Browse > Article
http://dx.doi.org/10.12989/scs.2017.24.5.579

Post-buckling responses of functionally graded beams with porosities  

Akbas, Seref D. (Department of Civil Engineering, Bursa Technical University, Yildirim Campus)
Publication Information
Steel and Composite Structures / v.24, no.5, 2017 , pp. 579-589 More about this Journal
Abstract
The objective of this work is to analyze post-buckling of functionally graded (FG) beams with porosity effect under compression load. Material properties of the beam change in the thickness direction according to power-law distributions with different porosity models. It is known that post-buckling problems are geometrically nonlinear problems. In the nonlinear kinematic model of the beam, total Lagrangian finite element model of two dimensional (2-D) continuum is used in conjunction with the Newton-Raphson method. In the study, the effects of material distribution, porosity parameters, compression loads on the post-buckling behavior of FG beams are investigated and discussed with porosity effects. Also, the effects of the different porosity models on the FG beams are investigated in post-buckling case.
Keywords
post-buckling; functionally graded material; porosity; total Lagragian; finite element method;
Citations & Related Records
Times Cited By KSCI : 7  (Citation Analysis)
연도 인용수 순위
1 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. Stabil. Dyn., 11(3), 513-534.   DOI
2 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.   DOI
3 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
4 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. Non-Linear Mech., 44(6), 696-703.   DOI
5 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
6 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. Thermal Stresses, 39(8), 942-959.   DOI
7 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
8 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., Int. M., 40(3), 347-371.   DOI
9 Kocaturk, T. and Akbas, S.D. (2012), "Post-buckling analysis of Timoshenko beams made offunctionally graded material under thermal loading", Struct. Eng. Mech., Int. M., 41(6), 775-789.   DOI
10 Kocaturk, T. and Akbas, S.D. (2013), "Thermal post-buckling analysis of functionally graded beams with temperaturedependent physical properties", Steel Compos. Struct., Int. J., 15(5), 481-505.   DOI
11 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(1-2), 21-34.   DOI
12 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
13 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.
14 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.
15 Li, S.-R., Zhang, J.-H. and Zhao, Y.-G. (2006), "Thermal postbuckling of functionally graded material Timoshenko Beams", Appl. Math. Mech. (English Ed.), 26(6), 803-810.
16 Marzocca, P., Fazelzadeh, S.A. and Hosseini, M. (2011), "A review of nonlinear aero-thermo-elasticity of functionally graded panels", J. Thermal Stresses, 34(5-6), 536-568.   DOI
17 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., Int., 49(6) 727-743.   DOI
18 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(8), 2193-2211.   DOI
19 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.   DOI
20 Mohanty, S.C., Dash, R.R. and Rout, T. (2012), "Static and dynamic stability analysis of a functionally graded Timoshenko Beam", Int. J. Struct. Stabil. Dyn., 12(4), 33 p.
21 Rastgo, A., Shafie, H. and Allahverdizadeh, A. (2005), "Instability of curved beams made of functionally graded material under thermal loading", Int. J. Mech. Mater. Design, 2(1), 117-128.   DOI
22 Reddy, J.N. (2004), An Introduction to Non-linear Finite Element Analysis, Oxford University Press Inc., New York, NY, USA.
23 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
24 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
25 Akbas, S.D. (2015b), "Post-buckling analysis of axially functionally graded three dimensional beams", Int. J. Appl. Mech., 7(3), 1550047. DOI: 10.1142/S1758825115500477   DOI
26 Sun, Y., Li, S.-R. and Batra, R.C. (2016), "Thermal buckling and post-buckling of FGM Timoshenko beams on nonlinear elastic foundation", J. Thermal Stresses, 39(1) 11-26.   DOI
27 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
28 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.   DOI
29 Akbas, S.D. (2013), "Geometrically nonlinear static analysis of edge cracked Timoshenko Beams composed of functionally graded material", Math. Problems Eng., 14 p. DOI: 10.1155/2013/871815   DOI
30 Akbas, S.D. (2015a), "On post-buckling behavior of edge cracked functionally graded beams under axial loads", Int. J. Struct. Stabil. Dyn., 15(4), 1450065. DOI: 10.1142/S0219455414500655   DOI
31 Akbas, S.D. and Kocaturk, T. (2011), "Post-buckling analysis of a simply supported beam under uniform thermal loading", Sci. Res. Essays, 6(5), 1135-1142.
32 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.
33 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., Int. J., 58(3), 515-532.   DOI
34 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
35 Yan, T., Yang, J. and Kitipornchai, S. (2012), "Nonlinear dynamic response of an edge-cracked functionally graded Timoshenko beam under parametric excitation", Nonlinear Dyn., 67(1), 527-540.   DOI
36 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.   DOI
37 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, Int. J., 44(1), 109-125.   DOI
38 Akbas, S.D. and Kocaturk, T. (2013), "Post-buckling analysis of functionally graded three-dimensional beams under the influence of temperature", J. Thermal Stresses, 36(12), 1235-1254.
39 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
40 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
41 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., Int. J., 36(5), 545-560.   DOI
42 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.   DOI
43 Babilio, E. (2014), "Dynamics of functionally graded beams on viscoelastic foundation", Int. J. Struct. Stabil. Dyn., 14(8), 1440014. DOI: 10.1142/S0219455414400148   DOI
44 Chen, D., Yang, J. and Kitipornchai, S. (2015), "Elastic buckling and static bending of shear deformable functionally graded porous beam", Compos. Struct., 133(1), 54-61.   DOI
45 Ebrahimi, F. and Jafari, A. (2016), "A higher-order thermomechanical vibration analysis of temperature-dependent FGM beams with porosities", J. Eng., 20 p. DOI: 10.1155/2016/9561504   DOI
46 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.
47 Hosseini, M. and Fazelzadeh, S.A. (2010), "Aerothermoelastic post-critical and vibration analysis of temperature-dependent functionally graded panels", J. Thermal Stresses, 33(12), 1188-1212.   DOI
48 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.   DOI