DOI QR코드

DOI QR Code

Thermal buckling and stability of laminated plates under non uniform temperature distribution

  • Widad Ibraheem Majeed (Department of Mechanical Engineering, College of Engineering, University of Baghdad) ;
  • Ibtehal Abbas Sadiq (Department of Mechanical Engineering, College of Engineering, University of Baghdad)
  • Received : 2020.05.02
  • Accepted : 2023.05.16
  • Published : 2023.05.25

Abstract

Stability of laminated plate under thermal load varied linearly along thickness, is developed using a higher order displacement field which depend on a parameter "m", whose value is optimized to get results closest to three-dimension elasticity results. Hamilton, s principle is used to derive equations of motion for laminated plates. These equations are solved using Navier-type for simply supported boundary conditions to obtain non uniform critical thermal buckling and fundamental frequency under a ratio of this load. Many design parameters of cross ply and angle ply laminates such as, number of layers, aspect ratios and E1/E2 ratios for thick and thin plates are investigated. It is observed that linear and uniform distribution of temperature reduces plate frequency.

Keywords

References

  1. Abdul-Majeed, W.R., Jweeg M.J., Jameel, A.N. and Dpt, M.E. (2011), "Thermal buckling of rectangular plates with different temperature distribution using strain energy method", J. Eng., 17(5), 1047-1065. https://search.emarefa.net/detail/BIM-287653 https://doi.org/10.31026/j.eng.2011.05.02
  2. Abualnour, M., Chikh, A., Hebali, H., Kaci, A., Tounsi, A., Bousahla, A.A. and Tounsi, A. (2019), "Thermomechanical analysis of antisymmetric laminated reinforced composite plates using a new four variable trigonometric refined plate theory", Comput. Concrete, 24(6), 489-498. https://doi.org/10.12989/cac.2019.24.6.489.
  3. Adhikari, B. and Singh, B. N. (2020), "Buckling characteristics of laminated functionally-graded CNT-reinforced composite plate under nonuniform uniaxial and biaxial in-plane edge loads", Int. J. Struct. Stabil. Dyn., 20(2), 2050022, https://doi.org/10.1142/S0219455420500224.
  4. Addou, F.Y., Meradjah, M., Bousahla, A.A., Benachour, A., Bourada, F., Tounsi, A. and Mahmoud, S.R. (2019), "Influences of porosity on dynamic response of FG plates resting on Winkler/Pasternak/Kerr foundation using quasi 3D HSDT", Comput. Concrete, 24(4), 347-367. https://doi.org/10.12989/cac.2019.24.4.347.
  5. Alimirzaei, S., Mohammadimehr, M. and Tounsi, A. (2019), "Nonlinear analysis of viscoelastic micro-composite beam with geometrical imperfection using FEM: MSGT electro-magneto-elastic bending, buckling and vibration solutions", Struct. Eng. Mech., 71(5), 485-502. https://doi.org/10.12989/sem.2019.71.5.485.
  6. Balubaid, M. (2019), "Free vibration investigation of FG nanoscale plate using nonlocal two variables integral refined plate theory", Comput. Concrete, 24(6), 579-586. https://doi.org/10.12989/cac.2019.24.6.579.
  7. Bellal, M., Hebali, H., Heireche, H., Bousahla, A.A., Tounsi, A., Bourada, F., Mahmoud, S.R., Bedia, E.A.A. and Tounsi A. (2020), "Buckling behavior of a single-layered graphene sheet resting on viscoelastic medium via nonlocal four-unknown integral model", Steel Comp. Struct., 34(5), 643-655. https://doi.org/10.12989/scs.2020.34.5.643.
  8. Belbachir, N., Draiche, K., Bousahla, A. A., Bourada, M., Tounsi, A. and Mohammadimehr, M. (2019), "Bending analysis of antisymmetric cross-ply laminated plates under nonlinear thermal and mechanical loadings", Steel Comp. Struct., 33(1), 81-92. https://doi.org/10.12989/scs.2019.33.1.081.
  9. Belbachir, N., Bourada, M., Draiche, K., Tounsi, A., Bourada, F., Bousahla, A.A. and 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.
  10. Berghouti, H., Adda Bedia, E.A.A., Benkhedda, A. and Tounsi, A. (2019), "Vibration analysis of nonlocal porous nanobeams made of functionally graded material", J. Adv. Nano Res., 7(5), 351-364. https://doi.org/10.12989/anr.2019.7.5.351.
  11. Boulefrakh, L., Hebali, H., Chikh, A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2019), "The effect of parameters of visco-Pasternak foundation on the bending and vibration properties of a thick FG plate", Geomech. Eng., 18(2), 161-178. https://doi.org/10.12989/gae.2019.18.2.161.
