DOI QR코드

DOI QR Code

Thermoelastic bending analysis of laminated plates subjected to linear and nonlinear thermal loads

  • Swami, Sandhya K. (Department of Civil Engineering, Marathwada Institute of Technology) ;
  • Ghugal, Yuwaraj M. (Department of Applied Mechanics, Government College of Engineering)
  • Received : 2021.04.05
  • Accepted : 2021.07.26
  • Published : 2021.05.25

Abstract

The paper presents the analytical solutions for thick orthotropic laminated plates using trignometric shear deformation theory. The effects transverse shear and transverse normal strains are included with linear and nonlinear thermal loads. The displacement field of the theory includes the trigonometric functions in thickness coordinate of plate to account for these effects. The displacement field enforces to give the realistic variation of shear stresses across the thickness of plate and thus obviates the need of shear correction factor. The main novelty of the present study is the inclusion of thickness stretching effect in the theory. Another novelty is the application of nonlinear thermal profile consistent with the displacement field of the theory. The principle of virtual work is used to obtain the governing equations and boundary conditions. Simply supported laminated square plates are considered for numerical study to evaluate thermoelastic response. The results obtained by present theory with thickness stretching effect are compared with other refined theories disregarding this effect. It is observed that the results of present theory deviate significantly from the results of other higher order shear deformation theories for antisymmetric crossply laminated plates. The results of symmetric cross-ply laminated plates subjected to linear sinusoidal thermal load are in close agreement with those of exact theory, which validates the accuracy of present shear and normal deformation theory.

