References
- 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
- 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
- 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
- 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
- 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
- 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.
- 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. https://doi.org/10.12989/sem.2012.44.1.109
- 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.
- 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
- 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
- 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
- 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. https://doi.org/10.12989/sem.2010.36.5.545
- Babilio, E. (2014), "Dynamics of functionally graded beams on viscoelastic foundation", Int. J. Struct. Stabil. Dyn., 14(8), 1440014. DOI: 10.1142/S0219455414400148
- 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. https://doi.org/10.1016/j.compstruct.2015.07.052
- 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
- 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
- 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.
- 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
- 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. https://doi.org/10.1080/01495739.2010.510754
- 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. https://doi.org/10.1142/S0219455411004154
- 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
- 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
- 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. https://doi.org/10.1016/j.ijnonlinmec.2009.02.016
- 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
- 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. https://doi.org/10.1080/01495739.2016.1188623
- 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
- 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. https://doi.org/10.12989/sem.2011.40.3.347
- 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. https://doi.org/10.12989/sem.2012.41.6.775
- 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. https://doi.org/10.12989/scs.2013.15.5.481
- 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. https://doi.org/10.1515/secm.2011.005
- 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
- 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.
- 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.
- 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.
- 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. https://doi.org/10.1080/01495739.2011.564016
- 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. https://doi.org/10.1007/s40430-015-0482-6
- 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
- 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.
- 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. https://doi.org/10.12989/sem.2014.49.6.727
- 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. https://doi.org/10.1007/s10999-005-4446-3
- Reddy, J.N. (2004), An Introduction to Non-linear Finite Element Analysis, Oxford University Press Inc., New York, NY, USA.
- 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
- 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
- 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. https://doi.org/10.1080/01495739.2015.1120627
- 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. https://doi.org/10.12989/sem.2016.58.3.515
- 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
- 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. https://doi.org/10.1007/s11071-011-0003-9
- 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.