  12. Boutaleb, S., Benrahou, K. H., Bakora, A., Algarni, A., Bousahla, A.A., Tounsi, A., Tounsi A. and Mahmoud S.R. (2019), "Dynamic Analysis of nanosize FG rectangular plates based on simple nonlocal quasi 3D HSDT", J. Adv. Nano Res., 7(3), 191-208. https://doi.org/10.12989/anr.2019.7.3.191.
  13. Boukhlif, Z. (2019), "A simple quasi-3D HSDT for the dynamics analysis of FG thick plate on elastic foundation", Steel Comp. Struct., 31(5), 503-516. https://doi.org/10.12989/scs.2019.31.5.503.
  14. Bousahla, A.A., Bourada, F., Mahmoud, S.R., Tounsi, A., Algarni, A., Bedia, E.A.A. and Tounsi, A. (2020), "Buckling and Dynamic Behavior of the Simply Supported CNT-RC Beams Using an Integral-First shear Deformation Theory", Comp. Concrete, 25(2), 155-166. https://doi.org/10.12989/cac.2020.25.2.155.
  15. Boussoula, A., Boucham, B., Bourada, M., Bourada, F., Tounsi, A., Bousahla, A.A. and Tounsi, A. (2020), "A simple nth-order shear deformation theory for thermomechanical bending analysis of - different configurations of FG sandwich plates", Smart Struct. Syst., 25(2), 197-218. https://doi.org/10.12989/sss.2020.25.2.197.
  16. Bourada, M., Tounsi, A., Houari, M.S.A. and Bedia, E.A.A. (2012), "A new four-variable refined plate theory for thermal buckling analysis of functionally graded sandwich plates", J. Sandwich Struct. Mater., 14(1), 5-33. doi.org/10.1177/1099636211426386.
  17. Cetkovic, M. and Gyorgy, L. (2016), "Thermo-elastic stability of angle-ply laminates application of layerwise finite elements", Struct. Integrity Life, 16(1), 43-48. http://grafar.grf.bg.ac.rs/handle/123456789/752.
  18. Cetkovic, M. (2016), "Thermal buckling of laminated composite plates using layerwise displacement model", Compos. Struct., 142, 238-253. https://doi.org/10.1016/j.compstruct.2016.01.082.
  19. Chen, C.S., Chen, W.R. and Lin, H.W. (2016), "Thermally induced stability and vibration of initially stressed laminated composite plates", Mech., 22(1), 51-58. https://doi.org/10.5755/j01.mech.22.1.8682.
  20. Chikh, A., Tounsi, A., Hebali, H. and Mahmoud, S.R. (2017), "Thermal buckling analysis of cross-ply laminated plates using a simplified HSDT", Smart Struct. Syst., 19(3), 289-297. https://doi.org/10.12989/sss.2017.19.3.289.
  21. Chikr, S.C., Kaci, A., Bousahla, A.A., Bourada, F., Tounsi, A., Bedia, E.A.A., Mahmoud S.R., Benrahou K.H. and Tounsi, A. (2020), "A novel four-unknown integral model for buckling response of FG sandwich plates resting on elastic foundations under various boundary conditions using Galerkin's approach", Geomech. Eng., 21(5), 471-487. https://doi.org/10.12989/gae.2020.21.5.471.
  22. Chaabane, L.A. (2019), "Analytical study of bending and free vibration responses of functionally graded beams resting on elastic foundation", Struct. Eng. Mech., 71(2), 185-196. https://doi.org/10.12989/sem.2019.71.2.185.
  23. Draiche, K., Bousahla, A.A., Tounsi, A., Alwabli, A.S., Tounsi, A. and Mahmoud, S.R. (2019), "Static analysis of laminated reinforced composite plates using a simple first-order shear deformation theory", Comp. Concrete, 24(4), 369-378. https://doi.org/10.12989/cac.2019.24.4.369.
  24. Draoui, A., Zidour, M., Tounsi, A. and Adim, B. (2019), "Static and dynamic behavior of nanotubes-reinforced sandwich plates using (FSDT)", J. Nano Res., 57, 117-135. https://doi.org/10.4028/www.scientific.net/JNanoR.57.117.
  25. Fazzolri, F.A. and Carrera, E. (2014), "Thermal stability of FGM sandwich plates under various through the thickness temperature distributions", J. Therm. Stresses, 37(12), 1449-1481. https://doi.org/10.1080/01495739.2014.93751.
  26. Fazzolri, F.A. (2015), "Natural frequencies and critical temperatures of functionally graded sandwich plates subjected to uniform and non-uniform temperature distributions", Compos. Struct., 121, 197-210. https://doi.org/10.1016/j.compstruct.2014.10.039.
  27. Ghomshei, M.M.M. and Mahmoudi, A. (2010), "Thermal buckling analysis of cross-ply laminated rectangular plates under nonuniform temperature distribution: A differential quadrature approach", J. Mech. Sci. Tech., 24(12), 2519-2527. https://doi.org/10.1007/s12206-010-0918-y.
  28. Jameel, A.N., Sadiq, I.A. and Nsaif, H.I. (2012), "Buckling analysis of composite plates under thermal and mechanical loading", J. Eng., 18(12), 1365-1390.
