membrane theory of shells

{{short description|Describes the mechanical properties of shells}}

{{confuse|M-theory}}

The membrane theory of shells, or membrane theory for short, describes the mechanical properties of shells when twisting or under bending and assumes that bending moments 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, Stresses in Shells (1973) 2nd edition, Preface, p. iv. {{isbn|978-3-642-88291-3}}. Originally published in German as Statik und Dynamik der Schalen (1937).