Pressure vessels, airplane wings and fuselages, pipes, ship and submarine hulls, the exteriors of rockets, missiles, automobile tires, incandescent lamps, caps, roof domes, chimneys, cooling towers, factory or car sheds, and a variety of containers represent typical shells. Interestingly, each of these examples has walls that are curved. Inasmuch as a curved plate can be viewed as a portion of a shell, the general equations for thin shells are also applicable to curved plates.

In this chapter, discussions are limited to a thin shell of constant thickness which is small compared to the other two dimensions. To describe the shape of a shell, we need only know the geometry of the midsurface and the thickness of the shell at each point. The thin-walled shell structure has more strength with respect to its self-weight and high stiffness. Membrane stresses in a typical shell structure such as a sphere, cylinder, cone, ellipsoid, toroid, hyperbolic paraboloid, and multisphere are discussed in numerous examples and a case study.