Steel and Composite Structures

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Static analysis of singly and doubly curved panels on rectangular plan-form

  • Bahadur, Rajendra (Department of Applied Mechanics, MNNIT) ;
  • Upadhyay, A.K. (Department of Applied Mechanics, MNNIT) ;
  • Shukla, K.K. (Department of Applied Mechanics, MNNIT)
  • Received : 2016.08.13
  • Accepted : 2017.05.22
  • Published : 2017.08.30
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Abstract

In the present work, an analytical solution for the static analysis of laminated composites, functionally graded and sandwich singly and doubly curved panels on the rectangular plan-form, subjected to uniformly distributed transverse loading is presented. Mathematical formulation is based on the higher order shear deformation theory and principle of virtual work is applied to derive the equations of equilibrium subjected to small deformation. A solution methodology based on the fast converging finite double Chebyshev series is used to solve the linear partial differential equations along with the simply supported boundary condition. The effect of span to thickness ratio, radius of curvature to span ratio, stacking sequence, power index are investigated. The accuracy of the solution is checked by the convergence study of non-dimensional central deflection and moments. Present results are compared with those available in the literature.

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References

  1. Alankaya, V. and Oktem, A.S. (2016), "Static analysis of laminated and sandwich composite doubly-curved shallow shells", Steel Compos. Struct., Int. J., 20(5), 1043-1066. https://doi.org/10.12989/scs.2016.20.5.1043
  2. Arefi, M. (2014), "Generalized shear deformation theory for thermo elastic analyses of the functionally graded cylindrical shells", Struct. Eng. Mech., Int. J., 50(3), 403-417. https://doi.org/10.12989/sem.2014.50.3.403
  3. Carrera, E., Brischetto, S., Cinefra, M. and Soave, M. (2011), "Effects of thickness stretching in functionally graded plates and shells", Compos. Part B, 42(2), 123-133. https://doi.org/10.1016/j.compositesb.2010.10.005
  4. Chakrabarti, A. and Sheikh, A.H. (2005), "Analysis of laminated sandwich plates based on inter-laminar shear stress continuous plate theory", J. Eng. Mech., 131(4), 377-384. https://doi.org/10.1061/(ASCE)0733-9399(2005)131:4(377)
  5. Chaudhuri, R.A. and Abu-Arja, K.R. (1988), "Exact solution of shear-flexible doubly curved anti-symmetric angle-ply shells", Int. J. Engng Sci., 26(6), 587-604. https://doi.org/10.1016/0020-7225(88)90056-0
  6. Chaudhuri, R.A. and Kabir, H.R.H. (1989), "On analytical solutions to boundary-value problems of doubly-curved moderately thick orthotropic shells", Int. J. Eng. Sci., 27(11), 1325-1336. https://doi.org/10.1016/0020-7225(89)90057-8
  7. Chaudhuri, R.A. and Kabir, H.R.H. (1993), "Sensitivity of the response of moderately thick cross-ply doubly-curved panels to lamination and boundary constraint-II application", Int. J. Solids Struct., 30(2), 273-286. https://doi.org/10.1016/0020-7683(93)90066-G
  8. Chaudhuri, R.A. and Kabir, H.R.H. (1994), "Static and dynamic Fourier analysis of finite cross-ply doubly curved panels using classical shallow shell theories", Compos. Struct., 28(1), 73-91. https://doi.org/10.1016/0263-8223(94)90007-8
  9. Fard, K.M., Livani, M., Vaisi, A. and Gholami, M. (2014), "Improved high-order bending analysis of double curved sandwich panels subjected to multiple loading conditions", Latin Am. J. Solid. Struct., 11(9), 1591-1614. https://doi.org/10.1590/S1679-78252014000900006
  10. Fox, L. and Parker, I.B. (1968), Chebyshev Polynomials in Numerical Analysis, Oxford University Press, London, UK.
  11. Kant, T. and Fafard, M. (1992), "Transient response of isotropic, orthotropic and anisotropic composite sandwich shells with the super-parametric element", Finite Elem. Anal. Design, 12(1), 63-73. https://doi.org/10.1016/0168-874X(92)90007-Y
  12. Kant, T. and Kommineni, J.R. (1992), "Geometrically non-linear analysis of doubly curved laminated and sandwich fibre reinforced composite shells with a higher order theory and $C^{\circ}$ finite elements", J. Reinf. Plast. Compos., 11(9), 1048-1076. https://doi.org/10.1177/073168449201100905
  13. Khare, R.K., Rode, V., Garg, A.K. and John, S.P. (2005), "Higherorder closed-form solutions for thick laminated sandwich shells", J. Sandw. Struct. Mater., 7(4), 335-358. https://doi.org/10.1177/1099636205050260
  14. Kiani, Y., Akbarzadeh, A.H., Chen, Z.T. and Eslami, M.R. (2012), "Static and dynamic analysis of an FGM doubly curved panel resting on the pasternak-type elastic foundation", Compos. Struct., 94(8), 2474-2484. https://doi.org/10.1016/j.compstruct.2012.02.028
  15. Nath, Y. and Shukla, K.K. (2001), "Non-linear transient analysis of moderately thick laminated composite plates", J. Sound Vib., 247(3), 509-526. https://doi.org/10.1006/jsvi.2001.3752
  16. Oktem, A.S. and Chaudhuri, R.A. (2007), "Fourier analysis of thick cross-ply levy type clamped doubly-curved panels", Compos. Struct., 80(4), 489-503. https://doi.org/10.1016/j.compstruct.2006.05.028
  17. Oktem, A.S. and Chaudhuri, R.A. (2009), "Higher-order theory based boundary-discontinuous Fourier analysis of simply supported thick cross-ply doubly curved panels", Compos. Struct., 89(3), 448-458. https://doi.org/10.1016/j.compstruct.2008.09.007
  18. Oktem, A.S. and Soares, C.G. (2011a), "Boundary discontinuous Fourier solution for plates and doubly curved panels using a higher order theory", Compos.: Part B, 42(4), 842-850. https://doi.org/10.1016/j.compositesb.2011.01.014
  19. Oktem, A.S. and Soares, C.G. (2011b), "Higher order theory based Fourier analysis of cross-ply plates and doubly curved panels". J. Compos. Mater., 46(21), 2675-2694. https://doi.org/10.1177/0021998311431641
  20. 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
  21. Ossadzow, C, Mulier, P. and Touratier, M. (1995), "A general doubly curved laminate shell theory", Compos. Struct., 32(1-4), 299-312. https://doi.org/10.1016/0263-8223(95)00032-1
  22. Pagano, N.J. (1970), "Exact solutions for rectangular bidirectional composite and sandwich plates", J. Compos. Mater., 4(1), 20- https://doi.org/10.1177/002199837000400102
  23. 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
  24. Sahoo, S.S., Panda S.K. and Mahapatra, T.R. (2016), "Static, free vibration and transient response of laminated composite curved shallow panel - An experimental approach", Eur. J. Mech. A/Solids, 59, 95-113. https://doi.org/10.1016/j.euromechsol.2016.03.014
  25. To, C.W.S. and Liu, M.L. (2001), "Geometrically nonlinear analysis of layerwise anisotropic shell structures by hybrid strain based lower order elements", Finite Eleme. Anal. Des., 37(1), 1-34. https://doi.org/10.1016/S0168-874X(00)00015-9