Numerical Solution Procedures for Nonlinear Elastic Curved Rods Using the Theory of a Cosserat Point

Abstract

The numerical solution of problems of curved rods can be formulated using rod elements developed within the context of the theory of a Cosserat point. Although the general theory is valid for curved rods, the constitutive coefficients have been determined by comparison with exact linear solutions only for straight beams. The objective of this paper is to explore the accuracy of the predictions of the Cosserat theory for curved rods by comparison with exact solutions. Specifically, these problems include: linearized axisymmetric deformation of a circular ring loaded with internal and external pressures; nonlinear axisymmetric inversion of a circular ring; and linearized pure bending of a section of a circular ring. In all cases, the Cosserat theory performs well with no modifications of the constitutive constants, even in the limit of reasonably thick rods. Also, it is shown that the Cosserat theory does not exhibit shear locking in the limit of thin rods.