A flexibility-based finite element for linear analysis of arbitrarily curved arches

A new finite element for linear analysis of arbitrarily curved plane beams is developed. Based on a flexibility formulation the exact stiffness matrix and nodal force vector are obtained. In this way the effectiveness of the arch element depends solely on the capability to describe accurately the arch geometry. To this purpose a cubic parametric representation is adopted, which is local to the element and capable to model curved beams of any shape, while preserving C1 continuity. In addition the proposed representation offers two inner parameters which can be used to locally adapt the arch shape. The resultant arch element is readily implementable into existing finite element codes and its effectiveness is validated through various benchmark problems, well established in the literature