Advances in aircraft and spacecraft science

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

A new higher-order displacement model for laminated composite cylindrical shells

  • Ali Meksi (University Mustapha Stambouli of Mascara) ;
  • Kada Draiche (Department of Civil Engineering, University of Tiaret) ;
  • Emrah Madenci (Department of Civil Engineering, Necmettin Erbakan University) ;
  • Abdelouahed Tounsi (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes)
  • Received : 2024.10.26
  • Accepted : 2025.05.09
  • Published : 2025.06.25
⟨ Previous Next ⟩

Abstract

This paper presents a unified solution approach to investigate the bending and free vibration behaviors of laminated composite cylindrical shells with varying radii of curvature and simply supported edges, using a new refined shear deformation shell theory (RSDST). The theoretical formulation of the proposed approach is based on a new displacement model that incorporates undetermined integral terms to account for the effects of transverse shear deformation. It also meets the shear stress-free boundary conditions on the upper and lower surfaces of the cylindrical shell. The governing equations are derived from the principle of virtual work and are resolved using Navier-type closed form solutions. The effects of material properties and geometric parameters on the static bending and free vibration of laminated composite cylindrical shells are presented and discussed in detail. Convergence and validation studies clearly indicate that the values for displacements and stresses derived from the present theory are highly consistent with those of previous higher-order shell theories. Furthermore, a satisfactory convergence was observed when compared with 3D elasticity solutions (the percentage errors for transverse shear stresses are a maximum of 1.38%, 3.19% and 21.33% for isotropic, orthotropic and laminated composite cylindrical shells, respectively). It is shown that the present model with only four variables is able to accurately predict the stress distributions and natural frequencies, with less computational effort compared to conventional HSDST models.

