Steel and Composite Structures

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Assessment of non-polynomial shear deformation theories for thermo-mechanical analysis of laminated composite plates

  • Joshan, Yadwinder S. (Department of Mechanical Engineering, Thapar Institute of Engineering and Technology) ;
  • Grover, Neeraj (Department of Mechanical Engineering, Thapar Institute of Engineering and Technology) ;
  • Singh, B.N. (Department of Aerospace Engineering, Indian Institute of Technology Kharagpur)
  • Received : 2017.04.21
  • Accepted : 2018.04.16
  • Published : 2018.06.25
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Abstract

In the present work, the recently developed non-polynomial shear deformation theories are assessed for thermo-mechanical response characteristics of laminated composite plates. The applicability and accuracy of these theories for static, buckling and free vibration responses were ascertained in the recent past by several authors. However, the assessment of these theories for thermo-mechanical analysis of the laminated composite structures is still to be ascertained. The response characteristics are investigated in linear and non-linear thermal gradient and also in the presence and absence of mechanical transverse loads. The laminated composite plates are modelled using recently developed six shear deformation theories involving different shear strain functions. The principle of virtual work is used to develop the governing system of equations. The Navier type closed form solution is adopted to yield the exact solution of the developed equation for simply supported cross ply laminated plates. The thermo-mechanical response characteristics due to these six different theories are obtained and compared with the existing results.

Keywords

Acknowledgement

Supported by : Science and Engineering Research Board (SERB)

