Geometrically nonlinear analysis of planar circular arches based on rigid element concept — A structural approach

To overcome the difficulty involved in selecting proper shape functions for simulating the bending-tension coupling of a curved beam, a non-conventional “structural” approach is presented in this paper. For curved-beam elements with small subtended angles, the elastic stiffness matrix is derived as the composition of two chordwise straight beam elements used to represent the curved beam. In contrast, the geometrical stiffness matrix of the curved beam is derived by the rigid element concept, through transformation of the geometrical stiffness matrix of the rigid straight beam spanning the two ends of the curved bean from the rectangular to the curvilinear coordinates. Compared with the conventional finite element procedures relying strongly on numerical integrations, the present approach has the advantage of being simple in formulation, but also explicit in expressions. The numerical studies indicate that the derived curved beam element has good convergence characteristics upon mesh refinement for the linear problems studied, and is capable of solving the stability and nonlinear problems involving large-displacement postbuckling response.