◾ Solutions for Rods, Beams, Membranes, Plates, and Shells
Similar approaches may be used to construct approximate solutions to many important problems. In this chapter, we will discuss (1) the deformation of slender rods and the simpler special case of a straight beam, and (2) the deformation of a thin 3D shell and the simpler cases of membranes and at plates. e theories outlined in this chapter were originally developed in the early part of the past century to help in mechanical vibration and structural design calculations. ey are still used for this purpose today but are also used to model biological systems, such as bacterial agellae or cell walls, and also to model nanoscale structures such as carbon nanotubes.