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Analysis of laminated and sandwich spherical shells using a new higher-order theory

  • Shinde, Bharti M. (Department of Civil Engineering, Sanjivani College of Engineering Kopargaon, Savitribai Phule Pune University) ;
  • Sayyad, Atteshamudin S. (Department of Civil Engineering, Sanjivani College of Engineering Kopargaon, Savitribai Phule Pune University)
  • Received : 2019.02.23
  • Accepted : 2019.05.30
  • Published : 2020.01.25
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Abstract

In the present study, a fifth-order shear and normal deformation theory using a polynomial function in the displacement field is developed and employed for the static analysis of laminated composite and sandwich simply supported spherical shells subjected to sinusoidal load. The significant feature of the present theory is that it considers the effect of transverse normal strain in the displacement field which is eliminated in classical, first-order and many higher-order shell theories, while predicting the bending behavior of the shell. The present theory satisfies the zero transverse shear stress conditions at the top and bottom surfaces of the shell. The governing equations and boundary conditions are derived using the principle of virtual work. To solve the governing equations, the Navier solution procedure is employed. The obtained results are compared with Reddy's and Mindlin's theory for the validation of the present theory.

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 shear deformation theories", Compos. Struct., 94(2), 494-500. https://doi.org/10.1016/j.compstruct.2011.08.011.
  2. Carrera, E. and Brischetto, S. (2009), "A comparison of various kinematic models for sandwich shell panels with soft core", J. Compos. Mater., 43(20), 2201-2221. https://doi.org/10.1177/0021998309343716.
  3. Carrera, E. and Brischetto, S., (2008) "Analysis of thickness locking in classical, refined and mixed theories for layered shells", Compos. Struct., 85 (1), 83-90. https://doi.org/10.1016/j.compstruct.2007.10.009.
  4. Carrera, E. and Valvano, S., (2017), "A variable kinematic shell formulation applied to thermal stress of laminated structures", J. Therm. Stress., 40(7), 803-827. https://doi.org/10.1080/01495739.2016.1253439.
  5. Cinefra, M., Carrera, E. and Fazzolari, F.A., (2013), "Some results on thermal stress of layered plates and shells by using unified formulation", J. Therm. Stress., 36(6), 589-625. https://doi.org/10.1080/01495739.2013.784122.
  6. Cinefra, M., Carrera, E., Brischetto, S. and Belouettar, S., (2010), "Thermo-mechanical analysis of functionally graded shells", J. Therm. Stress., 33(10), 942-963. https://doi.org/10.1080/01495739.2010.482379.
  7. Cinefra, M., Carrera, E., Lamberti, A. and Petrolo, M. (2015), "Results on best theories for metallic and laminated shells including layer-wise models", Compos. Struct., 126, 285-298. https://doi.org/10.1016/j.compstruct.2015.02.027.
  8. Lee, S.J. and Reddy, J.N. (2004) "Vibration suppression of laminated shell structures investigated using higher order shear deformation theory", Smart Mater. Struct., 13(5), 1176-1194. https://doi.org/10.1088/0964-1726/13/5/022.
  9. Liew, K.M., Zhao, X. and Ferreira, A.J.M. (2011), "A review of meshless methods for laminated and functionally graded plates and shells", Compos. Struct., 93(8), 2031-2041. https://doi.org/10.1016/j.compstruct.2011.02.018.
  10. Mantari, J.L. and Soares, C.G. (2012), "Analysis of isotropic and multilayered plates and shells by using a generalized higher-order shear deformation theory", Compos. Struct., 94(8), 2640-2656. https://doi.org/10.1016/j.compstruct.2012.03.018.
  11. Mantari, J.L. and Soares, C.G. (2014), "Optimized sinusoidal higher order shear deformation theory for the analysis of functionally graded plates and shells", Compos. Part B Eng., 56, 126-136. https://doi.org/10.1016/j.compositesb.2013.07.027.
  12. Mantari, J.L., Oktem, A.S. and Soares, C.G., (2012), "Bending and free vibration analysis of isotropic and multilayered plates and shells by using a new accurate higher-order shear deformation theory", Compos. Part B Eng., 43(8), 3348-3360. https://doi.org/10.1016/j.compositesb.2012.01.062.
  13. 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.
  14. Mindlin, R.D. (1951), "Influence of rotatory inertia and shear on flexural motions of isotropic elastic plates", ASME J. Appl. Mech., 18, 31-38. https://doi.org/10.1115/1.4010217
  15. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Cinefra, M., Roque, C.M.C., Jorge, R.M.N. and Soares, C.M.M. (2013), "Free vibration analysis of functionally graded shells by a higher-order shear deformation theory and radial basis functions collocation, accounting for through-the-thickness deformations", Eur. J. Mech. A/Solids, 37, 24-34. https://doi.org/10.1016/j.euromechsol.2012.05.005.
