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Elastic shells are thin curved solids bodies which resist deformation
owing to both the material of which they are composed and to their
shape. They are extremely important in structural mechanics and
engineering because a well-designed shell can sustain large loads with
remarkably little material. For this reason, shells are a favored
structural element in both natural and man-made constructions. Egg
shells, sea shells, and cell membranes are a few examples of natural
shells. Man-made shells have played a prominent role in construction
since antiquity, as in, for example, domed roofs, but in the past
century, as our understanding of the behavior of shells has increased,
they have become one of the most important and ubiquitous structural
elements.
While elastic shells can exhibit great strength, their behavior can also be very difficult to predict, and they can fail in a catastrophic fashion. The way a shell responds to external and internal forces and displacements is determined by a complex coupling of the mechanical properties of the material and the shell's geometry. Beginning in the late nineteenth century, and especially during the past few decades, there have been intense efforts to derive an accurate mathematical theory of shells. Despite much progress, and a very fruitful recent period, there remain many thorny issues concerning both the modeling and the numerical simulation of shells. In these talks I will try to give an overview of some of the main current in contemporary shell research, with an emphasis on open questions and directions and a minimum of technicality. |