Steel and Composite Structures

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Mechanical behaviour analysis of FGM plates on elastic foundation using a new exponential-trigonometric HSDT

  • Fatima Z. Zaoui (Laboratory of Science and Technology Environment and Valorization, Faculty of Sciences and Technology/Ibn Badis University) ;
  • Djamel Ouinas (Laboratory of Science and Technology Environment and Valorization, Faculty of Sciences and Technology/Ibn Badis University) ;
  • Abdelouahed Tounsi (Material and Hydrology Laboratory, Civil Engineering Department, Faculty of Technology / Djilali Liabes University) ;
  • Belkacem Achour (Civil Engineering Department, University of Ha'il) ;
  • Jaime A. Vina Olay (Department of Materials Science and Metallurgical Engineering, University of Oviedo, Viesques Campus) ;
  • Tayyab A. Butt (Civil Engineering Department, University of Ha'il)
  • Received : 2019.08.09
  • Accepted : 2023.02.16
  • Published : 2023.06.10
⟨ Previous Next ⟩

Abstract

In this research, a new two-dimensional (2D) and quasi three-dimensional (quasi-3D) higher order shear deformation theory is devised to address the bending problem of functionally graded plates resting on an elastic foundation. The displacement field of the suggested theories takes into account a parabolic transverse shear deformation shape function and satisfies shear stress free boundary conditions on the plate surfaces. It is expressed as a combination of trigonometric and exponential shear shape functions. The Pasternak mathematical model is considered for the elastic foundation. The material properties vary constantly across the FG plate thickness using different distributions as power-law, exponential and Mori-Tanaka model. By using the virtual works principle and Navier's technique, the governing equations of FG plates exposed to sinusoidal and evenly distributed loads are developed. The effects of material composition, geometrical parameters, stretching effect and foundation parameters on deflection, axial displacements and stresses are discussed in detail in this work. The obtained results are compared with those reported in earlier works to show the precision and simplicity of the current formulations. A very good agreement is found between the predicted results and the available solutions of other higher order theories. Future mechanical analyses of three-dimensionally FG plate structures can use the study's findings as benchmarks.

Keywords

Acknowledgement

The research reported herein was funded by the Deanship of Scientific Research at the University of Hail, Saudi Arabia, through the project number RG-21 084. The authors would like to express their deepest gratitude to the Deanship of Scientific Research and to the College of Engineering at the University of Hail for providing necessary support to conducting this research.

