Pareto optimum design of laminated composite truncated circular conical shells

  • Topal, Umut (Karadeniz Technical University, Of Faculty of Technology, Department of Civil Engineering)
  • Received : 2012.11.21
  • Accepted : 2013.03.12
  • Published : 2013.04.25


This paper deals with multiobjective optimization of symmetrically laminated composite truncated circular conical shells subjected to external uniform pressure load and thermal load. The design objective is the maximization of the weighted sum of the critical buckling load and fundamental frequency. The design variable is the fibre orientations in the layers. The performance index is formulated as the weighted sum of individual objectives in order to obtain optimal solutions of the design problem. The first-order shear deformation theory (FSDT) is used in the mathematical formulation of laminated truncated conical shells. Finally, the effect of different weighting factors, length-to-radius ratio, semi-cone angle and boundary conditions on the optimal design is investigated and the results are compared.


laminated composite truncated conical shells;multiobjective optimization;frequency;buckling


  1. Hu, H.T. and Ou, S.C. (2001), "Maximization of the fundamental frequencies of laminated truncated conical shells with respect to fiber orientations", Compos. Struct., 52(3-4), 265-275.
  2. Kabir, M.Z. and Shirazi, A.R. (2008), "Optimum design of filament-wound laminated conical shells for buckling using the penalty function" Iranian Aerospace Society, 5(3), 115-121.
  3. Patel, B.P., Singh, S. and Nath, Y. (2008), "Postbuckling characteristics of angle-ply laminated truncated circular conical shells", Commun. Nonlinear Sci. Num. Simul., 13(7), 1411-1430.
  4. Patel, B.P., Shukla, K.K. and Nath, Y. (2005), "Thermal postbuckling analysis of laminated cross-ply truncated circular conical shells", Compos. Struct., 71(1), 101-114.
  5. Shadmehri, F., Hoa, S.V. and Hojjati, M. (2012), "Buckling of conical composite shells", Compos. Struct., 94(2), 787-792.
  6. Singh, B.N. and Babu, J.B. (2009), "Thermal buckling of laminated composite conical shell panel with and without piezoelectric layer with random material properties", Int'l J. Crashworthiness, 14(1), 73-81.
  7. Sivadas, K.R. and Ganesan, N. (1991), "Vibration analysis of laminated conical shells with variable thickness", J. Sound Vib., 148(3), 477-491.
  8. Sofiyev, A.H. and Kuruoglu, N. (2011), "The non-linear buckling analysis of cross-ply laminated orthotropic truncated conical shells", Compos. Struct., 93(11), 3006-3012.
  9. Sofiyev, A.H. and Karaca, Z. (2009), "The vibration and buckling of laminated non-homogeneous orthotropic conical shells subjected to external pressure", Eur. J. Mech.- A/Solids, 28(2), 317-328.
  10. Tong, L., (1993), "Free vibration of composite laminated conical shells", Int'l J. Mech. Sci., 35(1), 47-61.
  11. Tripathi, V., Singh, B.N. and Shukla, K.K. (2007), "Free vibration of laminated composite conical shells with random material properties", Compos. Struct., 81(1), 96-104.
  12. Blom, A.W., Setoodeh, S., Hol, J.M.A.M. and Gürdal, Z. (2008), "Design of variable-stiffness conical shells for maximum fundamental eigenfrequency", Comput. Struct., 86(9), 870-878.
  13. Civalek, O. (2007), "Numerical analysis of free vibrations of laminated composite conical and cylindrical shells: Discrete singular convolution (DSC) approach", J. Comput. App. Math., 205(1), 251-271.
  14. Dey, S. and Karmakar, A. (2012), "Natural frequencies of delaminated composite rotating conical shells-A finite element approach", Finite Elem. Anal. Des., 56, 41-51.
  15. Fares, M.E., Yousiff, Y.G. and Alamir, A.E. (2004), "Design and control optimization of composite laminated truncated conical shells for minimum dynamic response including transverse shear deformation", Compos. Struct., 64(2), 139-150.
  16. Goldfeld, Y., Arbocz, J. and Rothwell, A. (2005), "Design and optimization of laminated conical shells for buckling", Thin-Walled Struct., 43(1), 107-133.

Cited by

  1. On the fabrication of carbon fabric reinforced epoxy composite shell without joints and wrinkling vol.15, pp.3, 2013,
  2. Multi-objective optimum design of TBR tire structure for enhancing the durability using genetic algorithm vol.31, pp.12, 2017,
  3. An investigation into the mechanics of fiber reinforced composite disk springs vol.18, pp.3, 2015,
  4. Experimental and numerical investigation of composite conical shells' stability subjected to dynamic loading vol.49, pp.5, 2014,
  5. Meshless local collocation method for natural frequencies and mode shapes of laminated composite shells vol.51, pp.6, 2014,
  6. Transient analysis of cross-ply laminated shells using FSDT: Alternative formulation vol.18, pp.4, 2015,