Hygro-Thermal Nonlinear Analysis of a Functionally Graded Beam

Document Type: Research Paper


Bursa Technical University, Department of Civil Engineering, Yıldırım Campus 16330, Yıldırım/Bursa, Turkey


Nonlinear behavior of a functionally graded cantilever beam is analyzed under non-uniform hygro-thermal effect. To solve this problem, finite element method is applied within plane solid continua. Total Lagrangian approach is utilized in the nonlinear kinematic relations. Newton-Raphson method with incremental displacement is used in nonlinear solution. Comparison study is performed. Effects of material distribution, temperature and moisture changes on nonlinear deflections of the functionally graded beam are presented and discussed.


Main Subjects

[1] Rastgoo A., Shafie H. and Allahverdizadeh A., Instability of curved beams made of functionally graded material under thermal loading, International Journal of Mechanics and Materials in Design 2 (2005) 117–128.

[2] Li S.-R., Zhang J.-H., Zhao Y.-G., Thermal Post-Buckling of Functionally Graded Material Timoshenko Beams, Applied Mathematics and Mechanics (English Edition) 26(6) (2006) 803-810.

[3] Song X. and Li S., Nonlinear stability of fixed-fixed FGM arches subjected to mechanical and thermal loads, Advanced Materials Research 33-37 (2008) 699-706.

[4] Anandrao K.S., Gupta R.K., Ramchandran P. and Rao V., Thermal post-buckling analysis of uniform slender functionally graded material beams, Structural Engineering and Mechanics 36(5) (2010) 545-560.

[5] Kiani, Y., Rezaei, M., Taheri, S. and Eslami, M.R., Thermo-electrical buckling of piezoelectric functionally graded material Timoshenko beams, International Journal of Mechanics and Materials in Design 7(3) (2011) 185-197.

[6] Fallah, A. and Aghdam, M.M., Thermo-mechanical buckling and nonlinear free vibration analysis of functionally graded beams on nonlinear elastic foundation, Composites Part B: Engineering 43(3) (2012) 1523-1530.

[7] Kocatürk, T. and Akbas, Ş.D., Post-buckling analysis of Timoshenko beams made of functionally graded material under thermal loading, Structural Engineering and Mechanics 41(6) (2012) 775-789.

[8] Kocatürk, T. and Akbas, Ş.D., Thermal post-buckling analysis of functionally graded beams with temperature-dependent physical properties, Steel and Composite Structures 15(5) (2013) 481-505.

[9] Akbaş, Ş.D. and Kocatürk, T., Post-buckling analysis of functionally graded three-dimensional beams under the influence of temperature, Journal of Thermal Stresses 36(12) (2013) 1233-1254.

[10] Esfahani, S.E., Kiani, Y. and Eslami, M.R., Non-linear thermal stability analysis of temperature dependent FGM beams supported on non-linear hardening elastic foundations, International Journal of Mechanical Sciences 69 (2013) 10-20.

[11] Esfahani, S.E., Kiani, Y., Komijani, M. and Eslami, M.R., Vibration of a temperature-dependent thermally pre/postbuckled FGM beam over a nonlinear hardening elastic foundation, Journal of Applied Mechanics 81(1) (2014) 011004.

[12] Ghiasian, S.E., Kiani, Y. and Eslami, M.R., Dynamic buckling of suddenly heated or compressed FGM beams resting on nonlinear elastic foundation, Composite structures 106 (2013) 225-234.

[13] Zhang D.G. and Zhou H.-M., Nonlinear bending and thermal post-buckling analysis of FGM beams resting on nonlinear elastic foundations, CMES Comput. Modell. Eng. 100(3) (2014) 201-222.

[14] Akgöz, B. and Civalek, Ö., Thermo-mechanical buckling behavior of functionally graded microbeams embedded in elastic medium, International Journal of Engineering Science 85 (2014) 90-104.

[15] Akbaş, Ş.D., Free vibration of axially functionally graded beams in thermal environment, International Journal Of Engineering & Applied Sciences 6(3) (2014) 37-51.

[16] Akbas, Ş.D., Wave propagation of a functionally graded beam in thermal environments, Steel and Composite Structures 19(6) (2015) 1421-1447.

[17] Ebrahimi F. and Jafari A., A Higher-Order Thermomechanical Vibration Analysis of Temperature-Dependent FGM Beams with Porosities, Journal of Engineering, 2016 (2016), 20 p.

[18] Ebrahimi F. Ghasemi F. and Salari E., Investigating thermal effects on vibration behavior of temperature-dependent compositionally graded Euler beams with porosities, Meccanica 51(1) (2016) 223-249.

[19] Akbaş, Ş.D., Thermal effects on the vibration of functionally graded deep beams with porosity, International Journal of Applied Mechanics 9(5) (2017) 1750076.

[20] Akbaş, Ş.D., Nonlinear static analysis of functionally graded porous beams under thermal effect, Coupled Systems Mechanics 6(4) (2017) 399-415.

[21] Kar V.R. and Panda S.K., Geometrical nonlinear free vibration analysis of FGM spherical panel under nonlinear thermal loading with TD and TID properties, Journal of Thermal Stresses 39(8) (2016) 942-959.

[22] Sun Y., Li S.-R. and Batra R.C., Thermal buckling and post-buckling of FGM Timoshenko beams on nonlinear elastic foundation, Journal of Thermal Stresses 39(1) (2016) 11-26.

[23] Dehrouyeh-Semnani, A.M., On the thermally induced non-linear response of functionally graded beams, International Journal of Engineering Science 125 (2018) 53-74.

