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http://dx.doi.org/10.12989/sem.2020.76.1.115

An investigation of the thermodynamic effect on the response of FG beam on elastic foundation  

Bouiadjra, Rabbab Bachir (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology)
Bachiri, Attia (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology)
Benyoucef, Samir (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology)
Fahsi, Bouazza (Laboratoire de Modelisation et Simulation Multi-echelle, Universite de Sidi Bel Abbes)
Bernard, Fabrice (Laboratoire de Genie Civil et Genie Mecanique, INSA de Rennes)
Publication Information
Structural Engineering and Mechanics / v.76, no.1, 2020 , pp. 115-127 More about this Journal
Abstract
This study presents an analytical approach to investigate the thermodynamic behavior of functionally graded beam resting on elastic foundations. The formulation is based on a refined deformation theory taking into consideration the stretching effect and the type of elastic foundation. The displacement field used in the present refined theory contains undetermined integral forms and involves only three unknowns to derive. The mechanical characteristics of the beam are assumed to be varied across the thickness according to a simple exponential law distribution. The beam is supposed simply supported and therefore the Navier solution is used to derive analytical solution. Verification examples demonstrate that the developed theory is very accurate in describing the response of FG beams subjected to thermodynamic loading. Numerical results are carried out to show the effects of the thermodynamic loading on the response of FG beams resting on elastic foundation.
Keywords
FGMs beams; Three-dimensional theory; undetermined integral forms; elastic foundation; thermodynamic effect;
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86 Gul, U., Aydogdu, M., Karacam, F. (2019), "Dynamics of a functionally graded Timoshenko beam considering new spectrums", Compos. Struct., 207, 273-291. https://doi.org/10.1016/j.compstruct.2018.09.021.   DOI
87 Hebbar, N., Bourada, M., Sekkal, M., Tounsi A., and. Mahmoud, S.R. (2018), "A novel four-unknown quasi-3D shear deformation theory for functionally graded plates", Steel Compos. Struct., 27(5), 599-611. https://doi.org/10.12989/scs.2018.27.5.599.   DOI
88 Hussain, M., Naeem, M.N. (2019), "Effects of ring supports on vibration of armchair and zigzag FGM rotating carbon nanotubes using Galerkin's method", Compos. Part B. Eng., 163, 548-561. https://doi.org/10.1016/j.compositesb.2018.12.144.   DOI
89 Timesli, A. (2020), "An efficient approach for prediction of the nonlocal critical buckling load of double-walled carbon nanotubes using the nonlocal Donnell shell theory", SN Appl. Sci., 2, 407. https://doi.org/10.1007/s42452-020-2182-9.   DOI
90 Tlidji, Y., Zidour, M., Draiche, K., Safa, A., Bourada, M., Tounsi, A., Bousahla, A.A., Mahmoud, S.R. (2019), "Vibration analysis of different material distributions of functionally graded microbeam", Struct. Eng. Mech., 69(6), 637-649. https://doi.org/10.12989/sem.2019.69.6.637.   DOI
91 Hussain, M., Naeem, M.N., Tounsi, A., Taj, M. (2019), "Nonlocal effect on the vibration of armchair and zigzag SWCNTs with bending rigidity", Adv. Nano Res., 7(6), 431-442. https://doi.org/10.12989/anr.2019.7.6.431.   DOI
92 Kaddari, M., Kaci, A., Bousahla, A.A.,Tounsi, A., Bourada, F., Tounsi, A., Adda Bedia, E.A., Al-Osta, M.A. (2020), "A study on the structural behaviour of functionally graded porous plates on elastic foundation using a new quasi-3D model: Bending and Free vibration analysis", Comput. Concrete, 25(1), 37-57. https://doi.org/10.12989/cac.2020.25.1.037.   DOI
93 Karami, B., Janghorban, M. and Tounsi, A. (2019b), "Galerkin's approach for buckling analysis of functionally graded anisotropic nanoplates/different boundary conditions", Eng. Comput., 35, 1297-1316. https://doi.org/10.1007/s00366-018-0664-9.   DOI
94 Barati, M.R. and Shahverdi, H. (2016), "A four-variable plate theory for thermal vibration of embedded FG nanoplates under non-uniform temperature distributions with different boundary conditions", Struct. Eng. Mech., 60(4), 707-727. https://doi.org/10.12989/sem.2016.60.4.707.   DOI
