Structural Engineering and Mechanics

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A new four-unknown equivalent single layer refined plate model for buckling analysis of functionally graded rectangular plates

  • Ibrahim Klouche Djedid (Laboratoire Materiaux et Structures (LMS), University of Tiaret) ;
  • Sihame Ait Yahia (Laboratoire Materiaux et Structures (LMS), University of Tiaret) ;
  • Kada Draiche (Department of Civil Engineering, University of Tiaret) ;
  • Emrah Madenci (Department of Civil Engineering, Necmettin Erbakan University) ;
  • Kouider Halim Benrahou (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes) ;
  • Abdelouahed Tounsi (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals)
  • Received : 2023.03.31
  • Accepted : 2024.05.23
  • Published : 2024.06.10
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Abstract

This paper presents a new four-unknown equivalent single layer (ESL) refined plate theory for the buckling analysis of functionally graded (FG) rectangular plates with all simply supported edges and subjected to in-plane mechanical loading conditions. The present model accounts for a parabolic variation of transverse shear stress over the thickness, and accommodates correctly the zero shear stress conditions on the top and bottom surfaces of the plate. The material properties are supposed to vary smoothly in the thickness direction through the rules of mixture named power-law gradation. The governing equilibrium equations are formulated based on the total potential energy principle and solved for simply supported boundary conditions by implementing the Navier's method. A numerical result on elastic buckling using the current theory was computed and compared with those published in the literature to examine the accuracy of the proposed analytical solution. The effects of changing power-law exponent, aspect ratio, thickness ratio and modulus ratio on the critical buckling load of FG plates under different in-plane loading conditions are investigated in detail. Moreover, it was found that the geometric parameters and power-law exponent play significant influences on the buckling behavior of the FG plates.

