Journal of Computational & Applied Research in Mechanical Engineering (JCARME)

Document Type : Research Paper

Authors

¹ Department of Mech. Eng., Rajeev Gandhi Memorial College of Eng.,and Tech., Nandyal, Kurnool (Dt), Andhra Pradesh, India-518 501. Fax:08514 275203

² Department of Mech. Eng., MLR Institute of Technology, Telangana, India-500043

³ Department of Mech. Eng., JNTUH, Telangana, India-500085

https://doi.org/10.22061/jcarme.2020.6370.1809

Abstract

The present paper considers the devise and development of a novel theory to examine the flexure analysis of exponentially graded plates exposed to thermal and mechanical loads. The properties such as elastic modulus and thermal modulus are assumed to vary exponentially along the thickness by keeping the poisson’s ratio constant. This theory fulfills the nullity conditions on the upper and lower sides of the exponentially graded plates for transverse shear stress. Hamilton’s principle is used to derive the equation of motion. The present theory’s numerical results are assessed with three-dimensional elasticity solutions and the results of other authors available in the literature. The influence of thermomechanical loads, thickness ratios, and aspect ratios on the bending response of exponentially graded plates are studied in detail. The analytical formulations and solutions presented herein could provide engineers with the potential for the design and development of exponentially graded plates for advanced engineering applications.

Graphical Abstract

Keywords

dor

20.1001.1.22287922.2021.11.1.20.2

Main Subjects

Mechanics of Materials

References

[1] J. N. Reddy, C. D. Chin, “Thermomechanical analysis of functionally graded cylinders and plates”. J Therm Stresses, Vol.21, No.6, pp. 593-626, (1998).

[2] A. M. Zenkour, “A comprehensive analysis of functionally graded sandwich plates: Part-1-Deflection and stresses”. Int J Solids Struct, Vol. 42, No.(18-19), pp.5224-5242, (2005).

[3] A. M. Zenkour, “A comprehensive analysis of functionally graded sandwich plates: Part-2-Buckling and free vibration”. Int J Solids Struct, Vol.42, No.(18-19), pp.5243-5258, (2005).

[4] A. M. Zenkour, “Generalized shear deformation theory for bending analysis of functionally graded plates”. Appl Math Model, Vol. 30, No.1, pp. 67-84, (2006).

[5] B. N. Pandya, T. Kant, “Higher-order shear deformable theories for flexure of sandwich plates-finite element evaluations”. Int J Solids Struct, Vol. 24, No. 12, pp.1267-1286, (1988).

[6] B. N. Pandya, T. Kant, “Finite element analysis of laminated composite plates using a higher order displacement model”. Compos Sci Technol, Vol. 32, No.2, pp.137-155, (1988).

[7] T. Kant, K. Swaminathan, “Analytical solutions for the static analysis of laminated composite and sandwich plates based on higher order refined theory”. Compos Struct, Vol. 56, No.4, pp.329-344, (2002).

[8] T.Kant, K.Swaminathan, “Analytical solutions for free vibration analysis of laminated composite and sandwich plates based on higher order refined theory”. Compos Struct, Vo. 53, No.1, pp.73-85, (2001).

[9] A. K. Garg, R. K. Khare, T. Kant, “Higher order closed form solutions for free vibration of laminated composite and sandwich shells”. J Sandw Struct Mater, Vol. 8, No.3, pp.205-235, (2006).

[10] M. E Golmakani, M. Kadkhodayan, “Nonlinear bending analysis of annular FGM plates using higher order shear deformation plate theories”. Compos Struct, Vol. 93. Pp.973-982, (2011).

[11] H. Matsunaga, “Free vibration and stability of functionally graded plates according to a 2-D higher-order deformation theory”. Compos Struct, Vol.82, pp.499-512 (2008).

[12] H. Matsunaga, “Stress analysis of functionally graded plates subjected to thermal and mechanical loadings”. Compos Struct, Vol. 87, pp.344-357, (2009).

[13] S. Xiang, G. Kang, “A nth-order shear deformation theory for the bending analysis on the functionally graded plates”. Eur J Mech A-Solid, Vol. 37, pp.336-343, (2013).