References

  1. Akavci, S. (2010), "Two new hyperbolic shear displacement models for orthotropic laminated composite plates", Mech. Compos. Mater., 46(2), 215-226. https://doi.org/10.1007/s11029-010-9140-3
  2. Aydogdu, M. (2009), "A new shear deformation theory for laminated composite plates", Compos. Struct., 89(1), 94-101. https://doi.org/10.1016/j.compstruct.2008.07.008
  3. Bhaskar, K., Varadan, T.K. and Ali, J.S.M. (1996), "Thermoelastic solution for orthotropic and anisotropic composite laminates", Compos. Part B, 27(5), 415-420. https://doi.org/10.1016/1359-8368(96)00005-4
  4. Bouchafa, A., Bachir Bouiadjra, M., Houari, M.S.A. and Tounsi, A. (2015), "Thermal stresses anddeflections of functionally graded sandwich plates using a new refined hyperbolic shear deformationtheory", Steel Compos. Struct., Int. J., 18(6), 1493-1515. https://doi.org/10.12989/scs.2015.18.6.1493
  5. Carrera, E. (1998), "Evaluation of layerwise mixed theories for laminated plates analysis", AIAA J., 36(5), 830-839. https://doi.org/10.2514/2.444
  6. Carrera, E. (2001), "Developments, ideas, and evaluations based upon Reissner's mixed variational theorem in the modeling of multilayered plates and shells", Appl. Mech. Rev., 54(4), 301-329. https://doi.org/10.1115/1.1385512
  7. Carrera, E. (2003a), "Theories and finite elements for multilayered plates and shells: a unified compact formulation with numerical assessment and benchmarking", Arch. Comput. Methods Eng., 10(3), 215-296. https://doi.org/10.1007/BF02736224
  8. Carrera, E. (2003b), "Historical review of zig-zag theories for multi-layered plates and shells", Appl. Mech. Rev., 56(3), 287-308. https://doi.org/10.1115/1.1557614
  9. Cetkovic, M. (2015), "Thermo-mechanical bending of laminated composite and sandwich plates using layerwise displacement model", Compos. Struct., 125, 388-399. https://doi.org/10.1016/j.compstruct.2015.01.051
  10. Chattibi, F., Benrahou, K.H., Benachour, A., Nedri, K. and Tounsi, A. (2015), "Thermomechanical effects on the bending of antisymmetric cross-ply composite plates using a four variable sinusoidal theory", Steel Compos. Struct., Int. J., 19(1), 93-110. https://doi.org/10.12989/scs.2015.19.1.093
  11. Daouadji, T.H., Tounsi, A. and Bedia, E.A.A. (2013), "A new higher order shear deformation model for static behavior of functionally graded plates", Adv. Appl. Math. Mech., 5(3), 351-364. https://doi.org/10.4208/aamm.11-m11176
  12. Fares, M.E. and Zenkour, A.M. (1999), "Mixed variational formula for the thermal bending of laminated plates", J. Therm. Stresses, 22(3), 347-365. https://doi.org/10.1080/014957399280913
  13. Ferreira, A.J.M., Roque, C.M.C. and Jorge, R.M.N. (2005), "Analysis of composite plates by trigonometric shear deformation theory and multiquadrics", Comput. Struct., 83(27), 2225-2237. https://doi.org/10.1016/j.compstruc.2005.04.002
  14. 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), 775-813. https://doi.org/10.1177/073168402128988481
  15. Grover, N., Maiti, D.K. and Singh, BN. (2013a), "New nonpolynomial shear-deformation theories for structural behavior of laminated composite and sandwich plates", AIAA J., 51(8), 1861-1871. https://doi.org/10.2514/1.J052399
  16. Grover, N., Maiti, D.K. and Singh, B.N. (2013b), "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
  17. Joshan, Y.S., Grover, N. and Singh, B.N. (2017), "A new non-polynomial four variable shear deformation theory in axiomatic formulation for hygro-thermo-mechanical analysis of laminated composite plates", Compos. Struct., 182, 685-693. https://doi.org/10.1016/j.compstruct.2017.09.029
  18. Kant, T. and Khare, R.K. (1997), "A higher-order facet quadrilateral composite shell element", Int. J. Numer. Meth. Eng., 40(24), 4477-4499. https://doi.org/10.1002/(SICI)1097-0207(19971230)40:24<4477::AID-NME229>3.0.CO;2-3
  19. Kant, T. and Swaminathan, K. (2002), "Analytical solution for the static analysis of laminated composite and sandwich plates based on a higher order refined theory", Compos. Struct., 56(4), 329-344. https://doi.org/10.1016/S0263-8223(02)00017-X
  20. Karama, M., Afaq, K.S. and Mistou, S. (2003), "Mechanical behaviour of laminated composite beam by the new multilayered laminated composite structures model with transverse shear stress continuity", Int. J. Solids Struct., 40(6), 1525-1546. https://doi.org/10.1016/S0020-7683(02)00647-9
  21. Khandan, R., Noroozi, S., Sewell, P. and Vinney, J. (2012), "The development of laminated composite plate theories: a review", J. Mater. Sci., 47(16), 5901-5910. https://doi.org/10.1007/s10853-012-6329-y
  22. Khare, R.K., Kant, T. and Garg, A.K. (2003), "Closed-form thermo-mechanical solutions of higher-order theories of cross-ply laminated shallow shells", Compos. Struct., 59(3), 313-340. https://doi.org/10.1016/S0263-8223(02)00245-3
  23. Khdeir, A.A. and Reddy, J.N. (1991), "Thermal stresses and deflections of crossply laminated plates using refined plate theories", J. Therm. Stresses, 14(4), 419-438. https://doi.org/10.1080/01495739108927077
  24. Maiti, D.K. and Sinha, P.K. (1994), "Bending, free vibration and impact response of thick laminated composite plates", Compos. Struct., 49(0), 115-129.
  25. Mantari, J.L. and Ore, M. (2015), "Free vibration of single and sandwich laminated composite plates by using a simplified FSDT", Compos. Struct., 22(4), 713-732.
  26. 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(1), 37-49. https://doi.org/10.1016/j.compstruct.2011.07.020