Keywords

References

  1. Altay, G.A. and Doekmeci, M.Q. (2003), "Some comments on the higher-order theories of piezoelectric, piezothermoelectric, and thermopiezoelectric rods and shells", Int. J. Solids Struct., 40(18), 4699-4706. https://doi.org/10.1016/S0020-7683(03)00185-9.
  2. Arefi, M. and Amabili, M. (2021), "A comprehensive electro-magneto-elastic buckling and bending analyses of three-layered doubly curved nanoshell, based on nonlocal three-dimensional theory", Compos. Struct., 257(1), 113101+18. https://doi.org/10.1016/j.compstruct.2020.113100.
  3. Arefi, M. and Arani, A.H.S. (2020), "Nonlocal vibration analysis of the three-layered FG nanoplates subjected to applied electric potential considering thickness stretching effect", Proc. Inst. Mech. E Part L J. Mat. Des. Appl., 234(9), 1183-1202. https://doi.org/10.1177/1464420720928378.
  4. Arefi, M. and Zenkour, A.M. (2016), "A simplified shear and normal deformations nonlocal theory for bending of functionally graded piezomagnetic sandwich nanobeams in magneto-thermo-electric environment", J. Sandw. Struct. Mater., 18(5), 1-28. https://doi.org/10.1177/1099636216652581.
  5. Arefi, M. and Zenkour, A.M. (2018), "Free vibration analysis of a three-layered microbeam based on strain gradient theory and three-unknown shear and normal deformation theory", Steel Compos. Struct., 26(4), 421-437. http://doi.org/10.12989/scs.2018.26.4.421.
  6. Arefi, M., Bidgoli, E.M.R. and Civalek, O. (2020), "Bending response of FG composite doubly curved nanoshells with thickness stretching via higher-order sinusoidal shear theory", Mech. Based Des. Struct. Mach., 1, 1-29. http://doi.org/10.1080/15397734.2020.1777157.
  7. Bhaskar, K., Varadan, T.K. and Ali, J.S.M. (1996), "Thermoelastic solutions for orthotropic and anisotropic composite laminates", Compos. Part B, 27(5), 415-420. https://doi.org/10.1016/1359-8368(96)00005-4.
  8. Carrera, E. (2000), "An assessment of mixed and classical theories for the thermal stress analysis of orthotropic multi-layered plates", J. Therm. Stresses, 23(9), 797-831. https://doi.org/10.1080/014957300750040096.
  9. Carrera, E. and Ciuffreda, A. (2004), "Closed-form solutions to assess multilayered plate theories for various thermal stress problems", J. Therm. Stresses, 27(11), 1001-1031. https://doi.org/10.1080/01495730490498584.
  10. Carrera, E. (2005), "Transverse normal strain effects on thermal stress analysis of homogeneous and layered plates", AIAA J., 43(10), 2232-2242. https://doi.org/10.2514/1.11230.
  11. Carrera, E., Cinefra, M. and Fazzolari, F.A. (2013), "Some results on thermal stress by using unified formulation for plates and shells", J. Therm. Stresses, 36(6), 589-625. https://doi.org/10.1080/01495739.2013.784122.
  12. Cho, K.N., Striz, A.G. and Bert, C.W. (1989), "Thermal stress analysis of laminate using higher-order theory in each layer", J. Therm. Stresses, 12(3), 321-332. https://doi.org/10.1080/01495738908961970.
  13. Dehsaraji M.L., Arefi M. and Loghman A. (2020), "Three dimensional free vibration analysis of functionally graded nano cylindrical shell considering thickness stretching effect", Steel Compos. Struct., 34(5), 657-670. http://doi.org/10.12989/scs.2020.34.5.657.
  14. Dehsaraji, M.L., Arefi, M. and Loghman, A. (2021), "Size dependent free vibration analysis of functionally graded piezoelectric micro/nano shell based on modified couple stress theory with considering thickness stretching effect", Defence Tech., 17(1), 119-134. https://doi.org/10.1016/j.dt.2020.01.001.
  15. Dehsaraji, M.L., Arefi, M. and Loghman, A. (2021), "Thermo electro-mechanical buckling of FGP nano shell with considering thickness stretching effect based on size dependent analysis", Mech. Based Des. Struct. Mach., 1-22. https://doi.org/10.1080/15397734.2021.1873146.
  16. Fares, M.E., Zenkour, A.M. and El-Marghany, M.Kh. (2000), "Non-linear thermal effects on the bending response of cross-ply laminated plates using refined first-order theory", Compos. Struct., 49(3), 257-267. https://doi.org/10.1016/S0263-8223(99)00137-3.
  17. Ghugal, Y.M. and Shimpi, R.P. (2002), "A review of refined shear deformation theories of isotropic and anisotropic laminated plates", J. Reinf. Plast. Compos., 21(9), 775-811. https://doi.org/10.1177/073168402128988481.
  18. Ghugal, Y.M. and Kulkarni, S.K. (2011), "Thermal stress analysis of cross-ply laminated plates using refined shear deformation theory", J. Exp. App. Mech., 2(1), 47-66.
  19. Ghugal, Y.M. and Kulkarni, S.K. (2013), "Thermal flexural analysis of cross-ply laminated plates using trigonometric shear deformation theory", Lat. Amer. J. Solids Struct., 10(5), 1001-1023. https://doi.org/10.1590/S1679-78252013000500008
  20. Ghugal, Y.M. and Kulkarni, S.K. (2012), "Effect of aspect ratio on transverse displacements for orthotropic and two layer laminated plates subjected to non-linear thermal loads and mechanical loads", Int. J. Civ. Struct. Eng., 3(1), 186-196.
  21. Ghugal, Y.M. and Kulkarni, S.K. (2013), "Flexural analysis of cross-ply laminated plates subjected to nonlinear thermal and mechanical loadings", Acta Mech., 224(3), 675-690. https://doi.org/10.1007/s00707-012-0774-1.