Keywords

References

  1. Abdelhak, Z., Benferhat, R., Hassaine Daouadji, T. and Tounsi, A. (2021), "Analysis on the buckling of imperfect functionally graded sandwich plates using new modified power-law formulations", Struct. Eng. Mech., 77(6), 797-807. https://doi.org/10.12989/sem.2021.77.6.797.
  2. Ahmed, R.A., Fenjan, R.M. and Faleh, N.M. (2019), "Analyzing post-buckling behavior of continuously graded FG nanobeams with geometrical imperfections'', Geomech. Eng., 17(2), 175-180. https://doi.org/10.12989/gae.2019.17.2.175.
  3. Akbas, S.D. (2018), "Bending of a cracked functionally graded nanobeam", Adv. Nano Res., 6(3), 219. https://doi.org/10.12989/anr.2018.6.3.219.
  4. Al-Osta, M.A. (2022a), "An exponential-trigonometric quasi-3D HSDT for wave propagation in an exponentially graded plate with microstructural defects", Compos. Struct., 297, 115984. https://doi.org/10.1016/j.compstruct.2022.115984.
  5. Al-Osta, M.A. (2022b), "Wave propagation investigation of a porous sandwich FG plate under hygrothermal environments via a new first-order shear deformation theory", Steel Compos. Struct., 43(1), 117-127. https://doi.org/10.12989/scs.2022.43.1.117.
  6. Arefi, M. and Meskini, M. (2019), "Application of hyperbolic shear deformation theory to free vibration analysis of functionally graded porous plate with piezoelectric face-sheets", Struct. Eng. Mech., 71(5), 459-467. https://doi.org/10.12989/sem.2019.71.5.459.
  7. Asrari, R., Ebrahimi, F. and Kheirikhah, M.M. (2020), "On scale-dependent stability analysis of functionally graded magneto-electro-thermo-elastic cylindrical nanoshells", Struct. Eng. Mech., 75(6), 657-674. https://doi.org/10.12989/sem.2020.75.6.657.
  8. Birman, V., Keil, T. and Hosder, S. (2013), "Functionally graded materials in engineering", Structural Interfaces and Attachments in Biology, Springer, New York.
  9. Chakraverty, S. and Pradhan, K.K. (2014), "Free vibration of exponential functionally graded rectangular plates in thermal environment with general boundary conditions", Aerosp. Sci. Technol., 36, 132-156. https://doi.org/10.1016/j.ast.2014.04.005.
  10. Chi, S.H. and Chung, Y.L. (2006), "Mechanical behavior of functionally graded material plates under transverse load, I: Analysis", Int. J. Solid. Struct., 43(13), 3657-3674. https://doi.org/10.1016/j.ijsolstr.2005.04.011.
  11. Ding, H.X. and She, G.L. (2021), "A higher-order beam model for the snap-buckling analysis of FG pipes conveying fluid", Struct. Eng. Mech., 80(1), 63-72. https://doi.org/10.12989/sem.2021.80.1.063.
  12. Duc, N.D., Cong, P.H., Tuan, N.D., Tran, P., Anh, V.M. and Quang, V.D. (2016), "Nonlinear vibration and dynamic response of imperfect eccentrically stiffened shear deformable sandwich plate with functionally graded material in thermal environment", J. Sandw. Struct. Mater., 18(4), 445-73. https://doi.org/10.1177/1099636215602142.
  13. Gupta, A. and Talha, M. (2015), "Recent development in modeling and analysis of functionally graded materials and structures", Progr. Aerosp. Sci., 79, 1-14. https://doi.org/10.1016/j.paerosci.2015.07.001.
  14. Hassaine Daouadji, T. and Adim, B. (2016), "An analytical approach for buckling of functionally graded plates", Adv. Mater Res., 5(3), 141-169. https://doi.org/10.12989/amr.2016.5.3.141.
  15. Jha, D.K., Kant, T. and Singh, R.K. (2011), "Stress analysis of transversely loaded functionally graded plates with a higher order shear and normal deformation theory", J. Eng. Mech., 139(12), 1663-1680. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000601.
  16. Jha, D.K., Tarun, K. and Singh, R.K. (2012), "Higher order shear and normal deformation theory for natural frequency of functionally graded rectangular plates", Nucl. Eng. Des., 250, 8-13. https://doi.org/10.1016/j.nucengdes.2012.05.001.
  17. Kar, V.R. and Panda, S.K. (2015), "Nonlinear flexural vibration of shear deformable functionally graded spherical shell panel", Steel Compos. Struct., 18(3), 693-709. https://doi.org/10.12989/scs.2015.18.3.693.
  18. Karakoti, A., Pandey, S. and Kar, V.R. (2021), "Dynamic responses analysis of P and S-FGM sandwich cylindrical shell panels using a new layerwise method", Struct. Eng. Mech., 80(4), 417-432. https://doi.org/10.12989/sem.2021.80.4.417.
  19. Kieback, B., Neubrand, A. and Riedel, H. (2003), "Processing techniques for functionally graded materials", Mater. Sci. Eng.: A, 362(1-2), 81-106. https://doi.org/10.1016/S0921-5093(03)00578-1.
  20. Kirchhoff, G. (1850), "uber das Gleichgewicht und die Bewegung einer elastischen Scheibe", J. fur die Reine und Angewandte Mathematik (Crelles J.), 1850(40), 51-88. https://doi.org/10.1515/crll.1850.40.51
