A model of a general elastic curved rod

Abstract

We indicate a new approach to the deformation of three-dimensional curved rods with variable cross-section. The model consists of a system of nine ordinary differential equations for which we prove existence and uniqueness via the coercivity of the association bilinear form. From the geometrical point of view, we are using the Darboux frame or a new local frame requiring just a C1-parameterization of the curve. Our model also describes the deformation occurring in the cross-sections of the rod. Copyright © 2002 John Wiley & Sons, Ltd.