A conforming solution to curved plate bending problems

A curved triangular element for plate bending is developed, using the displacement method of formulation. The element has one outwardly curved side and conforms on an arbitrary quadratic boundary. To the user, the element appears as a single curved triangle. Internally, however, the element is subdivided into a straight-sided triangle and a ‘curved segment’. The straight-sided triangle is extensively documented in the literature^2-5 and is referred to in the paper as the Cowper triangle. The curved segment is a two-noded element with 12 degrees-of-freedom. It has one straight side and one curved side. Independent expansions are assumed in each domain and explicit shape functions derived. The theoretical solution to a few practical problems is contained in each of the two expansions. In such cases, the curved triangle produces perfect results. Otherwise, the accuracy is of the same order as that obtained in similar problems with straight boundaries. The method is easily extended to elements of higher order.