Keywords

References

  1. Asadi, E., Wang, W. and Qatu, M.S. (2012), "Static and vibration analyses of thick deep laminated cylindrical shells using 3D and various deformation theories", Compos. Struct., 94(2), 494-500. https://doi.org/10.1016/j.compstruct.2011.08.011.
  2. Bhaskar, K. and Varadan, T.K. (1991), "A higher-order theory for bending analysis of laminated shells of revolution", Comput. Struct., 40(4), 815-819. https://doi.org/10.1016/0045-7949 (91)90310-I.
  3. Bhimaraddi, A. and Chandrashekhara, K. (1992), "Three-dimensional elasticity solution for static response of simply supported orthotropic cylindrical shells", Compos. Struct., 20(4), 227-235. https://doi.org/10.1016/0263-8223(92)90028-B.
  4. Civalek, O. (2013), "Vibration analysis of laminated composite conical shells by the method of discrete singular convolution based on the shear deformation theory", Compos. Part B Eng., 45(1), 1001-1009. https://doi.org/10.1016/j.compositesb.2012. 05.018.
  5. Dewangan, H.C. and Panda, S.K. (2022), "Nonlinear thermoelastic numerical frequency analysis and experimental verification of cutout abided laminated shallow shell structure", J. Press. Ves. Technol., 144(6), 061903. https://doi.org/10.1115/1.4054843.
  6. Draiche, K., Tounsi, A., Ibrahim, K.D. and Tlidji, Y. (2024), "An improved mathematical model for static and dynamic analysis of functionally graded doubly-curved shells", Arch. Appl. Mech., 94, 1589-1611. https://doi.org/10.1007/s00419-024-02595-5.
  7. Errico, F., Franco, F., Ichchou, M., De Rosa, S. and Petrone, G. (2019), "An investigation on the vibrations of laminated shells under aeroacoustic loads using a WFE approach", Adv. Aircraft Spacecraft Sci., 6(6), 463-478. https://doi.org/10.12989/aas.2019.6.6.463.
  8. Ghasemi, M.A., Yazdani, M. and Hosseini, S.M. (2013), "Analysis of effective parameters on the buckling of grid stiffened composite shells based on first order shear deformation theory", Modares Mech. Eng., 13(10), 51-61.
  9. Jafari, A.A., Khalili, S.M.R. and Azarafza, R. (2005), "Transient dynamic response of composite circular cylindrical shells under radial impulse load and axial compressive loads", Thin Wall. Struct., 43(11), 1763-1786. https://doi.org/10.1016/j.tws.2005. 06.009.
  10. Kar, V.R., Mahapatra, T.R. and Panda, S.K. (2015), "Nonlinear flexural analysis of laminated composite flat panel under hygro-thermo-mechanical loading", Steel Compos. Struct., 19(4), 1011-1033. https://doi.org/10.12989/scs.2015.19.4.1011.
  11. Karama, M., Afaq, K.S. and Mistou, S. (2009), "A new theory for laminated composite plates", Proc. Inst. Mech. Eng., Part L: J. Mater.: Des. Appl., 223(2), 53-62. https://doi.org/10.1243/14644207JMDA189.
  12. Kirchhoff, G.R. (1850), "Uber das Gleichgewicht und die Bewegung einer elastichen Scheibe", J. Pure Appl. Math., 40, 51-88. https://doi.org/10.1515/crll.1850.40.51.
  13. Kumar, A., Chakrabarti, A. and Bhargava, P. (2013), "Vibration of laminated composite cylindrical shells with cutouts using higher order theory", Int. J. Sci. Eng. Res., 4(5), 199-202.
  14. Kumar, P., Arya, R., Sharma, N., Hirwani, C.K. and Panda, S.K. (2023), "Curved fiber-reinforced laminated composite panel and variable stiffness influence on eigenfrequency responses: A higher-order FE approach", J. Vib. Eng. Technol., 11, 2349-2359. https://doi.org/10.1007/s42417-022-00706-6.
  15. Lai, A., Jia, J., Zhou, Z., Xu, X. and Lim, C.W. (2022), "Homotopic analysis for post-buckling of cylindrical shells with local thickness defects", Acta Astronautica, 193, 44-55. https://doi.org/10.1016/j.actaastro.2022. 01.005.
  16. Lam, K.Y. and Loy, C.T. (1994), "On vibrations of thin rotating laminated composite cylindrical shells", Compos. Eng., 4(11), 1153-1167. https://doi.org/10.1016/0961-9526(95)91289-S.
  17. Li, M., Guedes Soares, C., Liu, Z. and Zhang, P. (2024), "Free and forced vibration analysis of carbon/glass hybrid composite laminated plates under arbitrary boundary conditions", Appl. Compos. Mater., 31, 1687-1710. https://doi.org/10.1007/s10443-024-10235-y.
