DOI QR코드

DOI QR Code

Nonlinear static analysis of functionally graded porous beams under thermal effect

  • Akbas, Seref D. (Department of Civil Engineering, Bursa Technical University, Yildirim Campus)
  • 투고 : 2017.06.22
  • 심사 : 2017.10.10
  • 발행 : 2017.12.25

초록

This paper deals with the nonlinear static deflections of functionally graded (FG) porous under thermal effect. Material properties vary in both position-dependent and temperature-dependent. The considered nonlinear problem is solved by using Total Lagrangian finite element method within two-dimensional (2-D) continuum model in the Newton-Raphson iteration method. In numerical examples, the effects of material distribution, porosity parameters, temperature rising on the nonlinear large deflections of FG beams are presented and discussed with porosity effects. Also, the effects of the different porosity models on the FG beams are investigated in temperature rising.

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", J. Mech. Sci., 110(1), 160-169. https://doi.org/10.1016/j.ijmecsci.2016.03.006
  3. Akbas, S.D. and Kocaturk, T. (2011), "Post-buckling analysis of a simply supported beam under uniform thermal loading", Sci. Res. Ess., 6(5), 1135-1142.
  4. Akbas, S.D. (2013b), "Free vibration characteristics of edge cracked functionally graded beams by using finite element method", J. Eng. Trends Technol., 4(10), 4590-4597.
  5. Akbas, S.D. (2014), "Free vibration of axially functionally graded beams in thermal environment", J. Eng. Appl. Sci., 6(3), 37-51.
  6. Akbas, S.D. (2016a), "Post-buckling analysis of edge cracked columns under axial compression loads", J. Appl. Mech., 8(8), 1650086. https://doi.org/10.1142/S1758825116500861
  7. Akbas, S.D. and Kocatürk, T. (2013), "Post-buckling analysis of functionally graded three- dimensional beams under the influence of temperature", J. Therm. Stress., 36(12), 1235-1254.
  8. Akbas, S.D. (2011), "Static analysis of a functionally graded beam with edge cracks on elastic foundation", Proceedings of the 9th International Fracture Conference, Istanbul, Turkey.
  9. Akbas, S.D. (2013), "Geometrically nonlinear static analysis of edge cracked timoshenko beams composed of functionally graded material", Math. Prob. Eng., 14.
  10. Akbas, S.D. (2015a), "On post-buckling behavior of edge cracked functionally graded beams under axial loads", J. Struct. Stab. Dyn., 15(4), 1450065. https://doi.org/10.1142/S0219455414500655
  11. Akbas, S.D. (2015b), "Post-buckling analysis of axially functionally graded three dimensional beams", J. Appl. Mech., 7(3), 1550047. https://doi.org/10.1142/S1758825115500477
  12. 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
  13. Akbas, S.D. (2016b) "Wave propagation in edge cracked functionally graded beams under impact force", J. Vibr. Contr., 22(10), 2443-2457. https://doi.org/10.1177/1077546314547531
  14. Akbas, S.D. (2017a), "Thermal effects on the vibration of functionally graded deep beams with porosity", J. Appl. Mech., 9(5), 1750076. https://doi.org/10.1142/S1758825117500764
  15. Akbas, S.D. (2017b), "Post-buckling responses of functionally graded beams with porosities", Steel Compos. Struct., 24(5), 481-579-589. https://doi.org/10.12989/SCS.2017.24.5.579
  16. Akbas, S.D. (2017c), "Vibration and static analysis of functionally graded porous plates", J. Appl. Comput. Mech., 3(3), 199-207.
  17. Akbas, S.D. (2017d), "Stability of a non-homogenous porous plate by using generalized differantial quadrature method", J. Eng. Appl. Sci., 9(2), 147-155.
  18. Akbas, S.D. (2017e), "Free vibration of edge cracked functionally graded microscale beams based on the modified couple stress theory", J. Struct. Stab. Dyn., 17(3),1750033. https://doi.org/10.1142/S021945541750033X
  19. Akbas, S.D. and Kocatürk, T. (2012), "Post-buckling analysis of Timoshenko beams with temperaturedependent physical properties under uniform thermal loading", Struct. Eng. Mech., 44(1), 109-125. https://doi.org/10.12989/sem.2012.44.1.109
  20. 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
  21. 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
  22. Amara, K., Bouazza, M. and Fouad, B. (2016), "Postbuckling analysis of functionally graded beams using nonlinear model", Period. Polytech. Eng. Mech. Eng., 60(2), 121-128. https://doi.org/10.3311/PPme.8854
  23. 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
  24. Babilio, E. (2014), "Dynamics of functionally graded beams on viscoelastic foundation", J. Struct. Stab. Dyn., 14(8), 1440014. https://doi.org/10.1142/S0219455414400148
  25. Ebrahimi, F. and Jafari, A. (2016), "A higher-order thermomechanical vibration analysis of temperaturedependent FGM beams with porosities", J. Eng., 20.
  26. Ebrahimi, F. Ghasemi, F. and Salari, E. (2016), "Investigating thermal effects on vibration behavior of temperature-dependent compositionally graded euler beams with porosities", Meccan., 51(1), 223-249. https://doi.org/10.1007/s11012-015-0208-y
  27. 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.
  28. 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/Sol., 30(4), 571-583. https://doi.org/10.1016/j.euromechsol.2011.01.005
