A General Theory of Rods

Abstract

Three main methods have been used to develop one dimensional theories of rods, mostly in the context of isothermal linear elasticity. The first consists of ad hoc assumptions which are apparently independent of any general theory. In the second approach one can start with the three-dimensional equations of elasticity and use an expansion or perturbation procedure, see for example Hay [1]. However, most of the authors who adopt the three-dimensional approach employ additional assumptions or variational methods. The third approach may be called the direct approach. This is the method employed by Green and Laws [2] whose work we discuss here. A further contribution has been given by Cohen [3) who uses a variational method to produce a theory of elastic rods, but his idea of a rod differs from that of Green and Laws.KeywordsWave SpeedTimoshenko Beam TheoryDirector ForcePerturbation ProcedureIdeal Incompressible FluidThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.