  18. Li, X., Du, C.C. and Li, Y.H. (2018), "Parametric resonance of a FG cylindrical thin shell with periodic rotating angular speeds in thermal environment", Appl. Math. Model., 59, 393-409. https://doi.org/10.1016/j.apm.2018.01.048.
  19. Liew, K.M. and Lim, C.W. (1996), "A higher-order theory for vibration of doubly curved shallow shells", ASME J. Appl. Mech., 63(3), 587-593. https://doi.org/10.1115/1.2823338.
  20. Mahapatra, T.R. and Panda, S.K. (2010), "Thermoelastic vibration analysis of laminated doubly curved shallow panels using non-Linear FEM", J. Therm. Stress., 38(1), 39-68. https://doi.org/10.1080/01495739.2014.976125.
  21. Mantari, J.L., Oktem, A.S. and Guedes Soares, C. (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.
  22. Matsunaga, H. (2007), "Vibration and stability of cross-ply laminated composite shallow shells subjected to in-plane stresses", Compos. Struct., 78(3), 377-391. https://doi.org/10.1016/j.compstruct.2005.10.013.
  23. 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.
  24. Monge, J.C., Mantari, J.L., Yarasca, J. and Arciniega, R.A. (2019), "On bending response of doubly curved laminated composite shells using hybrid refined models", J. Appl. Comput. Mech., 5(5), 875-899. https://doi.org/10.22055/jacm.2019.27297.1397.
  25. Naghdi, P.M. (1973), "The theory of shells and plates", Linear Theories of Elasticity and Thermoelasticity: Linear and Nonlinear Theories of Rods, Plates, and Shells, Springer Berlin Heidelberg, Berlin, Heidelberg.
  26. Panda, S.K. and Singh, B.N. (2010), "Nonlinear free vibration analysis of thermally post-buckled composite spherical shell panel", Int. J. Mech. Mater. Des., 6, 175-188. https://doi.org/10.1007/s10999-010-9127-1.
  27. Qatu, M.S. (1999), "Accurate equations for laminated composite deep thick shells", Int. J. Solid. Struct., 36(19), 2917-2941. https://doi.org/10.1016/S0020-7683(98)00134-6.
  28. Ramteke, P.M., Mehar, K., Sharma, N. and Panda, S.K. (2021), "Numerical prediction of deflection and stress responses of functionally graded structure for grading patterns (power-Law, sigmoid, and exponential) and variable porosity (even/uneven)", Scientia Iranica, 28(2), 811-829. https://doi.org/10.24200/sci. 2020.55581.4290.
  29. 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.
  30. Reddy, J.N. and Liu, C.F. (1985), "A higher-order shear deformation theory of laminated elastic shells", Int. J. Eng. Sci., 23(3), 319-330. https://doi.org/10.1016/0020-7225(85)90051-5.
  31. Reissner, E. (1955), "Non-linear effects in vibrations of cylindrical shells", Ramo-Wooldridge Corporation, Guided Missile Research Division, Aeromechanics Section.
  32. Remil, A., Benrahou, K.H., Draiche, K., Bousahla, A.A. and Tounsi, A. (2019), "A simple HSDT for bending, buckling and dynamic behavior of laminated composite plates", Struct. Eng. Mech., 70(3), 325-337. https://doi.org/10.12989/sem.2019.70.3.325.
  33. Saad, A.L., Nuwairan, M. and Javed, S. (2021), "Free vibration of composite cylindrical shells based on third-order shear deformation theory", J. Math., 2021(1), 3792164. https://doi.org/10.1155/2021/3792164.
  34. Sahoo, S.S., Panda, S.K. and Sen, D. (2016), "Effect of delamination on static and dynamic behavior of laminated composite plate", AIAA J., 54(8), 2530-2544. https://doi.org/10.2514/1.J054908.
  35. Sahu, P., Sharma, N., Dewangan, H.C. and Panda, S.K. (2022), "Thermo-mechanical transient flexure of Glass-Carbon-Kevlar-Reinforced hybrid curved composite shell panels: An experimental verification", Int. J. Appl. Mech., 14(01), 2150120. https://doi.org/10.1142/S1758825121501209.
  36. Satankar, R.K., Sharma, N., Panda, S.K. and Mohapatra, S.S. (2020), "Experimental and simulation study of eigen frequency responses of Luffa cylindrica sponge fibre polymer composite", Mater. Today: Proc., 33, 5561-5565. https://doi.org/10.1016/j.matpr.2020.03.552.
  37. Sayyad, A.S. and Ghugal, Y.M. (2022), "Assessment of refined higher order theories for the static and vibration analysis of laminated composite cylindrical shells", J. Mech. Eng. Sci., 16(2), 8848-8861. https://doi.org/10.15282/jmes.16.2.2022.04. 0700.
