On the Numerical Solution of One-Dimensional Continuum Problems Using the Theory of a Cosserat Point

Abstract

The theory of a Cosserat point is specialized to describe the motion of a one-dimensional continuum. Attention is focused on two problems of an elastic bar. Vibration of a linear-elastic bar is considered in the first problem and static deformation of a nonlinear-elastic bar subjected to a uniform body force is considered in the second problem. A closed-form solution is derived for each problem by dividing the bar into two elements, each of which is modeled as a Cosserat point. The predictions of the two-element approximation are shown to be very accurate.