Cosserat Shells

Abstract

A shell-like structure or shell is a three-dimensional body that has special geometric features. Most importantly, the shell is a three-dimensional body that is considered to be “thin” in one of its dimensions (see Fig. 4.1.1). In particular, the shell is characterized by its major surfaces (bottom and top) and its lateral surface. From another point of view, the shell is considered to be a material surface S which has some finite thickness bounded by the major surfaces. If this surface S is flat, then the shell-like structure is called a plate, otherwise it is called a shell. Such shell-like structures appear in practice in many applications. For example, the floors, walls and roofs of many buildings are flat surfaces that can be modeled as plates, whereas the surfaces of an airplane body or car body, the human skull and the veins and arteries in the human circulatory system are curved surfaces that can be modeled as shells.