References

  1. Abdelhak, Z., Hadji, L., Daouadji, T.H. and Adda Bedia, E.A. (2016), "Thermal buckling response of functionally graded sandwich plates with clamped boundary conditions", Smart Struct. Syst. Int. J., 18(2), 267-291. https://doi.org/10.12989/SSS.2016.18.2.267
  2. Abdulrazzaq, M A., Fenjan, R.M., Ahmed, R.A. and Faleh, N.M. (2020), "Thermal buckling of nonlocal clamped exponentially graded plate according to a secant function based refined theory", Steel Compos., Struct., 35(1), 147-157. https://doi.org/10.12989/SCS.2020.35.1.147.
  3. Akavci, S.S. and Tanrikulu, A.H. (2015), "Static and free vibration analysis of functionally graded plates based on a new quasi-3D and 2D shear deformation theories", Compos. Part B Eng., 83(15), 203-215. https://doi.org/10.1016/j.compositesb.2015.08.043.
  4. Aldousari, S.M. (2017), "Bending analysis of different material distributions of functionally graded beam", Appl. Phys. A., 123(4), 296. https://doi.org/10.1007/s00339-017-0854-0.
  5. Al Khateeb, S.A. and Zenkour, A.M. (2014), "A refined four-unknown plate theory for advanced plates resting on elastic foundations in hygrothermal environment", Compos. Struct., 111, 240-248. https://doi.org/10.1016/j.compstruct.2013.12.033.
  6. Amar, H.H.L., Kaci, A., Houari, M.S.A., Bourada, A., Tounsi, A. and Mahmoud, S.R. (2017), "A new simple three-unknown shear deformation theory for bending analysis of FG plates resting on elastic foundations", Steel Compos. Struct. 25(6), 717e26. https://doi.org/10.12989/scs.2017.25.6.717.
  7. Arefi, M. and Allam, M.N.M. (2015), "Nonlinear responses of an arbitrary FGP circular plate resting on the Winkler-Pasternak foundation", Smart Struct., Syst., 16(1), 81-100. https://doi.org/10.12989/sss.2015.16. 1.081.
  8. Barretta, R., Luciano F., Raimondo L., Francesco M.S. and Rosa P. (2016), "Functionally graded Timoshenko nanobeams: a novel nonlocal gradient formulation", Compos. Part B: Eng., 100, 208-219. https://doi.org/10.1016/j.compositesb.2016.05.052.
  9. Belkhodja, Y., Ouinas, D., Zaoui, F.Z. and Fekirini, H. (2019), "A higher order exponential-trigonometric shear deformation theory for bending, vibration and buckling analysis of functionally graded material (FGM) plates: Part I", Adv. Compos. Letters, 28, 1-19. https://doi.org/10.1177/0963693519875739.
  10. Belkhodja, Y., Ouinas, D., Fekirini, H., Vina Olay, J.A., Achour, B., Touahmia, M. and Boukendakdji, M. (2022), "A new hybrid HSDT for bending, free vibration, and buckling analysis of FGM plates (2D & quasi-3D)", Smart Struct. Syst., 29(3), 395-420. https://doi.org/10.12989/sss.2022.29.3.395.
  11. Benyoucef, S., Mechab, I., Tounsi, A., Fekrar, A., Ait Atmane, H. and Adda, B.E.A. (2010), "Bending of thick functionally graded plates resting on Winkler-Pasternak elastic foundations", Mech. Compos. Mater., 46, 425-434. https://doi.org/10.1007/s11029-010-9159-5.
  12. Carrera, E., Brischetto, S., Cinefra, M. and Soave, M. (2011), "Effects of thickness stretching in functionally graded plates and shells", Compos. Part B Eng., 42(2), 123-133. https://doi.org/10.1016 /j.compositesb. 2010.10.005. https://doi.org/10.1016/j.compositesb.2010.10.005
  13. Demirhan, P.A. and Taskin, V. (2019), "Bending and free vibration analysis of Levy-type porous functionally graded plate using state space approach", Compos. B Eng., 160, 661-676. http://dx.doi.org/10.1016/j.compositesb.2018.12.020.
  14. Grover, N., Maiti, D. and Singh, B. (2013), "A new inverse hyperbolic shear deformation theory for static and buckling analysis of laminated composite and sandwich plates", Compos. Struct., 95, 667-675. https://doi.org/10.1016/j.compstruct.2012.08.012.
  15. Guerroudj, H.Z., Yeghnem, R., Kaci, A., Zaoui, F.Z., Benyoucef, S. and Tounsi, A. (2018), "Eigen-frequencies of advanced composite plates using an efficient hybrid quasi-3D shear deformation theory", Smart Struct. Syst., 22(1), 121-132. https://doi.org/10.12989/SSS.2018.22.1.121.
  16. Hebbar, N., Hebbar, I., Ouinas D. and Bourada, M. (2020), "Numerical modeling of bending, buckling, and vibration of functionally graded beams by using a higher-order shear deformation theory", Frattura ed Integrita Strutturale, 14(52), 230-246. https://doi.org/10.3221/IGF-ESIS.52.18.