[14] J. Suresh Kumar, B. Sidda Reddy, C. Eswara Reddy, K. Vijaya Kumar Reddy, “Nonlinear Thermal Analysis of Functionally Graded Plates Using Higher Order Theory”. Innovat Syst Des Eng, Vol. 2, No. 5, pp.1-13, (2011).

[15] B. Sidda Reddy, J. Suresh Kumar, C. Eswara Reddy, K. Vijaya Kumar Reddy, “Buckling Analysis of Functionally Graded Material Plates Using Higher Order Shear Deformation Theory”,J. Compos., Vol. 2013, Article ID 808764, 12 pages, (2013).

[16] J. Suresh Kumar, B. Sidda Reddy, C. Eswara Reddy, “Nonlinear bending analysis of functionally graded plates using higher order theory”. Int. J. Eng. Sci. Technol., Vol. 3, No.4, pp.3010-3022, (2011).

[17] T. Mohammad, B. N. Singh, “Thermo-mechanical deformation behavior of functionally graded rectangular plates subjected to various boundary conditions and loadings” Int. J. Aerosp. Mech. Eng., Vol. 6, No.1, pp.14-25, (2012).

[18] A. M. Zenkour, N. A. Alghamdi, “Bending analysis of functionally graded sandwich plates under the effect of mechanical and thermal loads”. Mech Adv Mate Struc, Vol.17, No.6, pp. 419-432, (2010).

[19] H. A. Mechab, A. Ismail, H. A. Belhadej, A. E. A. Bedia, “A two variable refined plate theory for the bending analysis of functionally graded plates”. Act Mech Sin, Vol. 26, pp. 941-949, (2010).

[20] E. Carrera, S. Brischetto, M. Cinefra, M Soave, “Effects of thickness stretching in functionally graded plates and shells”. Compos. B. Eng., Vol. 42, pp.123-133, (2011).

[21] T. H. D. A. Henni, A. Tounsi, A. B. E. Abbes, “A New Hyperbolic Shear Deformation Theory for Bending Analysis of Functionally Graded Plates”. Model Simu Eng., Vol. 2012, pp. 1-10, (2012).

[22] A.M.A. Neves, A.J.M. Ferreira, E. Carrera, M. Cinefra, C.M.C. Roque, R.M.N. Jorge, “A quasi-3d sinusoidal shear deformation theory for the static and free vibration analysis of functionally graded plates”. Compos. B. Eng., Vol. 43, No.711-725, (2012).

[23] A. M. Zenkour, “Benchmark trigonometric and 3-D elasticity solutions for an exponentially graded thick rectangular plate”. Appl Math Model, Vol. 77, pp. 197-214, (2007).

[24] J. L. Mantari, C. Guedes Soares, “Bending analysis of thick exponentially graded plates using a new trigonometric higher order shear deformation theory”. Compos Struct Vol. 49, pp.1991-2000, (2012).

[25] J. L. Mantari, C. Guedes Soares, “A novel higher-order shear deformation theory with stretching effect for functionally graded plates”. Compos. B. Eng. Vol. 45, pp.268–281, (2013).

[26] A. M. A. Neves, A. J. M. Ferreira, E. Carrera, M. Cinefra, C. M. C. Roque, R. M. N. Jorge, C. M. M. Soares, “Static, free vibration and buckling analysis of isotropic and sandwich functionally graded plates using a quasi-3D higher-order shear deformation theory and a meshless technique”. Compos. B. Eng., Vol. 44 pp.657–674, (2013).

[27] G. N. Praveen, J. N. Reddy, “Nonlinear transient thermo elastic analysis of functionally graded ceramic-metal plates”. Int J Solids Struct, Vol. 35, pp. 4457-4476, (1998).

[28] A. Attia, A. A. Bousahla, A. Tounsi, S.R. Mahmoud and A. S. Alwabl, “A refined four variable plate theory for thermoelastic analysis of FGM plates resting on variable elastic foundations”, Struct. Eng Mech, Vol. 65, No. 4,pp.453-464,(2018).

[29] A. Fahsi, A. Tounsi, H. Hebali, A. Chikh, E.A. A. Bedia and S.R. Mahmoud, “A four variable refined nth-order shear deformation theory for mechanical and thermal buckling analysis of functionally graded plates”, Geomech Eng, Vol. 13, No. 3, pp. 385-410, (2017).

