Membrane theory of shells

The Membrane Theory of Shells

Published in Eduard Ventsel, Theodor Krauthammer, Thin Plates and Shells, 2001

It was shown in Chapter 12 that a thin elastic shell supports an arbitrary external loading by means of stress resultants (internal forces) and stress couples (bending and twisting moments). Under appropriate loading and boundary conditions, however, the resulting bending and twisting moments are either zero, or so small that they may be neglected. Such a state of stress is referred to as the membrane state of stress because of the analogy to membranes that cannot support bending and twisting moments. The corresponding theory of thin shells that deals with this state of stress is called the membrane theory of shells. It follows from the above that the membrane theory neglects all moments, i.e., () M1=M2=H=0.

Non-linear collapse behavior of externally pressurized resin toroidal and cylindrical shells: numerical and experimental studies

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Journal Information

Published in Ships and Offshore Structures, 2021

Jian Zhang, Xin Wang, Wenxian Tang, Fang Wang, Yongmei Zhu

To understand the collapse mechanism of shells, the strength performances of toroidal and cylindrical shells were analytically and numerically examined. The meridional and circumferential stresses of the toroidal shell can be respectively determined based on the membrane theory of shells (Methods 2002) as follows: and

Membrane theory of shells

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The Membrane Theory of Shells

Non-linear collapse behavior of externally pressurized resin toroidal and cylindrical shells: numerical and experimental studies