The Strain-Energy Expression for Thin Elastic Shells

1958 ◽  
Vol 25 (4) ◽  
pp. 546-552
Author(s):  
J. H. Haywood ◽  
L. B. Wilson
Keyword(s):  
Circular Cylinder ◽  
Plane Stress ◽  
Strain Energy ◽  
Middle Surface ◽  
Thin Shells ◽  
Elastic Shells ◽  
Energy Expression ◽  
Small Deflection ◽  
Deflection Theory

Abstract A strain-energy expression is derived for thin isotropic elastic shells in terms of the displacements of the middle surface of the shell. This expression is confined to small-deflection theory, and the condition of plane stress previously used in the theory of thin shells is retained. A simplified expression is also obtained by the introduction of the Kirchhoff-Love hypothesis, and the relative merits of these two expressions are discussed. The strain-energy expression is applied to the thin circular cylinder, and the result is compared with various strain-energy expressions developed by previous authors.

A Strain-Energy Expression for Thin Elastic Shells

1949 ◽  
Vol 16 (2) ◽  
pp. 183-189
Author(s):  
H. L. Langhaar
Keyword(s):  
Strain Energy ◽  
Elastic Shell ◽  
Strain Tensor ◽  
Middle Surface ◽  
Circular Cylinders ◽  
Flat Plates ◽  
Energy Expression ◽  
Deflection Theory ◽  
Large Deflection Theory ◽  
Elliptical Cylinders

Abstract A derivation is given for the strain energy of an isotropic elastic shell whose radii of curvature are sufficiently large that strains may be assumed to vary linearly throughout the thickness. The work of Love (1) has been the only previous general investigation which expresses the strain energy in terms of the displacements of the middle surface. The effects of the tangential displacements upon the energy due to bending are found to differ appreciably from Love’s results in the first-order terms. As in the classical large-deflection theory of flat plates, quadratic terms in the derivatives of the normal deflection are retained in the strain tensor, but quadratic terms which involve the tangential displacements are neglected. Special forms of the general energy expression derived in this paper are given for shells in the shapes of flat plates, circular cylinders, elliptical cylinders, ellipsoids of revolution, and spheres. These applications, as well as certain intuitive observations, provide checks on the theory.

On Stress-Strain Relations and Strain-Energy Expressions in the Theory of Thin Elastic Shells

1960 ◽  
Vol 27 (1) ◽  
pp. 104-106 ◽  
Author(s):  
J. K. Knowles ◽  
Eric Reissner
Keyword(s):  
Strain Energy ◽  
Middle Surface ◽  
Stress Strain ◽  
Elastic Shells ◽  
Energy Expression ◽  
Energy Formula

The stress-strain relations of Flu¨gge and Byrne for thin elastic shells are inverted to express strain quantities, and therewith the strain energy, in terms of stress resultants and couples. In this form, and upon omission of terms which are small of order h2/R2, the stress-strain relations and the strain-energy expression are shown to be simply related to corresponding results of Trefftz. The strain-energy formula of Trefftz is generalized to arbitrary orthogonal middle surface co-ordinates.

Bending of Sandwich Plates of Variable Thickness

1988 ◽  
Vol 55 (2) ◽  
pp. 419-424 ◽  
Author(s):  
N. Paydar ◽  
C. Libove
Keyword(s):  
Potential Energy ◽  
Variable Thickness ◽  
Middle Surface ◽  
Total Potential Energy ◽  
Sandwich Plates ◽  
Energy Principle ◽  
Total Potential ◽  
Small Deflection ◽  
The Face ◽  
Deflection Theory

A small deflection theory, consisting of differential equations and a total potential energy expression, is presented for determining the stresses and deformations in variable thickness elastic sandwich plates symmetric about a middle surface. The theory takes into account the contribution of the face-sheet membrane forces (by virtue of their slopes) to the transverse shear. A finite-difference formulation of the stationary total potential energy principle is presented along with an illustrative application.

Buckling of Circular Plate on Elastic Foundation

1965 ◽  
Vol 87 (3) ◽  
pp. 323-324 ◽  
Author(s):  
L. V. Kline ◽  
J. O. Hancock
Keyword(s):  
Circular Plate ◽  
Middle Surface ◽  
Elastic Plates ◽  
Buckling Loads ◽  
Simply Supported ◽  
Small Deflection ◽  
Edge Conditions ◽  
Deflection Theory ◽  
Plate On Elastic Foundation ◽  
Clamped Edge

The buckling loads are found for the simply supported and clamped-edge conditions for a circular plate on a springy foundation under the action of edge loading in the middle surface of the plate. The small deflection theory of bending of thin elastic plates has been used.

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