Membrane theory of shells

Summary

The membrane theory of shells is the simplest shell theory. It assumes that a thin shell carries its loads only by forces in its middle surface, without bending moments. The equilibrium equations then involve only the membrane forces and the curvature of the surface. For many smooth shells under smooth loads, such as tanks under pressure and domes under their own weight, this gives the main state of stress. Bending becomes important near edges, supports and point loads, where the membrane state cannot satisfy all the conditions.