  38. Sharma, N., Mahapatra, T.R. and Panda, S.K. (2017), "Vibro-acoustic behaviour of shear deformable laminated composite flat panel using BEM and the higher order shear deformation theory", Compos. Struct., 180, 116-129. https://doi.org/10.1016/j.compstruct.2017.08.012.
  39. Sharma, N., Mahapatra, T.R., Panda, S.K. and Hirwani, C.K. (2018), "Acoustic radiation and frequency response of higher-order shear deformable multilayered composite doubly curved shell panel-An experimental validation", Appl. Acoust., 133, 38-51. https://doi.org/10.1016/j.apacoust.2017.12.013.
  40. Sheng, G.G. and Wang, X. (2018), "The dynamic stability and nonlinear vibration analysis of stiffened functionally graded cylindrical shells", Appl. Math. Model., 56, 389-403. https://doi.org/10.1016/j.apm.2017.12.021.
  41. Shinde, B.M and Sayyad, A.S. (2020), "Analysis of laminated and sandwich spherical shells using a new higher-order theory", Adv. Aircraft Spacecraft Sci., 7(1), 19-40. https://doi.org/10.12989/aas.2020.7.1.019.
  42. Simitses, G.J. and Chen, Z. (1988), "Buckling of delaminated, long, cylindrical panels under pressure", Comput. Struct., 28(2), 173-184. https://doi.org/10.1016/0045-7949(88)90037-5.
  43. Singh, V.K., Mahapatra, T.R. and Panda, S.K. (2016), "Nonlinear transient analysis of smart laminated composite plate integrated with PVDF sensor and AFC actuator", Compos. Struct., 157, 121-130. https://doi.org/10.1016/j.compstruct.2016.08.020.
  44. Sivadas, K.R. and Ganesan, N. (1991), "Vibration analysis of laminated conical shells with variable thickness", J. Sound Vib., 148(3), 477-491. https://doi.org/10.1016/0022-460X(91)90479-4.
  45. Sobhani, E. (2023), "Improvement of vibrational characteristics of multipurpose structures (plate and shells) used in aerospace components by deploying Graphene Oxide Powders (GOPs) in a matrix as a nanoreinforcement: A comprehensive study", Eng. Anal. Bound. Elem., 146, 598-635. https://doi.org/10.1016/j.enganabound.2022.11.014.
  46. Soldatos, K.P. (1992), "A transverse shear deformation theory for homogeneous monoclinic plates", Acta Mechanica., 94(3) 195-220. https://doi.org/10.1007/BF01176650.
  47. Swami, S.K. and Ghugal, Y.M. (2021), "Thermoelastic bending analysis of laminated plates subjected to linear and nonlinear thermal loads", Adv. Aircraft Spacecraft Sci., 8(3), 213-237. https://doi.org/10.12989/aas.2021.8.3.213.
  48. Tang, D., Yao, X., Wu, G. and Peng, Y. (2017), "Free and forced vibration analysis of multi-stepped circular cylindrical shells with arbitrary boundary conditions by the method of reverberation-ray matrix", Thin Wall. Struct., 116, 154-168. https://doi.org/10.1016/j.tws.2017.03.023.
  49. Thakur, S.N., Ray, C. and Chakraborty, S. (2017), "A new efficient higher-order shear deformation theory for a doubly curved laminated composite shell", Acta Mechanica, 228(1), 69-87. https://doi.org/10.1007/s00707-016-1693-3.
  50. Topal, U. (2009), "Multiobjective optimization of laminated composite cylindrical shells for maximum frequency and buckling load", Mater. Des., 30(7), 2584-2594. https://doi.org/10.1016/j.matdes.2008.09.020.
  51. Torkamani, Sh., Navazi, H.M., Jafari, A.A. and Bagheri, M. (2009), "Structural similitude in free vibration of orthogonally stiffened cylindrical shells", Thin Wall. Struct., 47(11), 1316-1330. https://doi.org/10.1016/j.tws.2009.03.013.
  52. Tornabene, F., Viola, E. and Fantuzzi, N. (2013), "General higher-order equivalent single layer theory for free vibrations of doubly-curved laminated composite shells and panels", Compos. Struct., 104, 94-117. https://doi.org/10.1016/j.compstruct.2013.04.009.
  53. 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.
  54. Zenkour, A.M. (2015), "Thermal bending of layered composite plates resting on elastic foundations using four-unknown shear and normal deformations theory", Compos. Struct., 122, 260-270. https://doi.org/10.1016/j.compstruct.2014.11.064.
  55. Zhong, R., Tang, J., Wang, A., Shuai, C. and Wang, Q. (2019), "An exact solution for free vibration of cross-ply laminated composite cylindrical shells with elastic restraint ends", Comput. Math. Appl., 77(3), 641-661. https://doi.org/10.1016/j.camwa.2018.10.006.