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

[+] Author and Article Information
J. K. Knowles

Division of Engineering, California Institute of Technology, Pasadena, Calif.

Eric Reissner

Massachusetts Institute of Technology, Cambridge, Mass.

J. Appl. Mech 27(1), 104-106 (Mar 01, 1960) (3 pages) doi:10.1115/1.3643882 History: Received November 21, 1958; Online September 16, 2011


The stress-strain relations of Flügge 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.

Copyright © 1960 by ASME
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