Relative static and dynamic performances of composite conoidal shell roofs

  • Bakshi, Kaustav (Civil Engineering Department, Jadavpur University) ;
  • Chakravorty, Dipankar (Civil Engineering Department, Jadavpur University)
  • Received : 2012.11.04
  • Accepted : 2013.10.01
  • Published : 2013.10.25


Conoidal shells are doubly curved stiff surfaces which are easy to cast and fabricate due to their singly ruled property. Application of laminated composites in fabrication of conoidal shells reduces gravity forces and mass induced forces compared to the isotropic constructions due to the high strength to weight ratio of the material. These light weight shells are preferred in the industry to cover large column free open spaces. To ensure design reliability under service conditions, detailed knowledge about different behavioral aspects of conoidal shell is necessary. Hence, in this paper, static bending, free and forced vibration responses of composite conoidal shells are studied. Lagrange's equation of motion is used in conjunction with Hamilton's principle to derive governing equations of the shell. A finite element code using eight noded curved quadratic isoparametric elements is developed to get the solutions. Uniformly distributed load for static bending analysis and three different load time histories for solution of forced vibration problems are considered. Eight different stacking sequences of graphite-epoxy composite and two different boundary conditions are taken up in the present study. The study shows that relative performances of different shell combinations in terms of static behaviour cannot provide an idea about how they will relatively behave under dynamic loads and also the fact that the points of occurrence of maximum static and dynamic displacement may not be same on a shell surface.


conoidal shell;composite material;finite element method;forced vibration;Newmark's method


  1. Chakravorty, D., Sinha. P.K. and Bandyopadhyay, J.N. (1995a), "Finite element free vibration analysis of point supported laminated composite cylindrical shells", J. Sound Vib., 181(1), 43-52.
  2. Chakravorty, D., Sinha. P.K. and Bandyopadhyay, J.N. (1995b), "Free vibration analysis of point-supported laminated composite doubly curved shells-A finite element approach", Comput. Struct., 54(2), 191-198.
  3. Chakravorty, D., Sinha. P.K. and Bandyopadhyay, J.N. (1998), "Applications of FEM on free and forced vibration of laminated shells", J. Eng. Mech. ASCE, 124(1), 1-8.
  4. Das, H.S. and Chakravorty, D. (2007), "Design aids and selection guidelines for composite conoidal shell roofs - A finite element application", J. Reinf. Plast. Compos., 26(17), 1793-1819.
  5. Das, H.S. and Chakravorty, D. (2008), "Natural Frequencies and Mode Shapes of Composite Conoids with Complicated Boundary Conditions", J. Reinf. Plast. Compos., 27(13), 1397-1415.
  6. Das, H.S. and Chakravorty, D. (2009), "Composite full conoidal shell roofs under free vibration", Adv. Vib. Eng., 8(4), 303-310.
  7. Das, H.S. and Chakravorty, D. (2010), "Finite element application in analysis and design of point supported composite conoidal shell roofs suggesting selection guidelines", J. Strain Anal. Eng. Des., 45(3), 165-177.
  8. Das, H.S. and Chakravorty, D. (2011), "Bending analysis of stiffened composite conoidal shell roofs through finite element application", J. Compos. Mater., 45(5), 525-542.
  9. Ergatoudis, I., Irons, B.M. and Zienkiewicz, O.C. (1968), "Curved isoparametric quadrilateral elements for finite element analysis", Int. J. Solids Struct., 4(1), 31-42.
  10. Greene, B.E., Jones, R.E. and Strome, D.R. (1968), "Dynamic analysis of shells using doubly curved finite elements", Proceedings of 2nd Conference on Matrix Methods Structural Mechanics, Wright-Patterson Air Force Base, Ohio, October, 185-212.
  11. Kumari, S. and Chakravorty, D. (2010), "On the bending characteristics of damaged composite conoidal shells - a finite element approach", J. Reinf. Plast. Compos., 29(21), 3287-3296.
  12. Kumari, S. and Chakravorty, D. (2011), "Bending of delaminated composite conoidal shells under uniformly distributed load", J. Eng. Mech. ASCE, 137(10), 660-668.
  13. Lee, W.H. and Han, S.C. (2006), "Free and forced vibration analysis of laminated composite plates and shells using a 9-node assumed strain shell element", Comput. Mech., 39(1), 41-58.
  14. Nayak, A.N. and Bandyopadhyay, J.N. (2005), "Free vibration analysis of laminated stiffened shells", J. Eng. Mech. ASCE, 131(1), 100-105.
  15. Nayak, A.N. and Bandopadhyay J.N. (2006), "Dynamic response analysis of stiffened conoidal shells", J. Sound Vib., 291(3-5), 1288-1297.
  16. Nanda, N. and Bandyopadhyay, J.N. (2008), "Nonlinear transient response of laminated composite shells", J. Eng. Mech. ASCE, 134(11), 983-990.
  17. Nanda, N. and Bandyopadhyay, J.N. (2009), "Geometrically nonlinear transient analysis of laminated composite shells using the finite element method", J. Sound Vib., 325(1-2), 174-185.
  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.
  19. Pradyumna, S. and Bandyopadhyay, J.N. (2011), "Dynamic instability behavior of laminated hypar and conoid shells using a higher-order shear deformation theory", Thin-Wall. Struct., 49(1), 77-84.
  20. Reddy, J.N. (1984), "Exact solutions of moderately thick laminated shells", J. Eng. Mech. ASCE, 110(5), 794-809.
  21. Reddy, J.N. and Chandrashekhara, K. (1985), "Geometrically non-linear transient analysis of laminated doubly curved shells", Int. J. Non-linear Mech., 20(2), 79-80.
  22. Ribeiro, P. (2008), "Forced large amplitude periodic vibrations of cylindrical shallow shells", Finite Elem. Anal. Des., 44(11), 657-674.