Local linear Timoshenko rod

Abstract

In this article, we consider a variant of the Simo–Reissner theory for a rod but restrict the study to two-dimensional motion where the rod undergoes flexure, shear and extension but not torsion. Linear elastic behaviour is assumed to formulate constitutive equations; the constitutive equations of the Timoshenko theory adapted for extension and large rotation. We call the model the local linear Timoshenko rod model. We show that this model serves as a framework for a class of simpler mathematical models for slender solids in various applications. The advantage is that the more general model can be used to evaluate and compare the simpler models.