Three-Dimensional Elasticity Solutions of Laminated Annular Spherical Shells

A procedure is presented for determining the three-dimensional elasticity solutions for free vibration analysis of simply supported thick skew plates. The exact expressions of strain and kinetic energies are derived from linear, small-strain, three-dimensional elasticity theory. To allow the treatment of soft and hard simple support conditions, sets of three-dimensional spatial displacement functions are expressed in terms of unit normals to the edges. By virtue of the three-dimensional elasticity theory, the present method does not require a special treatment for stress singularity at the obtuse corners. This method is also demonstrated to be free from shear locking phenomena. The significant difference in the vibration response of skew plates with soft and hard simple support conditions is highlighted. The influence of skew angle on the eigenvalues of thick skew plate is discussed in the context of the three-dimensional elasticity solutions.

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Three-Dimensional Solutions for Antisymmetrically Laminated Anisotropic Plates

Journal of Applied Mechanics ◽

10.1115/1.2888300 ◽

1990 ◽

Vol 57 (1) ◽

pp. 182-188 ◽

Cited By ~ 89

Author(s):

Ahmed K. Noor ◽

W. Scott Burton

Keyword(s):

Three Dimensional ◽

Composite Plates ◽

Double Fourier Series ◽

Stress And Strain ◽

Anisotropic Plates ◽

Stress Components ◽

Strain Components ◽

Elasticity Solutions ◽

Vibration Problems ◽

Three Dimensional Elasticity

Analytic three-dimensional elasticity solutions are presented for the stress and free vibration problems of multilayered anisotropic plates. The plates are assumed to have rectangular geometry and antisymmetric lamination with respect to the middle plane. A mixed formulation is used with the fundamental unknowns consisting of the six stress components and the three displacement components of the plate. Each of the plate variables is decomposed into symmetric and antisymmetric components in the thickness direction, and is expressed in terms of a double Fourier series in the Cartesian surface coordinates. Extensive numerical results are presented showing the effects of variation in the lamination and geometric parameters of composite plates on the importance of the transverse stress and strain components.

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Three-dimensional elasticity solution for laminated cross-ply panel under localized moment

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1243/09544062jmes410 ◽

2007 ◽

Vol 221 (8) ◽

pp. 859-866

Author(s):

A Alibeigloo ◽

M Shakeri

Keyword(s):

Differential Equations ◽

Ordinary Differential Equations ◽

Three Dimensional ◽

Axial Direction ◽

Variable Coefficients ◽

Cylindrical Panel ◽

Fourier Series Expansion ◽

Simply Supported ◽

Elasticity Solutions ◽

Three Dimensional Elasticity

Three-dimensional elasticity solutions have been presented for thick laminated crossply circular cylindrical panel. The panel is under localized patch moment in axial direction and is simply supported at all edges with finite length. Ordinary differential equations with variable coefficients are obtained by means of Fourier series expansion for displacement field and loading in the circumferential and axial directions. Resulting ordinary differential equations are solved using Taylor series. Numerical results are presented for (0/90°) and (0/90/0°) lay-up, and compared with the results for simple form of loading published in literatures.

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