Steel and Composite Structures

  • 제52권5호
  • /
  • Pages.525-541
  • /
  • 2024
  • /
  • 1229-9367(pISSN)
  • /
  • 1598-6233(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Bending analysis of smart functionally graded plate using the state-space approach

  • Niloufar Salmanpour (Department of Mechanical Engineering, Shiraz University of Technology) ;
  • Jafar Rouzegar (Department of Mechanical Engineering, Shiraz University of Technology) ;
  • Farhad Abad (Department of Naval Architecture, Ocean and Marine Engineering, University of Strathclyde) ;
  • Saeid Lotfian (Department of Naval Architecture, Ocean and Marine Engineering, University of Strathclyde)
  • 투고 : 2023.04.06
  • 심사 : 2024.08.08
  • 발행 : 2024.09.10
⟨ 이전 논문 다음 논문 ⟩

초록

This study uses the state-space approach to study the bending behavior of Levy-type functionally graded (FG) plates sandwiched between two piezoelectric layers. The coupled governing equations are obtained using Hamilton's principle and Maxwell's equation based on the efficient four-variable refined plate theory. The partial differential equations (PDEs) are converted using Levy's solution technique to ordinary differential equations (ODEs). In the context of the state-space method, the higher-order ODEs are simplified to a system of first-order equations and then solved. The results are compared with those reported in available references and those obtained from Abaqus FE simulations, and good agreements between results confirm the accuracy and efficiency of the approach. Also, the effect of different parameters such as power-law index, aspect ratio, type of boundary conditions, thickness-to-side ratio, and piezoelectric thickness are studied.

