On Progressive Failure Study of Composite Hypar Shell Roofs

  • Arghya GhoshEmail author
  • Dipankar Chakravorty
Conference paper


Hyperbolic paraboloid (hypar) shell bounded by straight edges, an aesthetically appealing doubly curved anticlastic surface, which is easy to fabricate being doubly ruled, and is preferred as roofing units in many practical situations demanding large column free spaces. The skewed hypar shells are architecturally beautiful, easy to cast and are often preferred as roofing units. Laminated composite shells are frequently used in various engineering applications including aerospace, mechanical, marine and automotive engineering. Laminated composites gained popularity in civil engineering structures as use of these materials results in reduced mass and mass induced forces like seismic forces. Failure study of these materials is necessary, which includes the load value (first ply failure load) at which failure initiates and the failure propagation location and the ultimate load carrying capacity. The present article aims to study a comparative failure propagation of uniformly loaded simply supported hypar shells of different stacking orders using finite element method . An eight noded curved quadratic isoparametric shell element is used to develop the finite element program and validated through solution of benchmark problems. Well accepted failure criteria are used to evaluate the failure loads and failure propagation from engineering standpoint. While obtaining the failure loads, each lamina is considered to be under plane stress condition i.e. no transverse stresses are considered to act on any lamina. The results are analysed thoroughly and the paper ends with a number of conclusions of design significance.


Laminated composites Hypar shells Progressive failure Finite element method 


a, b

Length and width of the shell


Rise of hypar shell

u, v, w

In-plane and transverse displacements

α, β

Slopes along the plan directions

E11, E22,E33

Elastic moduli

G12, G13, G23

Shear moduli


Twist radius of curvature of the hypar shell

1, 2 and 3

Local coordinates of a lamina

x, y, z

Global coordinates of the laminate

εx, εy

In-plane normal strain components along x and y axis respectively


In-plane shear strain in x-y plane

ε1, ε2

In-plane normal strains along 1 and 2 axes of a lamina respectively


In-plane shear strain in 1–2 plane of a lamina

σ1, σ2 and σ6

In-plane lamina stresses


Poisson’s ratio

ξ, η

Natural co-ordinates of isoparametric elements

κx, κy, κxy

Curvatures of the shell due to load



The first author gratefully acknowledges the financial assistance of Technical Education Quality Improvement Programme, Phase-II (a World Bank aided project of Govt. of India) of serial no. 1893 of Jadavpur University, Kolkata-700032, India.


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Copyright information

© Springer India 2015

Authors and Affiliations

  1. 1.Civil Engineering DepartmentJadavpur UniversityKolkataIndia

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