  17. Hosseini-Hashemi, S.H., Fadaee, M. and Atashipour, S.R. (2011), "Study on the free vibration of thick functionally graded rectangular plates according to a new exact closed form procedure", Compos. Struct., 93(2), 722-735. https://doi.org/10.1016/j.compstruct.2010.08.007.
  18. Jha, D.K., Kant, T. and Singh, R.K. (2013), "Free vibration response of functionally graded thick plates with shear and normal deformations effects", Compos. Struct., 96, 799-823. https://doi.org/ 10.1016/j.compstruct.2012.09.034.
  19. Le, C.I., Pham, V.N. and Nguyen, D.K. (2020), "Free vibration of FGSW plates partially supported by Pasternak foundation based on refined shear deformation theories", Math. Prob. Eng., 2020, 7180453. https://doi.org/10.1155/2020/7180453.
  20. Lee, W.H., Han, S.C. and Park, W.T. (2015), "A refined higher order shear and normal deformation theory for E-, P-, and S-FGM plates on Pasternak elastic foundation", Compos. Struct., 122, 330-342. https://doi.org/10.1016/j.compstruct.2014.11.047.
  21. Mahmoudi, A., Benyoucef, S., Tounsi, A., Benachour, A. and Adda, B.EA. (2018), "On the effect of the micromechanical models on the free vibration of rectangular FGM plate resting on elastic foundation", Earthq. Struct., 14(2), 117-128. https://doi.org/10. 12989/eas.2018.14.2.117. https://doi.org/10.12989/eas.2018.14.2.117
  22. Mantari, J.L. and Granados, E.V. (2016), "An original FSDT to study advanced composites on elastic foundation", Thin-Walled Struct., 107, 80-89. https://doi.org/10.1016/j.tws.2016.05.024.
  23. Mantari, J.L., Granados, E.V., Hinostroza, M.A., Guedes Soares, C., (2014), "Modelling advanced composite plates resting on elastic foundation by using a quasi-3D hybrid type HSDT", Compos. Struct., 118, 455-471. https://doi.org/10.1016/j.compstruct.2014.07.039.
  24. Mantari, J.L. and Soares, C.G. (2013), "A novel higher-order shear deformation theory with stretching effect for functionally graded plates", Compos. Part B Eng., 45(1), 2682-2681. https://doi.org/ 10.1016/j.compositesb.2012.05.036.
  25. Mantari, J.L., Soares, C.G. (2015), "Five-unknowns generalized hybrid-type quasi- 3D HSDT for advanced composite plates", Appl. Math. Model., 39 (18), 5598-5615. https://doi.org/10.1016/j.apm.2015.01.020 .
  26. Meftah, A., Bakora, A., Zaoui, F. Z., Tounsi, A. and Bedia, E. A. A. (2017), "A non-polynomial four variable refined plate theory for free vibration of functionally graded thick rectangular plates on elastic foundation", Steel Compos. Struct., 23(3), 317-330. https://doi.org/10.12989/SCS. 2017.23.3.317
  27. Mengzhen, L., Renjun Y. and Guedes, C.S. (2021), "Free vibration of advanced composite plates using a new higher order shear deformation theory", Eur. J. Mech. A-Solid, 88, 104236. https://doi.org/10.1016/j.euromechsol.2021.104236.
  28. Meradjah, M., Bouakkaz, K., Zaoui, F.Z. and Tounsi, A. (2018), "A refined quasi-3D hybrid-type higher order shear deformation theory for bending and Free vibration analysis of advanced composites beams", Wind Struct., 27(4), 269-282. https://doi.org/10.12989/WAS. 2018.27.4.269.
  29. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Roque, C.M.C., Cinefra, M., Jorge, R.M.N. and Soares, C.M.M. (2012a), "A quasi-3D sinusoidal shear deformation theory for the static and free vibration analysis of functionally graded plates", Compos. Part B Eng., 43(2), 711-725. https://doi.org/10.1016/j.compositesb.2011.08.009.
  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. (2012b), "A quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", Compos. Struct., 94(5), 1814-1825. https://doi.org/10.1016/j.compstruct.2011.12.005.
  31. Nguyen, T.K. (2015), "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. Ouinas, D. and Achour, B. (2013), "Buckling analysis of laminated composite plates [(θ/-θ)] containing an elliptical notch", Compos. Part B Eng., 55, 575-579. https://doi.org/10.1016/j.compositesb.2013.07.011.
  33. Rachid, A., Ouinas, D., Lousdad, A., Zaoui, F.Z., Achour, B., Gasmi, H., Butt, T.A. and Tounsi, A. (2022), "Mechanical behavior and free vibration analysis of FG doubly curved shells on elastic foundation via a new modified displacements field model of 2D and Quasi-3D HSDTs", Thin-Walled Struct., 172, 108783. https://doi.org/10.1016/j.tws.2021.10878.
