Journal of Failure Analysis and Prevention

, Volume 15, Issue 3, pp 390–400 | Cite as

Progressive Failure Analysis of Laminated Composite Cylindrical Shell Roofs

  • Jayashree Sengupta
  • Arghya Ghosh
  • Dipankar Chakravorty
Technical Article---Peer-Reviewed


A progressive failure analysis of laminated composite cylindrical roofs under transverse uniformly distributed static loadings has been carried out in the present paper using the finite element method. In the finite element analysis, an eight-noded isoparametric shell elements are taken up. The first-ply failure load and the ultimate ply failure load are evaluated and compared using different stress-based failure criteria. The effect of orientation of fibers in a lamina, stacking sequence, and varying boundary conditions, on the strength of the laminate is carried out. Factors of safety and load factors are suggested based on the values of first and ultimate ply failure loads. The damage progression using the failure criterion corresponding to the first-ply failure load has been shown. The areas of damage are correlated with deflection values through explicit equations so as to get an idea about the damage extents without going into elaborate testing. The results are interpreted from practical engineering standpoint to extract meaningful conclusions.


Progressive failures Finite element method First-ply failure Ultimate ply failure 


a, b

Length and width of shell in plan


Flexural rigidity matrix of the laminate


Global displacement vector

E11, E22

Young’s moduli of a lamina along and transverse to the fibers, respectively

G12, G13, G23

Shear modulus of a lamina in 1–2, 1–3, and 2–3 planes corresponding to the local axes of that lamina


Shell thickness


Moment resultants per unit length of cylindrical shell


Torsion resultant per unit length of cylindrical shell


Shape functions for first to eight nodes of an element, respectively


In-plane normal force resultants per unit length in X- and Y-direction


In-plane shear force resultant per unit length of shell


Transverse shear resultants per unit length of shell


Intensity of uniformly distributed load

u, v, w

Translational degrees of freedom along X-, Y- and Z-direction, respectively


Transverse displacement in cm

X, Y and Z

Global co-ordinates of the laminate

Zk, Zk−1

Top and bottom distance of the kth ply from mid-plane of a laminate

α, β

Rotational degrees of freedom about Y- and X-axis, respectively

\(\sigma_{x}\), \(\sigma_{y}\), \(\sigma_{z}\)

Normal stresses in X-, Y- and Z-direction, respectively


Shear stress in XY-, YZ- and XZ -plane, respectively


Strain along X- and Y-direction, respectively


Shear strain


Angle of lamination with respect to the X axis of the cylindrical shell


Poisson’s ratio which characterizes compressive strain along x j-direction produced by a tensile strain applied in x i-direction

\(\varepsilon_{x}^{0} ,\varepsilon_{y}^{0} , \gamma_{xy}^{0} , \gamma_{xz}^{0} , \gamma_{yz}^{0}\)

In-plane and transverse strains of the mid-plane

\(\kappa_{x} , \kappa_{y} , \kappa_{xy} , \kappa_{xz} , \kappa_{yz}\)

Curvature of shell


Tensile strength in X-, Y- and Z-direction, respectively


Compressive strength in X-, Y- and Z-direction, respectively

\(F_{SXY}\), \(F_{SYZ} , F_{SXZ}\)

Shear strength in XY-, YZ- and XZ-plane, respectively


Allowable normal strain strengths of a lamina along the fiber direction in tension and compression, respectively


Allowable normal strain strengths of the matrix along the perpendicular to the fiber direction in tension and compression, respectively

\(\varepsilon_{{\text{S}}_{XY}},\,\varepsilon_{{\text{S}}_{YZ}},\, \varepsilon_{{\text{S}}_{XZ}},\)

Shear strain strengths of a lamina in 2–3, 1–3 and 1–2 planes, respectively



The second 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

© ASM International 2015

Authors and Affiliations

  • Jayashree Sengupta
    • 1
  • Arghya Ghosh
    • 1
  • Dipankar Chakravorty
    • 1
  1. 1.Department of Civil EngineeringJadavpur UniversityKolkataIndia

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