키워드

참고문헌

  1. Abad, F. and Rouzegar, J. (2017), "An exact spectral element method for free vibration analysis of FG plate integrated with piezoelectric layers", Compos. Struct., 180, 696-708.
  2. Abad, F. and Rouzegar, J. (2019), "Exact wave propagation analysis of moderately thick Levy-type plate with piezoelectric layers using spectral element method", Thin-Wall. Struct., 141, 319-31.
  3. Abad, F., Rouzegar, J. and Lotfian, S. (2023), "Application of the exact spectral element method in the analysis of the smart functionally graded plate", Steel Compos. Struct., 47, 297-313.
  4. Abbaspour, F. and Arvin, H. (2021), "Buckling treatment of piezoelectric functionally graded graphene platelets micro plates", Steel Compos. Struct., 38, 337-53.
  5. Arefi, M., Pourjamshidian, M. and Arani, A.G. (2019), "Dynamic instability region analysis of sandwich piezoelectric nano-beam with FG-CNTRCs face-sheets based on various high-order shear deformation and nonlocal strain gradient theory", Steel Compos. Struct., 32, 157-71.
  6. Arefi, M. and Soltan Arani, A.H. (2020), "Nonlocal vibration analysis of the three-layered FG nanoplates subjected to applied electric potential considering thickness stretching effect", Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, 234, 1183-202.
  7. Atmane, R.A., Mahmoudi, N. and Bennai, R. (2021), "Investigation on the dynamic response of porous FGM beams resting on variable foundation using a new higher order shear deformation theory", Steel Compos. Struct., 39, 95-107.
  8. Belabed, Z., Selim, M.M., Slimani, O., Taibi, N., Tounsi, A. and Hussain, M. (2021), "An efficient higher order shear deformation theory for free vibration analysis of functionally graded shells", Steel Compos. Struct., 40, 307-321.
  9. Boukhlif, Z. (2019), "A simple quasi-3D HSDT for the dynamics analysis of FG thick plate on elastic foundation", Steel Compos. Struct., 31, 503-16.
  10. Chan, D.Q., Quan, T.Q., Phi, B.G., Van Hieu, D. and Duc, N.D. (2022), "Buckling analysis and dynamic response of FGM sandwich cylindrical panels in thermal environments using nonlocal strain gradient theory", Acta Mechanica, 233, 2213-2235.
  11. Demirhan, P.A. and Taskin, V. (2017), "Levy solution for bending analysis of functionally graded sandwich plates based on four variable plate theory", Compos. Struct., 177, 80-95.
  12. Demirhan, P.A. and Taskin, V. (2019), "Bending and free vibration analysis of Levy-type porous functionally graded plate using state space approach", Compos. Part B: Eng., 160, 661-676.
  13. Fourn, H., Atmane, H.A., Bourada, M., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "A novel four variable refined plate theory for wave propagation in functionally graded material plates", Steel Compos. Struct., 27, 109-22.
  14. Franklin, J.N. (2012), Matrix Theory, Courier Corporation.
  15. Guellil, M., Saidi, H., Bourada, F., Bousahla, A.A., Tounsi, A., Al-Zahrani, M.M., Hussain, M. and Mahmoud, S. (2021), "Influences of porosity distributions and boundary conditions on mechanical bending response of functionally graded plates resting on Pasternak foundation", Steel Compos. Struct., 38, 1-15.
  16. Hachemi, H., Bousahla, A.A., Kaci, A., Bourada, F., Tounsi, A., Benrahou, K.H., Tounsi, A., Al-Zahrani, M.M. and Mahmoud, S. (2021), "Bending analysis of functionally graded plates using a new refined quasi-3D shear deformation theory and the concept of the neutral surface position", Steel Compos. Struct., 39, 51-64.
  17. Huang, W. and Tahouneh, V. (2021), "Frequency study of porous FGPM beam on two-parameter elastic foundations via Timoshenko theory", Steel Compos. Struct., 40, 139-156.
  18. Huang, Y., Li, Y., Zhang, L., Zhang, H. and Gao, Y. (2020), "Dynamic analysis of a multilayered piezoelectric two-dimensional quasicrystal cylindrical shell filled with compressible fluid using the state-space approach", Acta Mechanica, 231, 2351-2368.
  19. Kouider, D., Kaci, A., Selim, M.M., Bousahla, A.A., Bourada, F., Tounsi, A., Tounsi, A. and Hussain, M. (2021), "An original four-variable quasi-3D shear deformation theory for the static and free vibration analysis of new type of sandwich plates with both FG face sheets and FGM hard core", Steel Compos. Struct., 41, 167-191.
  20. Lee, J.S. and Jiang, L.Z. (1996), "Exact electroelastic analysis of piezoelectric laminae via state space approach", Int. J. Solids Struct., 33, 977-990.
  21. Liu, X., Wang, Y., Wang, G., Yang, B. and Xu, R. (2022), "Dynamic analysis of RC beams externally bonded with FRP plates using state space method", Eng. Struct., 253, 113788. https://doi.org/10.1016/j.engstruct.2021.113788.
  22. Mahamood, R.M. and Akinlabi, E.T. (2017), "Types of functionally graded materials and their areas of application. (Rasheedat Modupe Mahamood and Esther Titilayo Akinlabi), functionally graded materials", Springer International Publishing, Cham.
  23. Menasria, A., Kaci, A., Bousahla, A.A., Bourada, F., Tounsi, A., Benrahou, K.H., Tounsi, A., Bedia, E.A. and Mahmoud, S. (2020), "A four-unknown refined plate theory for dynamic analysis of FG-sandwich plates under various boundary conditions", Steel Compos. Struct., 36, 355-367.
  24. Mohammadimehr, M., Rostami, R. and Arefi, M. (2015), "Electro-elastic analysis of a sandwich thick plate considering FG core and composite piezoelectric layers on Pasternak foundation using TSDT", Steel Compos. Struct., https://doi.org/10.12989/scs.2016.20.3.513.
  25. Pham, Q.-H., Nguyen, P.-C., Tran, V.-K. and Nguyen-Thoi, T. (2021), "Finite element analysis for functionally graded porous nano-plates resting on elastic foundation", Steel Compos. Struct., 41, 149-166.
  26. Rahimi, Z., Sumelka, W. and Shafiei, S. (2018), "The analysis of non-linear free vibration of FGM nano-beams based on the conformable fractional non-local model", Bull. Polish Academy Sci. Tech. Sci., 66, 737-745.
  27. Razgordanisharahi, A., Alipour Ghassabi, A. and Hellmich, C. (2023), "Free vibration analysis of cylindrical honeycomb sandwich panels using state-space Levy method", Thin-Wall. Struct., 182, 110308. https://doi.org/10.1016/j.tws.2022.110308.
  28. Rouzegar, J. and Abad, F. (2015), "Free vibration analysis of FG plate with piezoelectric layers using four-variable refined plate theory", Thin-Wall. Struct., 89, 76-83.
  29. Rouzegar, J., Koohpeima, R. and Abad, F. (2020), "Dynamic analysis of laminated composite plate integrated with a piezoelectric actuator using four-variable refined plate theory", Iran. J. Sci. Technol. Transact. Mech. Eng., 44, 557-70. https://doi.org/10.1007/s40997-019-00284-1.
  30. Rouzegar, J., Salmanpour, N., Abad, F. and Li, L. (2022), "An analytical state-space solution for free vibration of sandwich piezoelectric plate with functionally graded core", Scientia Iranica, 29, 502-533.
  31. Stempin, P. and Sumelka, W. (2021), "Formulation and experimental validation of space-fractional Timoshenko beam model with functionally graded materials effects", Comput. Mech., 68, 697-708.
  32. Thai, H.-T. and Choi, D.-H. (2013a), "Analytical solutions of refined plate theory for bending, buckling and vibration analyses of thick plates", Appl. Mathem. Modelling, 37, 8310-8323.
  33. Thai, H.-T. and Choi, D.-H. (2013b), "Efficient higher-order shear deformation theories for bending and free vibration analyses of functionally graded plates", Archive Appl. Mech., 83, 1755-1771. https://doi.org/10.1007/s00419-013-0776-z.
  34. Thai, H.-T. and Choi, D.-H. (2013c), "Finite element formulation of various four unknown shear deformation theories for functionally graded plates", Finite Elements Anal. Des., 75, 50-61. https://doi.org/10.1016/j.finel.2013.07.003.
  35. 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.
  36. Tiersten, H.F. (2013), Linear Piezoelectric Plate Vibrations: Elements of the Linear Theory of Piezoelectricity and the Vibrations Piezoelectric Plates, Springer.
  37. Wang, Q., Quek, S., Sun, C. and Liu, X. (2001), "Analysis of piezoelectric coupled circular plate", Smart Mater Struct., 10, 229.
  38. Zarga, D. (2019), "Thermomechanical bending study for functionally graded sandwich plates using a simple quasi-3D shear deformation theory", Steel Compos. Struct., 32, 389-410.
  39. Zenkour, A.M. (2006), "Generalized shear deformation theory for bending analysis of functionally graded plates", Appl. Mathema. Modelling, 30, 67-84.
  40. Zenkour, A.M. and Radwan, A.F. (2020), "Bending and buckling analysis of FGM plates resting on elastic foundations in hygrothermal environment", Archives Civil Mech. Eng., 20, 112.
  41. Zhou, Y., Nyberg, T., Xiong, G. and Li, S. (2020), "State space finite element analysis for piezoelectric laminated curved beam with variable curvature", Mech. Adv. Mater. Struct., 27, 265-73.