucking configuration of a functionally graded material column under distributed load", Fuhe Cailiao Xuebao(Acta Materiae Compositae Sinica), 28(3), 192-196.
  71. Li, L.Q. and Shao, Q.H. (2014), "Non-linear analysis of a FGM cantilever beam supported on a winkler elastic foundation", Appl. Mech. Mater., 602, 131-134.
  72. Mechab, I., Mechab, B., Benaissa, S., Serier, B. and Bouiadjra, B.B. (2016a), "Free vibration analysis of FGM nanoplate with porosities resting on Winkler Pasternak elastic foundations based on two-variable refined plate theories", J. Braz. Soc. Mech. Sci. Eng., 38, 2193-2211. https://doi.org/10.1007/s40430-015-0482-6
  73. Mechab, B., Mechab, I., Benaissa, S., Ameri, M. and Serier, B. (2016b), "Probabilistic analysis of effect of the porosities in functionally graded material nanoplate resting on Winkler-Pasternak elastic foundations", Appl. Math. Model., 40(2), 738-749. https://doi.org/10.1016/j.apm.2015.09.093
  74. Mohanty, S.C., Dash, R.R. and Rout, T. (2012), "Static and dynamic stability analysis of a functionally graded Timoshenko beam", Int. J. Struct. Stab. Dynam., 12(4) Article ID 1250025, 33 pages.
  75. Mouaici, F., Benyoucef, S., Atmane, H.A. and Tounsi, A. (2016), "Effect of porosity on vibrational characteristics of nonhomogeneous plates using hyperbolic shear deformation theory", Wind Struct., 22(4), 429-454. https://doi.org/10.12989/was.2016.22.4.429
  76. Nguyen, D.K., Gan, B.S. and Trinh, T.H. (2014), "Geometrically nonlinear analysis of planar beam and frame structures made of functionally graded material", Struct. Eng. Mech., 49(6) 727-743. https://doi.org/10.12989/sem.2014.49.6.727
  77. Rastgo, A., Shafie, H. and Allahverdizadeh, A. (2005), "Instability of curved beams made of functionally graded material under thermal loading", Int. J. Mech. Mater. Des., 2, 117-128. https://doi.org/10.1007/s10999-005-4446-3
  78. Song, X. and Li, S. (2008), "Nonlinear stability of fixed-fixed FGM arches subjected to mechanical and thermal loads", Adv. Mater. Res., 33-37, 699-706. https://doi.org/10.4028/www.scientific.net/AMR.33-37.699
  79. Sun, Y., Li, S.R. and Batra, R.C. (2016), "Thermal buckling and post-buckling of FGM mTimoshenko beams on nonlinear elastic foundation", J. Therm. Stresses, 39(1), 11-26. https://doi.org/10.1080/01495739.2015.1120627
  80. Simsek, M. and Aydin, M. (2017), "Size-dependent forced vibration of an imperfect functionally graded (FG) microplate with porosities subjected to a moving load using the modified couple stress Theory", Compos. Struct., 160, 408-421. https://doi.org/10.1016/j.compstruct.2016.10.034
  81. Trinh, T.H., Nguyen, D.K., Gan, B.S. and Alexandrov, S. (2016), "Post-buckling responses of elastoplastic FGM beams on nonlinear elastic foundation", Struct. Eng. Mech., 58(3), 515-532. https://doi.org/10.12989/sem.2016.58.3.515
  82. 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
  83. Yahia, S.A., Atmane, H.A., Houari, M.S.A. and Tounsi, A. (2015), "Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories", Struct. Eng. Mech., 53(6), 1143-1165. https://doi.org/10.12989/sem.2015.53.6.1143
  84. Yan, T., Yang, J. and Kitipornchai, S. (2012), "Nonlinear dynamic response of an edge-cracked functionally graded Timoshenko beam under parametric excitation", Nonlinear Dynam., 67(1), 527-540. https://doi.org/10.1007/s11071-011-0003-9
  85. Zhang, D.G. and Zhou, H.M. (2014), "Nonlinear bending and thermal post-buckling analysis of FGM beams resting on nonlinear elastic foundations", CMES Comput. Model. Eng., 100(3) 201-222.
  86. Zouatnia, N., Hadji, L. and Kassoul, A. (2017), "An analytical solution for bending and vibration responses of functionally graded beams with porosities", Wind Struct., 25(4), 329-342.

피인용 문헌

  1. Dynamic analysis of functionally graded nonlocal nanobeam with different porosity models vol.36, pp.3, 2018, https://doi.org/10.12989/scs.2020.36.3.293
  2. Dynamic analysis of a laminated composite beam under harmonic load vol.9, pp.6, 2020, https://doi.org/10.12989/csm.2020.9.6.563
  3. Axisymmetric vibration analysis of graded porous Mindlin circular plates subjected to thermal environment vol.16, pp.3, 2018, https://doi.org/10.2140/jomms.2021.16.371
  4. Forced vibration of a functionally graded porous beam resting on viscoelastic foundation vol.24, pp.1, 2018, https://doi.org/10.12989/gae.2021.24.1.091