Journal of Failure Analysis and Prevention

, Volume 13, Issue 5, pp 624–633

# First Ply Failure Study of Composite Conoidal Shells Used as Roofing Units in Civil Engineering

• Kaustav Bakshi
• Dipankar Chakravorty
Technical Article---Peer-Reviewed

## Abstract

In practical civil engineering, the necessity of covering large column free open areas with shell surfaces is often an issue. Such areas in medicinal plants and automobile industries prefer entry of north light through the roofing units. Doubly curved singly ruled conoidal shells are stiff and easy to fabricate as surfaces and fit excellently to the above-mentioned industrial requirements. Today, the engineers intend to use laminated composites to fabricate these shell forms. Engineers are also concerned with the performance evaluation of different stacking sequences to maximize the stiffness for a given quantity of material consumption. First ply failure load analysis of composite plates appears abundantly in the literature, but on composite shells, only a few papers are found (though not on conoidal shells). This paper addresses an important issue with which the practical engineers are often concerned regarding performance evaluation of different laminations (including antisymmetric and symmetric cross and angle plies) in terms of first ply failure load of composite conoids. The paper uses the finite element method as the mathematical tool and concludes logically to a set of inferences of practical engineering significance.

## Keywords

Composite materials Conoidal shells Finite element method Failure investigations Failure loads Failure modes

## Symbols

A

Area of the shell

{d}

Displacements of the shell

{de}

Element displacements

E11, E22, E33

Elastic moduli

1, 2 and 3

Local coordinates of a lamina

G12,G23,G13

Shear moduli

ne

Number of elements

Ryy

Radius of curvature of the conoidal shell along the “y” axis

Rxy

Radius of cross curvature of the conoidal shell

T

Shear strength of lamina

Tε

Allowable shear strain of lamina

v/

Volume of the shell

XT, XC

Normal strengths of lamina in tension and compression, respectively

XεT,XεC

Allowable normal strains of lamina in tension and compression, respectively

$$\bar{y}$$

y/b

YT,YC

Normal strengths of matrix in tension and compression, respectively

YεT,YεC

Allowable normal strains of matrix in tension and compression, respectively

νij

Poisson’s ratio

σ1, σ2

Normal stresses acting along 1 and 2 axes of a lamina, respectively

σ6

Shear stress acting on 1–2 surface of a lamina

τxy, τxz, τyz

Shear stresses of the shell

kx, ky, kxy

## Notes

### Acknowledgments

The first author gratefully acknowledges the financial assistance of the Council of Scientific and Industrial Research (India) through the Senior Research Fellowship vide Grant No. 09/096 (0686) 2k11-EMR-I.

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