Cosserat Rods

Abstract

A rod-like structure, or rod, is a three-dimensional body that has special geometric features. Most importantly, the rod is a three-dimensional body that is considered to be “thin” in two of its dimensions (see Fig. 5.1.1). In particular, the rod is characterized by its ends and its lateral surface. From another point of view, the rod is considered to be a material curve C which has some finite thickness bounded by the rod’s lateral surface. If this curve C is a straight line, then the rod-like structure is called a beam, otherwise it is called a rod. Such rod-like structures appear in practice in many applications. For example, the main supporting structures in buildings, and the connecting bars in trusses can be modeled as beams, whereas the curved reinforcement ribs of airplane wings and submarines, and the double helix of DNA molecules can be modeled as rods.