95 Batou, B., Nebab, M., Bennai, R., Ait Atmane, H., Tounsi, A., Bouremana, M. (2019), "Wave dispersion properties in imperfect sigmoid plates using various HSDTs", Steel Composite Structures, 33(5), 699-716. https://doi.org/10.12989/scs.2019.33.5.699.   DOI
96 Behera, S., Kumari, P. (2018), "Free vibration of Levy-type rectangular laminated plates using efficient zig-zag theory", Adv. Comput. Design, 3(3), 213-232. https://doi.org/10.12989/acd.2017.2.3.165.   DOI
97 Belbachir, N., Draich, K., Bousahla, A.A., Bourada, M., Tounsi, A., Mohammadimehr, M. (2019), "Bending analysis of anti-symmetric cross-ply laminated plates under nonlinear thermal and mechanical loadings", Steel Compos. Struct., 33(1), 81-92. https://doi.org/10.12989/scs.2019.33.1.081.   DOI
98 Belbachir, N., Bourada, M., Draiche, K., Tounsi, A., Bourada, F., Bousahla, A.A., Mahmoud, S.R. (2020), "Thermal flexural analysis of anti-symmetric cross-ply laminated plates using a four variable refined theory", Smart Struct. Syst., 25(4), 409-422. https://doi.org/10.12989/sss.2020.25.4.409   DOI
99 Bellal, M., Hebali, H., Heireche, H., Bousahla, A.A., Tounsi, A., Bourada, F., Mahmoud, S.R., Adda Bedia, E.A., Tounsi, A. (2020), "Buckling behavior of a single-layered graphene sheet resting on viscoelastic medium via nonlocal four-unknown integral model", Steel Compos. Struct., 34(5), 643-655. https://doi.org/10.12989/scs.2020.34.5.643.   DOI
100 Karami, B., Janghorban, M., Tounsi, A. (2019a), "Wave propagation of functionally graded anisotropic nanoplates resting on Winkler-Pasternak foundation", Struct. Eng. Mech., 70(1), 55-66. https://doi.org/10.12989/sem.2019.70.1.055.   DOI
101 Karami, B., Janghorban, M., Tounsi, A. (2019c), "On pre-stressed functionally graded anisotropic nanoshell in magnetic field", J. Brazilian Soc. Mech. Sci. Eng., 41, 495. https://doi.org/10.1007/s40430-019-1996-0.   DOI
102 Khorasani, M., Eyvazian, A., Karbon, M., Tounsi, A., Lampani, L., Sebaey, T.A. (2020), "Magneto-Electro-Elastic Vibration Analysis of Modified Couple Stress-Based Three-Layered Micro Rectangular Plates Exposed to Multi-Physical Fields Considering the Flexoelectricity Effects", Smart Struct. Syst., (Accepted).
103 Lal, A.,Jagtap, K.R., Singh, B.N. (2017), "Thermo-mechanically induced finite element based nonlinear static response of elastically supported functionally graded plate with random system properties", Adv. Comput. Design, 2(3), 165-194. https://doi.org/10.12989/acd.2017.2.3.165.   DOI
104 Malikan, M. (2018), "Buckling Analysis of a Micro Composite Plate with Nano Coating Based on the Modified Couple Stress Theory", J. Appl. Comput. Mech., 4(1), 1-15. https://doi.org/10.22055/jacm.2017.21820.1117.
105 Tounsi, A., Al-Dulaijan, S.U., Al-Osta, M.A., Chikh, A., Al-Zahrani, M.M., Sharif, A., Tounsi, A. (2020), "A four variable trigonometric integral plate theory for hygro-thermo-mechanical bending analysis of AFG ceramic-metal plates resting on a two-parameter elastic foundation", Steel Compos. Struct., 34(4), 511-524. https://doi.org/10.12989/scs.2020.34.4.511.   DOI
106 Ying, J., Lu, C.F., Chen, W.Q., (2008), "Two-dimensional elasticity solutions for functionally graded beams resting on elastic foundations", Compos. Struct., 84, 209-219. 10.1016/j.compstruct.2007.07.004.   DOI
107 Zaoui, F.Z., Ouinas, D., Tounsi, A. (2019), "New 2D and quasi-3D shear deformation theories for free vibration of functionally graded plates on elastic foundations", Compos. Part B, 159, 231-247. https://doi.org/10.1016/j.compositesb.2018.09.051.   DOI
108 Zarga, D., Tounsi, A., Bousahla, A.A., Bourada, F., Mahmoud, S.R. (2019), "Thermomechanical bending study for functionally graded sandwich plates using a simple quasi-3D shear deformation theory", Steel Compos. Struct., 32(3), 389-410. https://doi.org/10.12989/scs.2019.32.3.389.   DOI
109 Bensattalah, T., Zidour, M. and Daouadji, T.H. (2019), "A new nonlocal beam model for free vibration analysis of chiral single-walled carbon nanotubes", Compos. Mater. Eng., 1(1), 21-31. https://doi.org/10.12989/cme.2019.1.1.021
110 Zenkour, A. M., Sobhy, M., (2013), "Dynamic bending response of thermoelastic functionally graded plates resting on elastic foundations", Aerosp. Sci. Technol., 29(1), 7-17. https://doi.org/10.1016/j.ast.2013.01.003.   DOI