scholarly journals Discussion: “A Strain-Energy Expression for Thin Elastic Shells” (Langhaar, H. L., 1949, ASME J. Appl. Mech., 16, pp. 183–189)

1950 ◽  
Vol 17 (1) ◽  
pp. 107
Author(s):  
W. T. Koiter
Keyword(s):  
Strain Energy ◽  
Elastic Shells ◽  
Energy Expression

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.

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.

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