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http://dx.doi.org/10.12989/csm.2017.6.4.399
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Nonlinear static analysis of functionally graded porous beams under thermal effect |

Akbas, Seref D. (Department of Civil Engineering, Bursa Technical University, Yildirim Campus) |

Publication Information

Abstract

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.

Keywords

functionally graded material; porosity; nonlinear analysis; total langragian finite element model; large deflections;

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Times Cited By KSCI :
10 (Citation Analysis)

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- Cited By KSCI

1 | 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. |

2 | 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. DOI |

3 | 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. DOI |

4 | 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. |

5 | 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. |

6 | Akbas, S.D. (2014), "Free vibration of axially functionally graded beams in thermal environment", J. Eng. Appl. Sci., 6(3), 37-51. |

7 | Akbas, S.D. (2016a), "Post-buckling analysis of edge cracked columns under axial compression loads", J. Appl. Mech., 8(8), 1650086. DOI |

8 | 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. |

9 | 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. |

10 | Akbas, S.D. (2013), "Geometrically nonlinear static analysis of edge cracked timoshenko beams composed of functionally graded material", Math. Prob. Eng., 14. |

11 | Akbas, S.D. (2015a), "On post-buckling behavior of edge cracked functionally graded beams under axial loads", J. Struct. Stab. Dyn., 15(4), 1450065. DOI |

12 | Akbas, S.D. (2015b), "Post-buckling analysis of axially functionally graded three dimensional beams", J. Appl. Mech., 7(3), 1550047. DOI |

13 | Akbas, S.D. (2015c), "Wave propagation of a functionally graded beam in thermal environments" Steel Compos. Struct., 19(6), 1421-1447. DOI |

14 | Akbas, S.D. (2016b) "Wave propagation in edge cracked functionally graded beams under impact force", J. Vibr. Contr., 22(10), 2443-2457. DOI |

15 | Akbas, S.D. (2017a), "Thermal effects on the vibration of functionally graded deep beams with porosity", J. Appl. Mech., 9(5), 1750076. DOI |

16 | Akbas, S.D. (2017b), "Post-buckling responses of functionally graded beams with porosities", Steel Compos. Struct., 24(5), 481-579-589. DOI |

17 | Akbas, S.D. (2017c), "Vibration and static analysis of functionally graded porous plates", J. Appl. Comput. Mech., 3(3), 199-207. |

18 | 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. |

19 | 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. DOI |

20 | 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. DOI |

21 | 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. DOI |

22 | 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. DOI |

23 | 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. DOI |

24 | 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. DOI |

25 | Babilio, E. (2014), "Dynamics of functionally graded beams on viscoelastic foundation", J. Struct. Stab. Dyn., 14(8), 1440014. DOI |

26 | Ebrahimi, F. and Jafari, A. (2016), "A higher-order thermomechanical vibration analysis of temperaturedependent FGM beams with porosities", J. Eng., 20. |

27 | 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. DOI |

28 | 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. |

29 | 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. DOI |

30 | 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. DOI |

31 | 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. DOI |

32 | 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. DOI |

33 | 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. DOI |

34 | 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. DOI |

35 | 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. DOI |

36 | 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. DOI |

37 | 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. |

38 | 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. DOI |

39 | 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. DOI |

40 | 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. DOI |

41 | 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. DOI |

42 | 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. DOI |

43 | 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. |

44 | 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. |

45 | 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. |

46 | 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. DOI |

47 | 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. DOI |

48 | 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. |

49 | 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. DOI |

50 | 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. DOI |

51 | Reddy, J.N. and Chin, C.D. (1998), "Thermoelastical analysis of functionally graded cylinders and plates", J. Therm. Stress., 21(6) 593-626. DOI |

52 | Reddy, J.N. (2004), An Introduction to Non-Linear Finite Element analysis, Oxford University Press Inc, New York, U.S.A. |

53 | 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. DOI |

54 | 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. DOI |

55 | 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. DOI |

56 | Touloukian, Y.S. (1967), Thermophysical Properties of High Temperature Solid Materials, Macmillan, New York, U.S.A. |

57 | 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. DOI |

58 | 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. DOI |

59 | 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. DOI |