ABSTRACT
All cases treated so far were bending resistant structures which, when in their equilibrium position, have a 0 or negligible stress level. In a very different category are skin structures, where the forces that restore the displaced skin to its equilibrium position are caused by stresses initially present that can be assumed to be independent of motion. Such skin structures are referred to as membranes. They can be flat, such as classical membranes, stretched over three-dimensional frames, or supported in shape and tension by internal air pressure, such as tires (Kung et al., 1985; Saigal et al., 1986). Tension may also be provided by gravity, as in hanging curtains or nets (see Sec. 15.8). Note that the restoring effect is entirely different from the membrane approximation for shells discussed earlier, where the restoring forces are caused by the changing membrane stresses as the deflection occurs. There is a slight problem in semantics, of course, since the word membrane is used in the context of both categories.