  21. Klouche Djedid, I., Draiche, K., Guenaneche, B., Bousahla, A.A., Tounsi, A. and AddaBedia, E.A. (2019), "On the modeling of dynamic behavior of composite plates using a simple nth-HSDT", Wind Struct., 29(6), 371-387. https://doi.org/10.12989/was.2019.29.6.371.
  22. Koizumi, M. (1992), "Recent progress of functionally gradient materials in Japan", 16th Annual Conference on Composites and Advanced Ceramic Materials, 13, 333.
  23. Koizumi, M. and Niino, M. (1995), "Overview of FGM research in japan", MRS Bulletin 20, 19-21. https://doi.org/10.1557/S0883769400048867
  24. Kumar, S. (2010), "Development of functionally graded materials by ultrasonic consolidation", CIRP J. Manuf. Sci. Tech., 3(1), 85-87. https://doi.org/10.1016/j.cirpj.2010.07.006.
  25. Li, D., Zhu, H. and Gong, X. (2021), "Buckling analysis of functionally graded sandwich plates under both mechanical and thermal loads", Mater., 14(23), 7194. https://doi.org/10.3390/ma14237194.
  26. Maalawi, K.Y. (2012), "Stability dynamic and aeroelastic optimization of functionally graded composite structures", Advances in Computational Stability Analysis., InTech, Rijeka. https://doi.org/10.5772/45878.
  27. Markworth, A., Ramesh, K. and Parks, W. (1995), "Modelling studies applied to functionally graded materials", J. Mater. Sci., 30(9), 2183-2193. https://doi.org/10.1007/BF01184560.
  28. Mindlin, R.D. (1951), "Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates", ASME J. Appl. Mech., 18, 31-38. https://doi.org/10.1115/1.4010217
  29. Miyamoto, Y., Kaysser, W.A., Rabin, B.H., Kawasaki, A. and Ford, R.G. (1999), Functionally Graded Materials: Design, Processing and Applications, Springer, New York, NY.
  30. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Cinefra, M., Roque, C.M.C., Jorge, R.M.N. and Soares, C.M.M. (2013), "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.: Part B, 44, 657-674. https://doi.org/10.1016/j.compositesb.2012.01.089.
  31. Nguyen, T.K. (2014), "A higher-order hyperbolic shear deformation plate model for analysis of functionally graded materials", Int. J. Mech. Mater. Des., 11(2), 203-219. https://doi.org/10.1007/s10999-014-9260-3.
  32. Niino, A. and Maeda, S. (1990), "Recent development status of functionally gradient materials", ISIJ Int., 30, 699-703. https://doi.org/10.2355/isijinternational.30.699
  33. Nishida, I.A. (1994), "Thermoelectric energy conversion material", FGM-News J. FGM Forum, 24, 32-37.
  34. Reddy, J.N. and Chin, C.D. (1998), "Thermoelastical analysis of functionally graded cylinders and plates", J. Therm. Stress., 21, 593-626. https://doi.org/10.1080/01495739808956165
  35. Remil, A., Benrahou, K.H., Draiche, K., Bousahla, A.A. and Tounsi, A. (2019), "A simple HSDT for bending, buckling and dynamic behavior of laminated composite plates", Struct. Eng. Mech., 70(3), 325-337. https://doi.org/10.12989/sem.2019.70.3.325.
  36. Sidda Reddy, B., Suresh Kumar, J., Eswara Reddy, C. and Vijaya Kumar Reddy, K. (2013), "Buckling analysis of functionally graded material plates using higher order shear deformation theory", J. Compos., 2013, Article ID 808764. https://doi.org/10.1155/2013/808764.
  37. Swaminathan, K., Naveenkumar, D.T., Zenkour, A.M. and Carrera, E. (2015), "Stress, vibration and buckling analyses of FGM plates-A state-of-the-art review", Compos. Struct., 120, 10-31. https://doi.org/10.1016/j.compstruct.2014.09.070.
  38. Talha, M. and Singh, B.N. (2010), "Static response and free vibration analysis of FGM plates using higher order shear deformation theory", Appl. Math. Model., 34(12), 3991-4011. https://doi.org/10.1016/j.apm.2010.03.034.
  39. Thai, H.T. and Choi, D.H. (2012), "An efficient and simple refined theory for buckling analysis of functionally graded plates", Appl. Math. Model., 36, 1008-1022. https://doi.org/10.1016/j.apm.2011.07.062.
  40. Uemura, S. (2003), "The activities of FGM on new application", Mater. Sci. Forum, 423, 1-10. https://doi.org/10.4028/www.scientific.net/MSF.423-425.1.
  41. Yamanouchi, M., Koizumi, M., Hirai, T. and Shiota, I. (1990). Proceedings of the First International Symposium on Functionally Gradient Materials, Sendai, Japan.
  42. Zenkour, A.M. and Aljadani, M.H. (2018), "Mechanical buckling of functionally graded plates using a refined higher-order shear and normal deformation plate theory", Adv Aircraft Spacecraft Sci., 5(6), 615-632. https://doi.org/10.12989/aas.2018.5.6.615.
  43. Zenkour, AM. (2005), "A comprehensive analysis of functionally graded sandwich plates: Part 2-Buckling and free vibration", Int. Solid. Struct. 42(18-19), 5243-58. https://doi.org/10.1016/j.ijsolstr.2005.02.016.