Analytical solution of spatial elastica and its application to kinking problem

An analytical solution is presented for the spatially large deformation of a thin elastic rod (spatial elastica) which is naturally straight and uniform with equal principal stiffnesses and is subjected to terminal loads. The elastica can suffer not only flexure and torsion as in the classical Kirchhoff theory, but also extension and shear. The present solution is expressed in integral form and described in terms of only four parameters. This solution clears the difficulty with the polar singularity in the use of Euler angles. Hence, the numerical analysis is possible for various boundary value problems with no limitation. In this paper we study the post-buckling behavior of an elastica under the terminal twist and uniaxial end-shortening, and give a theoretical explanation to commonly observed phenomena such as secondary bifurcation, formation of a kink, snap-through behavior. The contact problem is analyzed in the case where the elastica contacts with itself and forms a kink. These results are available for other analysis, e.g., based on finite element approximations. © 1997 Elsevier Science Ltd.