Stiffness of a curved beam subjected to axial load and large displacements

The deformation of an inextensible, curved elastic beam subjected to axial load is studied using the Bernouilli-Euler hypothesis and including the effect of large displacements. The axial displacement of the beam was expressed as a function of the axial load in terms of two incomplete elliptic integrals and contained a singularity as the beam was fully straightened. The nature of the singularity was determined and the load-axial displacement curves were accurately fitted to a rational expression with the same type of singularity, which provides an analytical expression for the evolution of the beam stiffness during deformation. Another analytical expression (although implicit) was obtained in the case of extensible beams, where the elongation due to normal stresses cannot be neglected. These results are relevant to the simulation of the elastic deformation of non-woven felts.