[24] Dehrouyeh-Semnani, A.M., On boundary conditions for thermally loaded FG beams, International Journal of Engineering Science 119 (2017) 109-127.

[25] Dehrouyeh-Semnani, A.M., Mostafaei, H., Dehrouyeh, M. and Nikkhah-Bahrami, M., Thermal pre-and post-snap-through buckling of a geometrically imperfect doubly-clamped microbeam made of temperature-dependent functionally graded materials, Composite Structures 170 (2017) 122-134.

[26] Zenkour, A., Hygrothermal analysis of exponentially graded rectangular plates, Journal of Mechanics of Materials and Structures 7(7) (2013) 687-700.

[27] Akbarzadeh, A.H. and Chen, Z.T., Hygrothermal stresses in one-dimensional functionally graded piezoelectric media in constant magnetic field, Composite Structures 97 (2013) 317-331.

[28] Beldjelili, Y., Tounsi, A. and Mahmoud, S.R., Hygro-thermo-mechanical bending of S-FGM plates resting on variable elastic foundations using a four-variable trigonometric plate theory, Smart Structures and Systems 18(4) (2016) 755-786.

[29] Laoufi, I., Ameur, M., Zidi, M., Bedia, E.A.A. and Bousahla, A.A., Mechanical and hygrothermal behaviour of functionally graded plates using a hyperbolic shear deformation theory, Steel and Composite Structures 20(4) (2016) 889-911.

[30] Boukhelf, F., Bouiadjra, M.B., Bouremana, M. and Tounsi, A., Hygro-thermo-mechanical bending analysis of FGM plates using a new HSDT, Smart Structures and Systems 21(1) (2018) 75-97.

[31] Mohammadimehr, M., Salemi, M. and Navi, B.R., Bending, buckling, and free vibration analysis of MSGT microcomposite Reddy plate reinforced by FG-SWCNTs with temperature-dependent material properties under hgyro-thermo-mechanical loadings using DQM, Composite Structures 138 (2016) 361-380.

[32] Bakhshizadeh, A., Zamani Nejad, M. and Davoudi Kashkoli, M., Time-Dependent Hygro-Thermal Creep Analysis of Pressurized FGM Rotating Thick Cylindrical Shells Subjected to Uniform Magnetic Field, Journal of Solid Mechanics 9(3) (2017) 663-679.

[33] Barati, M.R., Investigating dynamic response of porous inhomogeneous nanobeams on hybrid Kerr foundation under hygro-thermal loading, Applied Physics A 123(5) (2017) 332.

[34] Barati, M.R., Vibration analysis of FG nanoplates with nanovoids on viscoelastic substrate under hygro-thermo-mechanical loading using nonlocal strain gradient theory, Structural Engineering and Mechanics 64(6) (2017) 683-693.

[35] Mouffoki, A., Bedia, E.A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R., Vibration analysis of nonlocal advanced nanobeams in hygro-thermal environment using a new two-unknown trigonometric shear deformation beam theory, Smart Structures and Systems 20(3) (2017) 369-383.

[36] Ebrahimi, F. and Habibi, S., Nonlinear eccentric low-velocity impact response of a polymer-carbon nanotube-fiber multiscale nanocomposite plate resting on elastic foundations in hygrothermal environments, Mechanics of Advanced Materials and Structures 25(5) (2018) 425-438.

[37] Ebrahimi, F. and Barati, M.R., Effect of three-parameter viscoelastic medium on vibration behavior of temperature-dependent non-homogeneous viscoelastic nanobeams in a hygro-thermal environment, Mechanics of Advanced Materials and Structures 25(5) (2018) 361-374.

[38] Barati, M.R. and Zenkour, A., Forced vibration of sinusoidal FG nanobeams resting on hybrid Kerr foundation in hygro-thermal environments, Mechanics of Advanced Materials and Structures 25(8) (2018) 669-680.

[39] Ebrahimi, F. and Barati, M.R., A modified nonlocal couple stress-based beam model for vibration analysis of higher-order FG nanobeams, Mechanics of Advanced Materials and Structures 25(13) (2018) 1121-1132.

[40] Hosseini, H. and Kolahchi, R., Seismic response of functionally graded-carbon nanotubes-reinforced submerged viscoelastic cylindrical shell in hygrothermal environment, Physica E: Low-dimensional Systems and Nanostructures 102 (2018) 101-109.

[41] Jouneghani, F.Z., Dimitri, R. and Tornabene, F., Structural response of porous FG nanobeams under hygro-thermo-mechanical loadings, Composites Part B: Engineering 152 (2018) 71-78.

[42] Barati, M.R. and Shahverdi, H., Aero-hygro-thermal stability analysis of higher-order refined supersonic FGM panels with even and uneven porosity distributions, Journal of Fluids and Structures 73 (2017) 125-136.

[43] Nguyen, T.K., Nguyen, B.D., Vo, TP. and Thai, H.T., Hygro-thermal effects on vibration and thermal buckling behaviours of functionally graded beams, Composite Structures 176 (2017) 1050-1060.

[44] Reddy J.N. and Chin C.D., Thermoelastical Analysis of Functionally Graded Cylinders and Plates, Journal of Thermal Stresses 21(6) (1998) 593–626.

[45] Sobhy, M., An accurate shear deformation theory for vibration and buckling of FGM sandwich plates in hygrothermal environment, International Journal of Mechanical Sciences 110 (2011) 62-77.

[46] ANSYS Workbench Release 14.0, SAS IP, Inc, 2012.