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Higher-order shear and normal deformable theory for functionally graded incompressible linear elastic plates

Batra, R.C.

AbstractWe use the principle of virtual work to derive a higher-order shear and normal deformable theory for a plate comprised of a linear elastic incompressible anisotropic material. The theory does not use a shear correction factor and employs three components of displacement and the hydrostatic pressure as independent variables. For a $K$ th order plate theory, a set of $4 (K + 1)$ coupled equations need to be solved for the $(K + 1)$ pressures and the $3 (K + 1)$ displacements defined on the reference surface of the plate.Equations for free vibrations of a plate are derived, and equations for the determination of frequencies and the corresponding mode shapes of a simply supported rectangular plate are given.

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Higher-order shear and normal deformable theory for functionally graded incompressible linear elastic plates

Batra, R.C.

AbstractWe use the principle of virtual work to derive a higher-order shear and normal deformable theory for a plate comprised of a linear elastic incompressible anisotropic material. The theory does not use a shear correction factor and employs three components of displacement and the hydrostatic pressure as independent variables. For a $K$ th order plate theory, a set of $4 (K + 1)$ coupled equations need to be solved for the $(K + 1)$ pressures and the $3 (K + 1)$ displacements defined on the reference surface of the plate.Equations for free vibrations of a plate are derived, and equations for the determination of frequencies and the corresponding mode shapes of a simply supported rectangular plate are given.

Higher-order shear and normal deformable theory for functionally graded incompressible linear elastic plates

Batra, R.C.

AbstractWe use the principle of virtual work to derive a higher-order shear and normal deformable theory for a plate comprised of a linear elastic incompressible anisotropic material. The theory does not use a shear correction factor and employs three components of displacement and the hydrostatic pressure as independent variables. For a $K$ th order plate theory, a set of $4 (K + 1)$ coupled equations need to be solved for the $(K + 1)$ pressures and the $3 (K + 1)$ displacements defined on the reference surface of the plate.Equations for free vibrations of a plate are derived, and equations for the determination of frequencies and the corresponding mode shapes of a simply supported rectangular plate are given.

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Title:

Higher-order shear and normal deformable theory for functionally graded incompressible linear elastic plates

Contributors:

Batra, R.C. (author)

Published in:

Thin-Walled Structures ; 45 ; 974-982

Publication date:

2007-07-19

Size:

9 pages

ISSN:

DOI:

https://doi.org/10.1016/j.tws.2007.07.008

Type of media:

Article (Journal)

Type of material:

Electronic Resource

Language:

English

Keywords:

Plate theory , Rubberlike materials , Free vibrations , Functionally graded material

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