  22. Jane, K.C. and Hong, C.C. (2000), "Thermal bending analysis of laminated orthotropic plates by the generalized differential quadrature method", Mech. Res. Commun., 27(2), 157-164. https://doi.org/10.1016/S0093-6413(00)00076-8.
  23. Kapania, R.K. and Mohan, P. (1996), "Static, free vibration and thermal analysis of composite plates and shells using a flat triangular shell element", Comput. Mech., 17, 343-357. https://doi.org/10.1007/BF00368557.
  24. Khare, R.K., Kant, T. and Garg, A.K. (2003), "Closed-form thermo-mechanical solutions of higher-order theories of cross-ply laminated shells", Compos. Struct., 59(3), 313-340. https://doi.org/10.1016/S0263-8223(02)00245-3.
  25. Khdeir, A.A. and Reddy, J.N. (1991), "Thermal stresses and deflections of cross-ply laminated plates using refined plate theories", J. Therm. Stresses, 14(4), 419-438. https://doi.org/10.1080/01495739108927077.
  26. Kirchhoff, G. (1850), "Uber das gleichgewicht und die bewegung einer elastischen scheibe", J. fur die Reine und Angew. Math., 40, 51-88. https://doi.org/10.1515/crll.1850.40.51.
  27. Matsunaga, H. (1992), "The application of a two-dimensional higher-order theory for the analysis of a thick elastic plate", Comput. Struct., 45(4), 633-648. https://doi.org/10.1016/0045-7949(92)90482-F.
  28. Matsunaga, H. (2002), "Assessment of a global higher-order deformation theory for laminated composite and sandwich plates", Compos. Struct., 56(3), 279-291. https://doi.org/10.1016/S0263-8223(02)00013-2.
  29. Matsunaga, H. (2003), "Interlaminar stress analysis of laminated composite and sandwich circular arches subjected to thermal/mechanical loading", Compos. Struct., 60(3), 345-358. https://doi.org/10.1016/S0263-8223(02)00340-9.
  30. Matsunaga H. (2004), "A Comparison between 2-D single-layer and 3-D layerwise theories for computing interlaminar stresses of laminated composite and sandwich plates subjected to thermal loadings", Compos. Struct., 64(2), 161-177. https://doi.org/10.1016/j.compstruct.2003.08.001.
  31. Matsunaga, H. (2005), "Thermal buckling of cross-ply laminated composite and sandwich plates according to a global higher-order deformation theory", Compos. Struct., 68(4), 439-454. https://doi.org/10.1016/j.compstruct.2004.04.010.
  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(2), 177-192. https://doi.org/10.1016/j.compstruct.2004.11.016.
  33. Matsunaga, H. (2007a), "Free vibration and stability of angle-ply laminated composite and sandwich plates under thermal loading", Compos. Struct., 77(2), 249-262. https://doi.org/10.1016/j.compstruct.2005.07.002.
  34. Matsunaga, H. (2007b), "Thermal buckling of cross-ply laminated composite shallow shells according to a global higher-order deformation theory", Compos. Struct., 81(2), 210-221. https://doi.org/10.1016/j.compstruct.2006.08.008.
  35. Mindlin, R.D. (1951), "Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates", J. Appl. Mech., 18(1), 31-38. https://doi.org/10.1115/1.4010217.
  36. Nguyen, T.N., Thai, C.H. and Xuan, H.N. (2016), "On the general framework of high order deformation theories for laminated composite plate structures: A novel unified approach", Int. J. Mech. Sci., 110, 242-255. https://doi.org/10.1016/j.ijmecsci.2016.01.012.
  37. Noor, A.K. and Burton, W.S. (1989), "Assessment of shear deformation theories for multilayered composite plates", Appl. Mech. Rev., 42(1), 1-13. https://doi.org/10.1115/1.3152418.
  38. Noor, A.K. and Burton, W.S. (1990), "Assessment of computational models for multilayered anisotropic plates", Compos. Struct., 14(3), 233-265. https://doi.org/10.1016/0263-8223(90)90050-O.
  39. Noor, A.K. and Burton, W.S. (1992), "Computational models for high- temperature multi-layered composite plates and shells", Appl. Mech. Rev., 45(10), 419-446. https://doi.org/10.1115/1.3119742.
  40. Reddy, J.N. (1984), "A simple higher-order theory for laminated composite plates", J. App. Mech., 51(4), 745-752. https://doi.org/10.1115/1.3167719.
  41. Reddy, J.N. (1993), "An evaluation of equivalent single layer and layerwise theories of composite laminates", Comput. Struct., 25(1-4), 21-35. https://doi.org/10.1016/0263-8223(93)90147-I.
  42. Vekua, I.N. (1985), Shell Theory: General Methods of Construction, Pitman Advanced Publishing Program, Boston, U.S.A.
  43. Yokoo, Y., and Matsunaga, H. (1974), "A general nonlinear theory of elastic shells", Int. J. Solids Struct., 10(2), 261-274. https://doi.org/10.1016/0020-7683(74)90023-7.
  44. Zenkour, A.M. (2004), "Analytical solution for bending of cross-ply laminated plates under thermomechanical loading", Compos. Struct., 65(3-4), 367-379. https://doi.org/10.1016/j.compstruct.2003.11.012.
  45. Zhavoronok, S.A. (2014), "Vekua-type linear theory of thick elastic shells", ZAMM J. Appl. Math. Mech., 94(1-2), 164-184. https://doi.org/10.1002/zamm.201200197.
  46. Zozulya, V.V. (2013), "A high order theory for linear thermoelastic shells: Comparison with classical theories", J. Eng., 1-19. https://doi.org/10.1155/2013/590480.
  47. Zozulya, V.V. (2015), "A higher order theory for shells, plates and rods", Int. J. Mech. Sci., 103, 40-54. https://doi.org/10.1016/j.ijmecsci.2015.08.025.