SAMS Subject Classification Number: 20

In this presentation a mathematical model for large planar motion of elastic rods which undergo flexure, shear and extension but not torsion is derived. (We use the term rod for one-dimensional solids, i.e. beams, cables, ropes, hoses. etc.) Since the Timoshenko theory provides an excellent approximation for three-dimensional elastic behaviour with plane stress, we adapted the constitutive equations for application to large rotations to complete the model, which we call the the Local Linear Timoshenko rod (LLT) model. We demonstrated that this model serves as a framework for a class of simpler mathematical models for slender solids in various applications with the advantage that the more general model can be used to evaluate and compare the simpler models.

Each mathematical model in this presentation consists of a system of nonlinear partial differential equations.