Limitations of certain curved finite elements when applied to arches

Abstract Several segmental arch problems were solved by finite elements using three shape functions, namely, I, cubic expression for radial, linear for circumferential displacements; II, a form of Cantin and Clough's shape function for cylindrical shells; III, a shallow element form of II. For a moderately deep arch with a thick rib all shape functions converged rapidly to correct solutions with increasing number of elements. For a deep arch with a thin rib, no shape function gave satisfactory solutions for a number of elements up to 34. For intermediate cases, II was superior to III which was superior to I. The relevance to shell studies is pointed out and several conclusions drawn.