Three-dimensional elasticity solutions are obtained for finite length, cross-ply cylindrical shells, simply supported at both ends and subjected to transverse sinusoidal loading. By assuming suitable displacement functions, the boundary value problem is reduced to a set of coupled ordinary differential equations and then solved by the method of Frobenius. Displacement and stresses are presented for 90°, (90°/0°), (90°/0°/90°), (90°/0°/90°/0°/90°)s shells. Deviations from laminated plate behaviour are described. The method presented is shown to give results identical to those of a stress function approach for a plane strain problem. The paper includes extensive tabulated results to serve as a basis for assessment of improved shell theories. © 1990.

K. Bhaskar

Department of Aerospace Engineering

T. K. Varadan

LAMINATED PRODUCTS--ELASTICITY

Mathematical Techniques--Differential Equations

stresses

Structural Design--Loads

CROSS-PLY SHELLS

LAMINATED PLATE DISPLACEMENTS

STRESS DISTRIBUTION

Stress functions

DOMES AND SHELLS

IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

Bending of laminated orthotropic cylindrical shells—An elasticity approach

Composite Structures

With the advancement of aerospace engineering and the progress made in the allied industries, new forms of structural components having high strength-to-weight ratio have been developed. Fibre-reinforced laminate structures are one such type of construction. In the present study, linear behaviour of laminated composite shells under static loading is investigated using ANSYS, the finite element software, by varying the parameters such as laminate thickness, fibre orientation, stacking sequence, fibre strength and radius-to-thickness ratio. It has been observed that the deflection remains constant beyond four layers in the case of anti-symmetric arrangement and for the same angle of fibre orientation, deflection is not influenced by the lamination sequence. The non-dimensional deflection decreases with increase in material anisotropy and included angle, while it increases with increase in radius-to-thickness ratio. © 2013, The Institution of Engineers (India).

Journal of The Institution of Engineers (India): Series A

Static Behaviour of Laminated Composite Shells

Clamped cross-ply plates are analyzed here using a higher-order theory based on a realistic thickness-wise displacement field that accounts for a zig-zag variation of the in-plane displacements. Rigorous analytical solutions are obtained for this difficult problem using a methodology developed recently wherein simple Fourier series solutions of a corresponding simply-supported plate are superposed, each such component solution being summed without truncation using MATHEMATICA. Numerical results, for square homogeneous and three-layer plates under uniform and central point loads, are compared with those based on the classical and first-order theories. © 2005 Elsevier Ltd. All rights reserved.

Analytical solutions for flexure of clamped rectangular cross-ply plates using an accurate zig-zag type higher-order theory

The purpose of this work is to present baseline elasticity solutions for laminated composite shells subjected to localized moments. For simply supported cross-ply cylindrical shells, the problem reduces to one of coupled ordinary differential equations which are solved in terms of Taylor's series. Results, in the form of tables and graphs, are presented for the cases of longitudinal and circumferential moments. These results would be very useful for judging the accuracy of approximate two-dimensional shell theories. They are used herein to study the errors of a shell theory based on the classical Love-Kirchhoff hypothesis.

Journal of Pressure Vessel Technology, Transactions of the ASME

Elasticity solutions for laminated orthotropic cylindrical shells subjected to localized longitudinal and circumferential moments

The objective of this work is to provide a three-dimensional elasticity solution with tabulated numerical results for a laminated composite cylindrical shell subjected to a localized circumferential shear force. The three-dimensional solution is valuable because it enables the validity of simple two-dimensional laminate theories such as the classical lamination theory to be judged for such analysis. It is shown here that the classical theory yields unacceptably erroneous predictions of the stresses in the vicinity of the local load even if the shell is thin. © 2002 Elsevier Science Ltd. All rights reserved.

International Journal of Pressure Vessels and Piping

Three-dimensional analysis of a cross-ply cylindrical shell subjected to a localized circumferential shear force

Semi-infinite laminated cylindrical shells subjected to axisymmetric end shear or end moment loading are analyzed here by a classical shell theory, a higher-order shear deformation theory and the three-dimensional (3-D) theory of elasticity. While the 3-D results are obtained using finite element method, results by the shell theories are obtained using analytical solutions. The corresponding predictions of the deformations and stresses due to localized bending in the neighborhood of the applied load are compared to show that the classical Love-Kirchhoff hypothesis leads to unacceptable errors while a shear deformation theory can be employed as a viable alternative to 3-D analysis without much loss of accuracy. © 2002 Elsevier Science Ltd. All rights reserved.

Journal	Composite Structures
ISSN	02638223
Open Access	No