Three-dimensional elasticity solutions for plate/shell structures serve as a standard benchmark for the assessment of various two-dimensional theories. Such a solution, for assessment of laminated shell theories, is presented here. The problem is that of a simply supported cross-ply cylindrical shell pinched by two diametrically opposite local patch loads. The solution is developed by using Taylor series, and results are tabulated for a three-layer shell with various radius-to-thickness ratios. Finally, these results are used to throw light on the accuracy of the classical Love-Kirchhoff hypothesis and a recently proposed higher order shear deformation theory. © 1994 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.

K. Bhaskar

Department of Aerospace Engineering

T. K. Varadan

ELASTICITY

BENCHMARK ELASTICITY SOLUTIONS

CLASSICAL LOVE-KIRCHHOFF HYPOTHESIS

HIGHER ORDER SHEAR DEFORMATION

Plates (structural components)

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

Benchmark elasticity solution for locally loaded laminated orthotropic cylindrical shells

AIAA Journal

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.

Composite Structures

Accurate analysis of end-loaded laminated orthotropic cylindrical shells

A three-dimensional elasticity solution is obtained for finite-length laminated anisotropic cylindrical shells, simply supported at both ends and subjected to axisymmetric transverse loading. Suitable displacement functions are used to reduce the problem to a set of coupled homogeneous ordinary differential equations in terms of the radial coordinate, and these are then solved by employing a Taylor series. Displacements and stresses at critical locations are tabulated for different angle-ply layups and radius-to-thickness ratios for two types of loading. These results will be useful for the assessment of various two-dimensional laminated shell theories. As an example, the accuracy of the Love-type classical shell theory is discussed. © 1993.

Composites Engineering

A benchmark elasticity solution for an axisymmetrically loaded angle-ply cylindrical shell

An exact three-dimensional elasticity solution is obtained for cylindrical bending of simply-supported laminated anisotropic cylindrical shell strips subjected to transverse loading. Displacements and stresses are presented for different angle-ply layups and radius-to-thickness ratios, so as to serve as useful benchmark results for the assessment of various two-dimensional shell theories. Finally, in the light of these results, the accuracy of the Love-type classical shell theory is examined. © 1993 by ASME.

Journal of Applied Mechanics, Transactions ASME

Exact elasticity solution for laminated anisotropic cylindrical shells

A new higher-order shear deformation theory is presented for the analysis of laminated anisotropic shells of revolution. The theory is based on realistic approximation of the in-plane displacements through the thickness. The accuracy of the theory is verified by comparison with three-dimensional elasticity results for a laminated orthotropic cylindrical shell. Finally, an isoparametric quadrilateral shell of revolution finite element is presented. The example problems solved illustrate the performance of the element and the effects of transverse shear deformation. © 1991.

Computers and Structures

A higher-order theory for bending analysis of laminated shells of revolution

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.

Bending of laminated orthotropic cylindrical shells-An elasticity approach

Plant Science

Biochemistry and Molecular Biology of Plants, Edited by Bob B. Buchanan, Wilhelm Gruissem and Russel L. Jones, American Society of Plant Physiologists, P.O. Box 753, Waldorf, MD 20604-0753, USA, (Drake International Services, Market House, Market Place, Deddington, Oxford OX15 OSE, UK). Hardback ISBN-0943088-37-2; £.135.00, Paperback ISBN-0943088-39-9; £.75.00

Journal	AIAA Journal
ISSN	00011452
Open Access	No