  29. Hosseini, M. and Fazelzadeh, S.A. (2011), "Thermomechanical stability analysis of functionally graded thinwalled cantilever pipe with flowing fluid subjected to axial load", J. Struct. Stab. Dyn., 11(3), 513-534. https://doi.org/10.1142/S0219455411004154
  30. Hui-Shen, S. and Wang, Z.X. (2014), "Nonlinear analysis of shear deformable FGM beams resting on elastic foundations in thermal environments", J. Mech. Sci., 81, 195-206. https://doi.org/10.1016/j.ijmecsci.2014.02.020
  31. 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
  32. Kang, Y.A. and Li, X.F. (2009), "Bending of functionally graded cantilever beam with power-law nonlinearity subjected to an end force", J. Non-Lin. Mech., 44(6), 696-703. https://doi.org/10.1016/j.ijnonlinmec.2009.02.016
  33. Kang, Y.A. and Li, X.F. (2010), "Large deflections of a non-linear cantilever functionally graded beam", J. Reinf. Plast. Compos., 29(12), 1761-1774. https://doi.org/10.1177/0731684409103340
  34. Kar, V.R. and Panda, S.K. (2016), "Geometrical nonlinear free vibration analysis of FGM spherical panel under nonlinear thermal loading with TD and TID properties", J. Therm. Stress., 39(8), 942-959. https://doi.org/10.1080/01495739.2016.1188623
  35. 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
  36. Kocatürk, 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.
  37. Kocatürk, 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
  38. Kocatürk, 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
  39. Kocatürk, T. and Akbas, S.D. (2012), "Post-buckling analysis of Timoshenko beams made of functionally graded material under thermal loading", Struct. Eng. Mech., 41(6), 775-789. https://doi.org/10.12989/sem.2012.41.6.775
  40. Kocaturk, T. and Akbas, S.D. (2013), "Thermal post-buckling analysis of functionally graded beams with temperature-dependent physical properties", Steel and Composite Structures, 15(5), 481-505-1254. https://doi.org/10.12989/scs.2013.15.5.481
  41. 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
  42. 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.
  43. Li, Q. and Li, S. (2011), "Post-bucking configuration of a functionally graded material column under distributed load", Fuhe Cailiao Xuebao(Acta Mater. Compos. Sin.), 28(3), 192-196.
  44. Li, S.R., Zhang, J.H. and Zhao, Y.G. (2006), "Thermal post-buckling of functionally graded material timoshenko beams", Appl. Math. Mech., 26(6), 803-810.
  45. 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. Modell., 40(2),738-749. https://doi.org/10.1016/j.apm.2015.09.093
  46. 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. Brazil. Soc. Mech. Sci. Eng., 38, 2193-2211. https://doi.org/10.1007/s40430-015-0482-6
  47. Mohanty, S.C., Dash, R.R. and Rout, T. (2012), "Static and dynamic stability analysis of a functionally graded timoshenko beam", J. Struct. Stab. Dyn., 12(4), 33.
  48. 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
  49. Rastgo, A., Shafie, H. and Allahverdizadeh, A. (2005), "Instability of curved beams made of functionally graded material under thermal loading", J. Mech. Mater. Des., 2, 117-128. https://doi.org/10.1007/s10999-005-4446-3
  50. Reddy, J.N. and Chin, C.D. (1998), "Thermoelastical analysis of functionally graded cylinders and plates", J. Therm. Stress., 21(6) 593-626. https://doi.org/10.1080/01495739808956165
  51. Reddy, J.N. (2004), An Introduction to Non-Linear Finite Element analysis, Oxford University Press Inc, New York, U.S.A.
  52. 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
  53. 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
  54. Sun, Y., Li, S.R. and Batra, R.C. (2016), "Thermal buckling and post-buckling of FGM timoshenko beams on nonlinear elastic foundation", J. Therm. Stress., 39(1) 11-26. https://doi.org/10.1080/01495739.2015.1120627
  55. Touloukian, Y.S. (1967), Thermophysical Properties of High Temperature Solid Materials, Macmillan, New York, U.S.A.
  56. 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
  57. 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
  58. Yan, T., Yang, J. and Kitipornchai, S. (2012), "Nonlinear dynamic response of an edge-cracked functionally graded timoshenko beam under parametric excitation", Nonlin. Dyn., 67(1), 527-540. https://doi.org/10.1007/s11071-011-0003-9
  59. 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. Modell. Eng., 100(3) 201-222.

피인용 문헌

  1. Dynamic analysis of functionally graded nonlocal nanobeam with different porosity models vol.36, pp.3, 2017, 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, 2017, https://doi.org/10.2140/jomms.2021.16.371
  4. Finite Element Modeling for Static Bending Behaviors of Rotating FGM Porous Beams with Geometrical Imperfections Resting on Elastic Foundation and Subjected to Axial Compression vol.2021, pp.None, 2017, https://doi.org/10.1155/2021/3835440
  5. Forced vibration of a functionally graded porous beam resting on viscoelastic foundation vol.24, pp.1, 2017, https://doi.org/10.12989/gae.2021.24.1.091
  6. Effect of suction on flow of dusty fluid along exponentially stretching cylinder vol.10, pp.3, 2017, https://doi.org/10.12989/anr.2021.10.3.263