Finite Element Analysis of Hyperbolic Paraboloid Composite Shells for Static Analysis Under Uniform Pressure

  • Anil Garhwal
  • Yogesh Kaushik
  • Sabita Madhvi Singh
  • Divya
Conference paper
Part of the Lecture Notes in Mechanical Engineering book series (LNME)


The present study reports finite element analysis of hyperbolic paraboloid composite shells for static analysis under uniform pressure to examine the maximum stresses and deflections. The matrix used in the present study is Epoxy resin reinforced with E-glass fiber. Parameter used for the analysis is rise-to-span-ratio (c/a). The ratio used for the study varies from 0 to 0.5 with linear increment of 0.05. Thickness of composite layer is kept equal in the shell. Eight-nodded iso-parametric shell element with five degrees of freedom on each node is used for the present study. Boundary conditions with all sides clamped, all sides simply supported and alternate sides simply supported and clamped are applied with cross-ply and angle-ply laminations.


Angle-ply Composites Cross-ply Hyperbolic paraboloid Orthotropic Shells 


a, b

Length and width of the shell in plan


Rise of the hyperbolic paraboloid shell


Global displacement vector


Element displacement vector

E1, E2, E3

Moduli of elasticity

G12, G23, G13

Shear moduli of a lamina

μ12, μ23, μ13

Poison’s ratio


Rise-to-span ratio


All sides clamped


All sides simply supported


Alternately clamped and simply supported


Cross-ply laminate


Angle-ply laminate

u, v, w

Translational degrees of freedom at each node

α, β

Rotational degrees of freedom at each node


  1. 1.
    Bolster ED, Cuypers H, Itterbeeck PV, Wastiels J, Wilde WPD (2008) Use of hypar-shell structure with textile reinforced cement matrix composites in lightweight constructions. Compos Sci Technol ElsevierGoogle Scholar
  2. 2.
    Bernasconi J (2012) Buckling studies into large scale hyperbolic paraboloid shell and lattice structures. PhD thesis, University of QueenslandGoogle Scholar
  3. 3.
    Bakshi K, Chakravorty D (2013) Static and dynamic characteristics of composite conoidal shell roofs. Hindawi Publishing Corporation, advances in acoustic and vibrationGoogle Scholar
  4. 4.
    Chen D, Hao J, Wang Z (2011) Study on shape formation of post-tensioned and shaped hypar space truss. Adv Mater Res 243–249Google Scholar
  5. 5.
    Das HS, Chakravorty D (2009) A finite element application in the analysis and design of point-supported composite conoidal shell roofs: suggesting selection guidelines. JSA582Google Scholar
  6. 6.
    Kim JW, Kim JJ, Rhew HJ (2005) Analysis and experiment for the formation and ultimate load testing of a hypar space truss. J Constr Steel Res ElsevierGoogle Scholar
  7. 7.
    Kumari S, Chakravorty D (2010) Study of static characteristics of delaminated composite conoidal shell subjected to point load. Adv Mater ResGoogle Scholar
  8. 8.
    Kumari S, Chakravorty D (2011) Bending of delaminated composite conoidal shells under uniformly distributed load. Am Soc Civil EngGoogle Scholar
  9. 9.
    Kumar A, Bhargava P, Chakrabarti A (2012) Vibration of laminated composite skew hypar shells using higher order theory. Thin Wall Struct ElsevierGoogle Scholar
  10. 10.
    Kumar A, Bhargava P, Chakrabarti A (2012) Natural frequencies and mode shapes of laminated composite skew hypar shells with complicated boundary conditions using finite element method. Adv Mater Res 585Google Scholar
  11. 11.
    Laursen PT, Saliklis EP (2012) Finite-element limit analysis of the tucker high school gymnasium roof failure. J Arch Eng 18, ©ASCEGoogle Scholar
  12. 12.
    Neogi SD, Karmakar A, Chakravorty D (2011) Impact response of simply supported skewed hypar shell roofs by finite element. J Reinf Plast ComposGoogle Scholar
  13. 13.
    Pradyumna S, Bandyopadhyay JN (2010) Dynamic instability behaviour of laminated hypar and conoidal shells using a higher-order shear deformation theory. Thin Wall Struct ElsevierGoogle Scholar
  14. 14.
    Pradhan N, Jena J (2012) Static characteristics of stiffened conoidal shell roofs under concentrated load. Int J Adv Eng TechnolGoogle Scholar
  15. 15.
    Rha CS, Kim SN, Yu E (2015) Behaviour of gabled hyperbolic paraboloid shells. J Asian Arch Build EngGoogle Scholar
  16. 16.
    Sahoo S, Chakravorty D (2005) Deflections, forces, and moments of composite stiffened hypar shell roofs under concentrated load. JSA117 IMechEGoogle Scholar
  17. 17.
    Sahoo S, Chakravorty D (2005) Finite element vibration characteristics of composite hypar shallow shells with various edge supports. J Vib Control SageGoogle Scholar
  18. 18.
    Sahoo S, Chakravorty D (2006) Stiffened composite hypar shell roofs under free vibration: behaviour and optimization aids. J Sound Vib ElsevierGoogle Scholar
  19. 19.
    Sahoo S (2012) Design and selection guidelines for composite hypar shell roofs with cutouts. Acad Res J IJACEAGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  • Anil Garhwal
    • 1
  • Yogesh Kaushik
    • 1
  • Sabita Madhvi Singh
    • 1
  • Divya
    • 2
  1. 1.Department of Civil EngineeringAmity UniversityNoidaIndia
  2. 2.Department of Civil EngineeringSouth Point Technical CampusSonepatIndia

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