[30] A. Chikh, A. Tounsi, H. Hebali and S. R. Mahmoud, “Thermal buckling analysis of cross-ply laminated plates using a simplified HSDT”, Smart Struct. Systems., Vol. 19, No. 3, pp. 289-297, (2017).

[31] F. El-Haina, A. Bakora, A. A. Bousahla, A. Tounsi and S.R. Mahmoud, “A simple analytical approach for thermal buckling of thick functionally graded sandwich plates”, Struct Eng Mch, Vol. 63, No. 5, pp. 585-595, (2017).

[32] A. Menasria, A. Bouhadra, A. Tounsi, A. A. Bousahla, S.R. Mahmoud, , “A new and simple HSDT for thermal stability analysis of FG sandwich plates”, Steel Compos Struct, Vo. 25, No. 2, pp.157-175 (2017).

[33] Y. Beldjelili, A. Tounsi and S.R. Mahmoud, “Hygro-thermo-mechanical bending of S-FGM plates resting on variable elastic foundations using a four-variable trigonometric plate theory”, Smart Struct Syst, Vol. 18, No. 4, pp. 755-786, (2016).

[34] S. Boutaleb, K. H. Benrahou, A. Bakora, A. Algarni, A. A. Bousahla, A. Tounsi, and S.R. Mahmoud, “Dynamic analysis of nanosize FG rectangular plates based on simple nonlocal quasi 3D HSDT”, Advances in Nano Research, Vol. 7, No. 3, pp.189-206, (2019).

[35] Z. Boukhlif, M. Bouremana, F. Bourada, A. A. Bousahla, M. Bourada, A. Tounsi and M. A. Al-Osta, “A simple quasi-3D HSDT for the dynamics analysis of FG thick plate on elastic foundation”, Steel Compos Struct, Vol. 31, No. 5, pp.503-516, (2019).

[36] S. Bouanati, K. H. Benrahou, A. A. Hassen, A. Y. Sihame, F. Bernard, A. Tounsi and E.A. A. Bedia, “Investigation of wave propagation in anisotropic plates via quasi 3D HSDT”, Geomech Eng, Vol. 18, No. 1, pp. 85-96 (2019).

[37] A. A. Hassen, A. Tounsi, & F. Bernard, “Effect of thickness stretching and porosity on mechanical response of a functionally graded beams resting on elastic foundations”. Int. J. of Mech Mater Des., Vol. 13, No. 1, pp. 71-84, ((2017).

[38] A. Benahmed, M. S. A. Houari, S. Benyoucef, K. Belakhdar and A. Tounsi, “A novel quasi-3D hyperbolic shear deformation theory for functionally graded thick rectangular plates on elastic foundation”, Geomech Eng, Vol. 12, No. 1, pp. 9-34, (2017).

[39] B. Karami, M. Janghorban, D. Shahsavari and A. Tounsi, “A size-dependent quasi-3D model for wave dispersion analysis of FG nanoplates”, Steel Compos Struc Vol. 28, No. 1, pp. 99-110, (2018).

[40] F. Z. Zaoui, O. Djamel & A. Tounsi, “New 2D and quasi-3D shear deformation theories for free vibration of functionally graded plates on elastic foundations”, Compos. B. Eng., Vol.159, pp. 231-247 ((2019).

[41] A. Bouhadra, A. Tounsi, A. A. Bousahla, S. Benyoucef and S.R. Mahmoud, “Improved HSDT accounting for effect of thickness stretching in advanced composite plates”, Vol. 6 STRUCT ENG MECH, No. 1, pp. 61-73 (2018).

[42] A. Younsi, A. Tounsi, F. Z. Zaoui, A. A. Bousahla and S.R. Mahmoud, “Novel quasi-3D and 2D shear deformation theories for bending and free vibration analysis of FGM plates”, Geomech Eng, Vol. 14, No. 6, pp. 519-532, (2018).

[43] M. Abualnour, M.S.A. Houari, A. Tounsi, E.A.A. Bedia, S.R. Mahmoud, “A novel quasi-3D trigonometric plate theory for free vibration analysis of advanced composite plates”, Compos Struct (2017).

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Journal of Computational & Applied Research in Mechanical Engineering (JCARME)

Volume 11, Issue 1
September 2021
Pages 257-277

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