Further studies in the application of curved finite elements to circular arches

Abstract The work of Ashwell and Sabir, 1 assessing the power of curved finite elements by applying them to circular arches, is extended. An element I based on the cylindrical shell element of Bogner et al. , 3 converges satisfactorily for deflexions, for all arch types, but is inferior to a new element II based on simple strain functions. A natural (“exact”) shape function is also presented. When stress resultants are calculated, both I and II converge rapidly if the stress resultants are calculated from an element stiffness matrix, but are sometimes unsatisfactory (except for mid-element stress resultants) if a normal type of stress matrix is used. I becomes unsatisfactory if nodal continuity of the gradient of circumferential displacement is imposed.