  27. Mantari, J.L., Oktem, A.S. and Soares, C.G. (2012), "A new trigonometric shear deformation theory for isotropic, laminated composite and sandwich plates", Int. J. Solids Struct., 49(1), 43-53. https://doi.org/10.1016/j.ijsolstr.2011.09.008
  28. Mechab, B., Mechab, I. and Benaissa, S. (2012), "Analysis of thick orthotropic laminated composite plates based on higher order shear deformation theory by the new function under thermo-mechanical loading", Compos. Part B Eng., 43(3), 1453-1458. https://doi.org/10.1016/j.compositesb.2011.11.037
  29. Meiche, N.E., Tounsi, A., Zlane, N., Mechab, I. and Bedia, E.A.A. (2011), "A new hyperbolic shear deformation theory for buckling and vibration of functionally graded sandwich plate", Int. J. Mech. Sci., 53(4), 237-247. https://doi.org/10.1016/j.ijmecsci.2011.01.004
  30. Merdaci, S., Tounsi, A. and Bakora, Y. (2016), "A novel four variable refined plate theory for laminated composite plates", Steel Compos. Struct., Int. J., 18(4), 1063-1081.
  31. Mindlin, R.D. (1951), "Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates", J. Appl. Mech., Trans. ASME, 18(1), 31-38.
  32. Pai, P.F. (1995), "A new look at shear correction factors and warping functions of anisotropic laminates", Int. J. Solids Struct., 32(16), 2295-2313. https://doi.org/10.1016/0020-7683(94)00258-X
  33. Panduro, R.M.R. and Mantari, J.L. (2017), "Hygro-thermo-mechanical behavior of classical composites", Ocean Eng., 137, 224-240. https://doi.org/10.1016/j.oceaneng.2017.03.049
  34. Ramos, I.A., Mantari, J.L. and Zenkour, A.M. (2016), "Laminated composite plates subject tothermal load using trigonometric theory based on Carrera Unified Formulation", Compos. Struct., 143, 324-335. https://doi.org/10.1016/j.compstruct.2016.02.020
  35. Reddy, J.N. (1984), "A simple higher-order theory for laminated composite plates", J. Appl. Mech., 51(4), 745-752. https://doi.org/10.1115/1.3167719
  36. Reddy, J.N. (1990), "A review of refined theories of laminated composite plates", Shock Vib. Dig., 22(7), 3- 17. https://doi.org/10.1177/058310249002200703
  37. Reddy, J.N. (2004), Mechanics of Laminated Composite Plate: Theory and Analysis, CRC Press, New York, NY, USA.
  38. Reddy, J.N. and Hsu, Y.S. (1980), "Effects of shear deformation and anisotropy on the thermal bending of layered composite plates", J. Therm. Stresses, 3(4), 475-493. https://doi.org/10.1080/01495738008926984
  39. Reddy, J.N. and Robbins, D.H. Jr. (1994), "Theories and computational models for composite laminates", Appl. Mech. Rev., 47(6), 147-169. https://doi.org/10.1115/1.3111076
  40. Reissner, E. (1945), "The effect of transverse shear deformation on the bending of elastic plates", J. Appl. Mech., Trans. ASME, 12(2), 69-77.
  41. Sahoo, R. and Singh, B.N. (2013), "A new inverse hyperbolic zigzag theory for the static analysis of laminated composite and sandwich plates", Compos. Struct., 105, 385-397. https://doi.org/10.1016/j.compstruct.2013.05.043
  42. Sahoo, R. and Singh, B.N. (2014), "A new trigonometric zigzag theory for buckling and free vibration analysis of laminated composite and sandwich plates", Compos. Struct., 117, 316-332. https://doi.org/10.1016/j.compstruct.2014.05.002
  43. Shimpi, R.P. and Patel, H.G. (2006), "Free vibrations of plate using two variable refined plate theory", J. Sound. Vib., 296(4-5), 979-999. https://doi.org/10.1016/j.jsv.2006.03.030
  44. Shimpi, R.P., Arya, H. and Naik, N.K. (2003), "A higher order displacement model for the plate analysis", J. Reinf. Plast. Compos., 22(18), 1667-1688. https://doi.org/10.1177/073168403027618
  45. Singh, B.N. and Grover, N. (2013), "Stochastic methods for the analysis of uncertain composites", J. Ind. Instt. Sci. A Multidisciplinary Rev. J., 93(4), 603-620.
  46. Soldatos, K.P. and Timarci, T. (1993), "A unified formulation of laminated composite, shear deformable, five-degrees-of-freedom cylindrical shell theories", Compos. Struct., 25, 165-171. https://doi.org/10.1016/0263-8223(93)90162-J
  47. 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
  48. Thai, H.T. and Vo, T.P. (2013), "A new sinusoidal shear deformation theory for bending, buckling, and vibration of functionally graded plates", Appl. Math. Model., 37(5), 3269-3281. https://doi.org/10.1016/j.apm.2012.08.008
  49. Thai, C.H., Ferreira, A.J.M., Bordas, S.P.A., Rabczuk, T. and Xuan, H.N. (2015), "Isogeometric analysis of laminated composite and sandwich plates using a new inverse trigonometric shear deformation theory", Eur. J. Mech. A/Solids., 43, 89-108.
  50. Tounsi, A., Houari, M.S.A., Benyoucef, S. and Bedia, E.A.A. (2013), "A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates", Aero. Sci. Technol., 24(1), 209-220. https://doi.org/10.1016/j.ast.2011.11.009
  51. Touratier, M. (1991), "An efficient standard plate theory", Int. J. Eng. Sci., 29(8), 901-916. https://doi.org/10.1016/0020-7225(91)90165-Y
  52. Wu, C.H. and Tauchert, T.R. (1980), "Thermoelastic analysis of laminated plates. 2: antisymmetric cross-ply and angle-ply laminates", J. Therm. Stresses, 3(3), 65-78.
  53. Zenkour, A.M. (2004), "Analytical solution for bending of cross-ply laminated plates under thermo-mechanical loading", Compos. Struct., 65(3-4), 367-379. https://doi.org/10.1016/j.compstruct.2003.11.012
  54. Zenkour, A.M. (2013), "A simple four-unknown refined theory for bending analysis of functionally graded plates", Appl. Math. Model., 37(20-21), 9041-9051. https://doi.org/10.1016/j.apm.2013.04.022
  55. Zhang, Y.X. and Yang, C.H. (2009), "Recent developments in finite element analysis for laminated composite plates", Compos. Struct., 88(1), 147-157. https://doi.org/10.1016/j.compstruct.2008.02.014