Curvilinear Coordinate Systems

Abstract

Shells involve thin walled elastic bodies wherein one dimension is considerably smaller than the other two, but in which the midsurface is curved in at least one direction. Thus, to describe a shell succinctly, curvilinear coordinates must be employed. This causes considerable complications in the mathematical descriptions and operations, not existing in the same equations posed in a Cartesian coordinate system. It would be proper to introduce the subject of shell theory by preceding it with a course in topology. However, in what follows, the description of mathematics involving curvilinear coordinates is given, sufficient only to derive the general shell equations. In no way is the presentation rigorous or inclusive. Other texts such as Malvern (Reference 1.1) and Sokolnikoff [1.2] should be consulted by those who wish to learn more.