First Ply Failure Study of Composite Conoidal Shells Used as Roofing Units in Civil Engineering
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TECHNICAL ARTICLE—PEER-REVIEWED
First Ply Failure Study of Composite Conoidal Shells Used as Roofing Units in Civil Engineering Kaustav Bakshi • Dipankar Chakravorty
Submitted: 26 February 2013 / in revised form: 3 July 2013 Ó ASM International 2013
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.
Symbols A {d} {de} E11, E22, E33 1, 2 and 3 G12, G23, G13 ne Ryy
Keywords Composite materials Conoidal shells Finite element method Failure investigations Failure loads Failure modes
YeT, YeC
Rxy T Te v/ XT, X C XeT, XeC y YT, YC
mij r1, r2 K. Bakshi (&) D. Chakravorty Department of Civil Engineering, Jadavpur University, Kolkata 700 032, India e-mail: [email protected] D. Chakravorty e-mail: [email protected]
r6 sxy, sxz, syz kx, ky, kxy
Area of the shell Displacements of the shell Element displacements Elastic moduli Local coordinates of a lamina Shear moduli Number of elements Radius of curvature of the conoidal shell along the ‘‘y’’ axis Radius of cross curvature of the conoidal shell Shear strength of lamina Allowable shear strain of lamina Volume of the shell Normal strengths of lamina in tension and compression, respectively Allowable normal strains of lamina in tension and compression, respectively y/b Normal strengths of matrix in tension and compression, respectively Allowable normal strains of matrix in tension and compression, respectively Poisson’s ratio Normal stresses acting along 1 and 2 axes of a lamina, respectively Shear stress acting on 1–2 surface of a lamina Shear stresses of the shell Curvature changes of the shell due to loading
123
J Fail. Anal. and Preven.
Introduction In civil engineering, it is advantageous to use thin shells instead of flat plates to cover large column free open spaces as one sees in airports, parking lots, hangers, and the like. Doubly curved shell forms
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