The membrane theory of shells, or membrane theory for short, describes the mechanical properties of
shells when twisting and
bending moment
In solid mechanics, a bending moment is the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend. The most common or simplest structural element subjected to bending mome ...
s are small enough to be negligible.
The spectacular simplification of membrane theory makes possible the examination of a wide variety of shapes and supports, in particular, tanks and shell roofs. There are heavy penalties paid for this simplification, and such inadequacies are apparent through critical inspection, remaining within the theory, of solutions. However, this theory is more than a first approximation. If a shell is shaped and supported so as to carry the load within a membrane stress system it may be a desirable solution to the design problem, i.e., thin, light and stiff.
Wilhelm Flügge
Gottfried Wilhelm Flügge (March 18, 1904 – March 19, 1990) was a German engineer, and Professor of Applied Mechanics at Stanford University.J.J. O'Connor and E.F. Robertson.Gottfried Wilhelm Flügge" at ''history.mcs.st-and.ac.uk.'' School of M ...
, ''Stresses in Shells'' (1973) 2nd edition, Preface, p. iv. . Originally published in German as ''Statik und Dynamik der Schalen'' (1937).
See also
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Theory of plates and shells
In continuum mechanics, plate theories are mathematical descriptions of the mechanics of flat plates that draws on the theory of beams. Plates are defined as plane structural elements with a small thickness compared to the planar dimensions ...
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Stress resultants in plates and shells
References
Literature
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* Practical industry example for plates and shell analysis
animated video
Scientific theories
Continuum mechanics
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