  34. Sidhoum, I.A., Boutchicha, D., Benyoucef, S. and Tounsi, A. (2018), "An original HSDT for free vibration analysis of functionally graded plates", Steel Compos. Struct., 25(6), 735-745. https://doi.org/10.12989/scs.2017.25.6.735.
  35. Thai, H.T. and Kim, S.E. (2013), "A simple higher-order shear deformation theory for bending and free vibration analysis of functionally graded plates", Compos. Struct., 96, 165-173. https://doi.org/10.1016/j.compstruct.2012.08.025.
  36. Thai, H.T., Park, M. and Choi, D.H. (2013), "A simple refined theory for bending, buckling, and vibration of thick plates resting on elastic foundation", Int. J. Mech. Sci., 73, 40-52. https://doi.org/10.1016/j.ijmecsci.2013.03.017.
  37. Vaghefi, R., Baradaran, G.H. and Koohkan, H. (2010), "Three-dimensional static analysis of thick functionally graded plates by using meshless local Petrov-Galerkin (MLPG) method", Eng. Anal. Bound. Elem., 34, 564-573. https://doi.org/10.1016/j.enganabound.2010.01.005.
  38. Vu, T.V., Khosravifard, A., Hematiyan, M.R. and Bui, T.Q. (2019), "Enhanced mesh free method with new correlation functions for functionally graded plates using a refined inverse sin shear deformation plate theory", Eur. J. Mech. Solid., 74, 160-175. https://doi.org/10.1016/j.euromechsol.2018.11.005.
  39. Xiang, S. and Kang, G. (2013), "A nth-order shear deformation theory for the bending analysis on the functionally graded plates", Eur. J. Mech. Solid., 37, 336-343. https://doi.org/10.1016/j.euromechsol.2012.08.005.
  40. Yarasca, J., Mantari, J.L. and Arciniega, R.A. (2016), "Hermite-Lagrangian finite element formulation to study functionally graded sandwich beams", Compos. Struct., 140, 567-581. https://doi.org/10.1016/j.compstruct.2016.01.015.
  41. Younsi, A., Tounsi, A., Zaoui, F.Z., Bousahla, A.A. and Mahmoud, S.R. (2018), "Novel quasi-3D and 2D shear deformation theories for bending and free vibration analysis of FGM plates", Geomech. Eng. Int. J., 14(6), 519-532. https://doi.org/10.12989/GAE.2018.14.6.519.
  42. Zaoui, F.Z., Hanifi, H.A.L., Younsi, A., Meradjah, M., Tounsi, A. and Ouinas, D. (2017b), "Free vibration analysis of functionally graded beams using a higher-order shear deformation theory". Math. Model. Eng. Probl., 4(1), 7-12. https://doi.org/10.18280/mmep.040102.
  43. Zaoui, F.Z., Ouinas, D., Achour, B., Touhamia, M., Boukendakdji, M., Latifee, E.R., Al-Naghi, A.A.A. and Vina Olay, J.A. (2022b), "Mathematical approach for mechanical behaviour analysis of FGM plates on elastic foundation", Math., 10, 4764. https://doi.org/10.3390/math10244764.
  44. Zaoui, F.Z., Ouinas, D., Achour, B., Tounsi, A., Latifee, E.R. and Al-Naghi, A.A.A. (2022a), "A hyperbolic shear deformation theory for natural frequencies study of functionally graded plates on elastic supports", J. Compos. Sci., 6(10), 285. https://doi.org/10.3390/jcs6100285.
  45. Zaoui, F.Z., Ouinas, D. and Tounsi, A. (2019), "New 2D and quasi-3D shear deformation theories for free vibration of functionally graded plates on elastic foundations", Compos. Part B Eng., 159, 231-347. https://doi.org/10.1016/j.compositesb.2018.09.051.
  46. Zaoui, F.Z., Ouinas, D., Tounsi, A. Vina Olay, J.A., Achour, B. and Touahmia, M. (2021), "Fundamental frequency analysis of functionally graded plates with temperature-dependent properties based on improved exponential-trigonometric two-dimensional higher shear deformation theory", Archive Appl. Mech., 91(3), 859-881. https://doi.org/10.1007/s00419-020-01793-1.
  47. Zaoui, F.Z., Tounsi, A. and Ouinas, D. (2017a), "Free vibration of functionally graded plates resting on elastic foundations based on quasi-3D hybrid-type higher order shear deformation theory", Smart Struct. Syst. Int. J., 20(4), 509-524. https://doi.org/10.12989/sss.2017.20.4.509.
  48. Zaoui, F.Z., Tounsi, A. Ouinas, D. and Vina Olay, J.A. (2020), "A refined HSDT for bending and dynamic analysis of FGM plates", Struct. Eng. Mech. Int. J., 74(1), 105-119. http://dx.doi.org/ 10. 12989/ sem. 2020.74.1.105. https://doi.org/10.12989/sem.2020.74.1.105
  49. Zhang, H., Jiang, J.K. and Zhang, Z.C. (2014), "Three-dimensional elasticity solutions for bending of generally supported thick functionally graded plates", Appl. Math. Mech., 35(11), 1467-1478. https://doi.org/10.1007/s10483-014-1871-7.