Analytical solutions are presented for the static analysis of laminated orthotropic spherical shells subjected to asymmetric loading. The analysis is based on the application of Chebyshev-Galerkin spectral method for the solution of decoupled equilibrium equations in the meridional direction, the circumferential variation of displacements and stresses being represented using Fourier series. Numerical results are presented to show the validity and accuracy of the proposed method. Results of parametric studies for laminated annular hemispherical shells with different orthotropy ratios, opening angles and lamination sequences are also presented. © 1991.

R. S. Alwar

DOMES AND SHELLS--STRUCTURAL ANALYSIS

LAMINATED PRODUCTS--STRUCTURAL ANALYSIS

Mathematical Techniques--Numerical Methods

ASYMMETRIC LOADS

LAMINATED ORTHOTROPIC SHELLS

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

Analysis of laminated orthotropic spherical shells subjected to asymmetric loads

Computers and Structures

A comparative study of the interlaminar stresses in shells of revolution has been made between first order shear deformation theory (FSDT), higher order shear deformation theory with thickness stretch (HSDTY), higher order shear deformation theory with higher order inplane displacement terms (HSDT9) and three-dimensional finite element (3D) models. A semi-analytical approach is used for all the models. Interlaminar stresses are evaluated using equilibrium equations in the cases of FSDT, HSDT7 and HSDT9 models as interlaminar stresses obtained from constitutive equations are not correct. For the 3D model an eight-noded quadratic quadrilateral semi-analytic solid element is used whereas for equivalent single layer (ESL) theories a three-noded isoparametric curved element is used. Crossply parabolic and hyperbolic caps subjected to uniform external pressure and a simply supported cylindrical shell subjected to an internal sinusoidal pressure are considered in the present study. © 1996 by John Wiley & Sons, Ltd.

Mechanics of Composite Materials and Structures

Interlaminar stresses in shells of revolution

The dynamic axisymmetric behavior of clamped laminated composite spherical caps subjected to suddenly applied loads is investigated using an eight-noded quadrilateral doubly curved shear flexible shell element based on the field-consistency approach. Geometric nonlinearity is considered using von Karman’s strain-displacement relations. The solution is obtained using the Wilson- θ numerical integration scheme. The pressure corresponding to a sudden jump in the maximum average deflection in the time history of the shell structure is taken as dynamic buckling pressure. A detailed parametric study is carried out to bring out the effects of shell geometries and material properties, number of layers, lamination schemes, and type of loading on a dynamic buckling load. © 1995 by ASME.

Journal of Applied Mechanics, Transactions ASME

Dynamic buckling of laminated anisotropic spherical caps

Dynamic response of laminated orthotropic spherical shells under axisymmetric dynamic load is investigated. The shell is assumed to be composed of layers of orthotropic materials whose principal material directions coincide with the shell curvature directions. The motion of the shell is described by a displacement field so as to include the effects of transverse shear deformation. Three coupled differential equations in terms of three generalized displacements at a point of the shell reference surface are written neglecting the rotatary inertia effects. These equations are then discretized in the time domain using the unconditionally stable Newmark- integration scheme. The time discretized equations at any time step are solved by the method of global interior collocation at zeros of a Chebyshev polynomial of suitable order. Numerical results are presented to show the efficacy of the method. Results of parametric studies are presented to bring out the effects of the opening angle, material orthotropy, and shear deformation on the transient response. © 1992, Acoustical Society of America. All rights reserved.

Journal of the Acoustical Society of America

Dynamic response of laminated orthotropic spherical shells

Analytical solutions are presented for the static analysis of laminated orthotropic spherical shells. Chebyshev polynomial series are used for the solution of equilibrium equations of first-order shear deformation theory. Numerical results are presented to indicate the applicability of the method. Parametric studies are conducted to evaluate the magnitude of shear deformation effects in layered spherical caps. The analytical solutions presented here will serve as benchmark solutions for results obtained by finite element methods and other numerical methods. © 1990.

Composite Structures

Application of chebyshev polynomials to the analysis of laminated axisymmetric spherical shells

Chebyshev polynomials have been used to solve the problem of the large deflection of circular plates and the results have been compared with existing results. The nonlinear equations are treated as linear differential equations with variable coefficients and the analysis with Chebyshev polynomials results in a solution of linear algebraic equations. It is shown that the present analysis in the form of Chebyshev series has the property of rapid convergence. This technique has also been applied to postbuckling behaviour of circular plates with initial curvature. © 1976.

Journal	Computers and Structures
ISSN	00457949
Open Access	No