  29. Kaddari, M., Kaci, A., Bousahla, A.A., Tounsi, A., Bourada, F., Tounsi, A., Bedia, E.A.A. and Al-Osta Mohammed, 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", Comp. Concrete, 25(1), 37-57. https://doi.org/10.12989/cac.2020.25.1.037.
  30. Karami, B., Janghorban, M. and Tounsi, A. (2019), "Galerkin's approach for buckling analysis of functionally graded anisotropic nanoplates/different boundary conditions", Eng. Comp., 35, 1297-1316. https://doi.org/10.1007/s00366-018-0664-9.
  31. Karami, B., Janghorban, M., Shahsavari, D. and Tounsi, A. (2018), "A size-dependent quasi-3D model for wave dispersion analysis of FG nanoplates", Steel Compos. Struct., 28, 99-110. https://doi.org/10.12989/scs.2018.28.1.099.
  32. Matsunaga, H. (2006), "Thermal buckling of angle-ply laminated composite and sandwich plates according to a global higher-order deformation theory", Compos. Struct., 72, 177-192. https://doi.org/10.1016/j.compstruct.2004.11.016.
  33. Mahmoudi, A., Benyoucef, S., Tounsi, A., Benachour, A., Bedia, E.A.A. and Mahmoud S.R. (2017), "A refined quasi-3D shear deformation theory for thermo-mechanical behavior of functionally graded sandwich plates on elastic foundations", J. Sandw. Struct. Mater., 21(6), 1906-1929. https://doi.org/10.1177/1099636217727577.
  34. Majeed, W.I. and Sadiq I. A. (2018), "Buckling and pre stressed vibration analysis of laminated plates using new shear deformation", IOP Conf. Series: Mater. Sci. Eng., Istanbul, 454, 012006, https://doi:10.1088/1757-899X/454/1/012006.
  35. Mantari, J.L., Oktem, A.S. and Soares, C.G. (2011), "Static and dynamic analysis of laminated composite and sandwich plates and shells by using a new higher-order shear deformation theory", Compos. Struct., 94, 37-49. https://doi.org/10.1016/j.compstruct.2011.07.020.
  36. Narayana, D.A., Ganapathia, M., Pradyumnaa, B. and Haboussib, M. (2019), "Investigation of thermo-elastic buckling of variable stiffness laminated composite shells using finite element approach based on higher-order theory", Compos. Struct., 211. 24-40. https://doi.org/10.1016/j.compstruct.2018.12.012.
  37. Reddy, J.N. (2004), Mechanics of Laminated Composite Plates Shells, CRC Press, USA.
  38. Refrafi, S., Bousahla, A. A., Bouhadra, A., Menasria, A., Bourada, F., Tounsi, A., Bedia, E.A.A., Mahmoud, S.R., Benrahou, K. H. and Tounsi, A. (2020), "Effects of hygro-thermo-mechanical conditions on the buckling of FG sandwich plates resting on elastic foundations", Comp. Concrete, 25(4), 311-325. https://doi.org/10.12989/cac.2020.25.4.311.
  39. Rahmani, M.C., Kaci, A., Bousahla, A.A., Bourada, F., Tounsi, A., Bedia, E.A.A., Mahmoud, S.R., Benrahou K.H. and Tounsi A. (2020), "Influence of boundary conditions on the bending and free vibration behavior of FGM sandwich plates using a four-unknown refined integral plate theory", Comp. Concrete, 25(3), 225-244. https://doi.org/10.12989/cac.2020.25.3.225.
  40. Sahla, M. (2019), "Free vibration analysis of angle-ply laminated composite and soft core sandwich plates", Steel Compos. Struct., 33(5), 663-679. https://doi.org/10.12989/scs.2019.33.5.663.
  41. Shiau, L.C., Kuo, S.Y. and Chen, C.Y. (2010), "Thermal buckling behavior of composite laminated plates", Compos. Struct., 92, 508-514. https://doi.org/10.1016/j.compstruct.2009.08.035.
  42. Sadiq, I.A. (2019), "Thermal buckling of angle-ply laminated plates using new displacement function", J. Eng., 25(12), 96-113. https://doi.org/10.31026/j.eng.2019.12.08.
  43. Tlidji, Y., Zidour, M., Draiche, K., Safa, A., Bourada, M., Tounsi, A., Bousahla, A.A. and 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.
  44. Tounsi, A., Al-Dulaijan, S.U., Al-Osta, M.A., Chikh, A., Al-Zahrani, M.M., Sharif, A. and Tounsi, A. (2020), "A four variable trigonometric integral plate theory for hygro-thermomechanical 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.
  45. Xing, Y. and Wang, Z. (2017), "Closed form solutions for thermal buckling of functionally graded rectangular thin plates", Appl. Sci., 7(12), 1256-1274, https://doi.org/10.3390/app7121256.
  46. Vescovini, R., Ottavio, M.D., Dozio, L. and Polit, O. (2017), "Thermal buckling response of laminated and sandwich plates using refined 2-D models", Compos. Struct., 176, 313-328. http://dx.doi.org/10.1016/j.compstruct.2017.05.021.
  47. Zarga, D. (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.