Deformation Analysis of Cosserat Rods Using Piecewise Clothoid Approximation

Abstract This paper presents an alternative to isogeometric analysis (IGA) for static analysis of planar curved slender beams. Geometrically exact Cosserat rod model is employed to establish the governing equations. In contrast to conventional IGA, which uses NURBS as the basis function, our method incorporates clothoid curves to represent the curved geometry. We use piecewise clothoid curves to approximate the initial curvature of the undeformed beam, facilitating a seamless integration into the Cosserat rod model. A straightforward solution of the governing equations is implemented using shooting method, verifying applicability across a range of problems. Interestingly, the parameters that define the clothoid segments also appear in the governing equations of the beam. This bridges the gap between the geometric design of the beams and their static simulations. In this way, we present the proposed formulation as an alternative to conventional IGA. The notable features of the method are easy implementation, good accuracy, and convergence. Moreover, the method predicts bending stress in the beam, capturing the nonlinearity of the deformation.