The structural analysis of shells has had a long and difficult history.
Shells were developed and reached their peak popularity just
before the ready availability of computers and the FE method.
This was unfortunate for the designers of these complex structures
because in lieu of rigorous methods they went to considerable
effort to verify their designs. Model analysis was one such
technique, where plexiglass models, or rarely cementitious models,
were strain gauged and loaded with weights. However, model
analysis was laborious, expensive, and impractical for testing
various trial shapes as easily as in the FE method.
Many cylindrical shells were analyzed using approximate
methods, in that when extended in the long direction they approach
beams in behavior, and when shortened in the same direction
approach arches in behavior. Hence, they fall between the
limiting cases of beams and arches. Corrugated iron, which is a
collection of cylindrical shells side-by-side, may be analyzed as a
beam of corrugated cross section. For short shells such as aircraft
hangars, where spacing of the arches is small compared to their
span, loads are mostly carried by the arches, not the shell itself.
Another method was to get the funicular or nonbending shape
of the shell using hanging weights from a mesh. The Swiss engineer,
Isler, froze suspended wet cloth to get the funicular. The
dimensions of the prototype were then taken from measurements
made on the model. A certain amount of error was thus introduced
in the prototype. Also, the funicular shape for dead load is not the
same as for partial span loads, which can occur with wind and shells is very different. Positive curvature shells are subject to
buckling, as the entire shell is subject to compression forces. In
contrast, material failure is more common in negative curvature
shells with brittle materials such as concrete.