  16. Oktem, A.S., Mantari, J.L. and Soares, C.G. (2012), "Static response of functionally graded plates and doubly-curved shells based on a higher order shear deformation theory", Eur. J. Mech. A/Solids, 36, 163-172. https://doi.org/10.1016/j.euromechsol.2012.03.002.
  17. Pagano, N.J. (1970), "Exact solutions for rectangular bidirectional composites and sandwich plates", J. Compos. Mater., 4(1), 20-34. https://doi.org/10.1177/002199837000400102.
  18. Pradyumna, S. and Bandyopadhyay, J.N., (2008), "Static and free vibration analyses of laminated shells using a higher-order theory", J. Reinf. Plast. Compos., 27(2), 167-186. https://doi.org/10.1177/0731684407081385.
  19. Qatu, M.S. (2002), "Recent research advances in the dynamic behavior of shells: 1989-2000, Part 1: Laminated composite shells", Appl. Mech. Rev., 55, 325-350. https://doi.org/10.1115/1.1483079.
  20. Qatu, M.S. (2002), "Recent research advances in the dynamic behavior of shells: 1989-2000, Part 2: Homogeneous shells", Appl. Mech. Rev., 55, 415-434. https://doi.org/10.1115/1.1483078.
  21. Qatu, M.S. and Asadi, E. (2012), "Vibration of doubly curved shallow shells with arbitrary boundaries", Appl. Acoust., 73(1), 21-27. https://doi.org/10.1016/j.apacoust.2011.06.013.
  22. Reddy, J.N. (1984a), "Exact solutions of moderately thick laminated shells", J. Eng. Mech., 110(5), 794-809. https://doi.org/10.1061/(ASCE)0733-9399(1984)110:5(794).
  23. Reddy, J.N. (1984b), "A simple higher-order theory for laminated composite plates", J. Appl. Mech., 51(4), 745-752. https://doi.org/10.1115/1.3167719.
  24. Sayyad, A.S. and Ghugal, Y.M. (2015), "On the free vibration analysis of laminated composite and sandwich plates: A review of recent literature with some numerical results", Compos. Struct., 129, 177-201. https://doi.org/10.1016/j.compstruct.2015.04.007.
  25. Sayyad, A.S. and Ghugal, Y.M. (2017), "Bending, buckling and free vibration of laminated composite and sandwich beams: A critical review of literature", Compos. Struct., 171, 486-504. https://doi.org/10.1016/j.compstruct.2017.03.053.
  26. Sayyad, A.S. and Ghugal, Y.M. (2019), "Static and free vibration analysis of laminated composite and sandwich spherical shells using a generalized higher-order shell theory", Compos. Struct., 219, 129-146. https://doi.org/10.1016/j.compstruct.2019.03.054.
  27. Tornabene, F. (2011), "2-D GDQ solution for free vibrations of anisotropic doubly-curved shells and panels of revolution", Compos. Struct., 93(7), 1854-1876. https://doi.org/10.1016/j.compstruct.2011.02.006.
  28. Tornabene, F. (2011), "Free vibrations of anisotropic doubly-curved shells and panels of revolution with a free-form meridian resting on Winkler-Pasternak elastic foundations", Compos. Struct., 94(1), 186-206. https://doi.org/10.1016/j.compstruct.2011.07.002.
  29. Tornabene, F. (2011), "Free vibrations of laminated composite doubly-curved shells and panels of revolution via the GDQ method", Comput. Methods Appl. Mech. Eng., 200(9-12), 931-952. https://doi.org/10.1016/j.cma.2010.11.017.
  30. Tornabene, F. and Viola, E. (2013), "Static analysis of functionally graded doubly-curved shells and panels of revolution", Meccanica, 48(4), 901-930. https://doi.org/10.1007/s11012-012-9643-1.
  31. Tornabene, F., Fantuzzi, N. and Bacciocchi, M. (2016), "On the mechanics of laminated doubly-curved shells subjected to point and line loads", Int. J. Eng. Sci., 109, 115-164. https://doi.org/10.1016/j.ijengsci.2016.09.001.
  32. Tornabene, F., Fantuzzi, N., Bacciocchi, M. and Viola, E. (2015), "Accurate inter-laminar recovery for plates and doubly-curved shells with variable radii of curvature using layer-wise theories", Compos. Struct., 124, 368-393. https://doi.org/10.1016/j.compstruct.2014.12.062.
  33. Tornabene, F., Fantuzzi, N., Viola, E. and Carrera, E. (2014), "Static analysis of doubly-curved anisotropic shells and panels using CUF approach, differential geometry and differential quadrature method", Compos. Struct., 107, 675-697. https://doi.org/10.1016/j.compstruct.2013.08.038.
  34. Tornabene, F., Liverani, A. and Caligiana, G. (2012), "General anisotropic doubly-curved shell theory: A differential quadrature solution for free vibrations of shells and panels of revolution with a free-form meridian", J. Sound Vib., 331(22), 4848-4869. https://doi.org/10.1016/j.jsv.2012.05.036.
  35. 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.
  36. Tornabene, F., Viola, E. and Inman, D.J. (2009), "2-D differential quadrature solution for vibration analysis of functionally graded conical, cylindrical shell and annul plate structures", J. Sound Vib., 328(3), 259-290. https://doi.org/10.1016/j.jsv.2009.07.031.
  37. Viola, E., Tornabene F. and Fantuzzi, N. (2013), "Static analysis of completely doubly-curved laminated shells and panels using general higher-order shear deformation theories", Compos. Struct., 101, 59-93. https://doi.org/10.1016/j.compstruct.2013.01.002.