Analysis of swept plates with structural reduction using transition element concept

Abstract

Near the fixed end boundaries of cantilever swept plates, a high stress variation, especially in a near singular fashion at the re-entrant corner, requires that at least at this region, one requires an analysis with a high precision triangular plate bending element. An idealisation of an entire swept plate, especially one of large aspect ratio, by high precision elements may be uneconomical and the approximation of regions away from the boundary by a suitable beam element will achieve a considerable reduction in problem size. Thus one can achieve a structural reduction of the swept plate problem by the use of plate elements in regions of high stress variation, beam elements in regions away from the kinematically constrained boundaries and a variationally condensed transition plate/beam element which will have the nodes and degrees of freedom of high precision C 1 continuous plate elements along one boundary and the node and degrees of freedom of a beam element along the other boundary. This interphase element will provide the required transition from thin plate to thin beam behaviour. In this paper, extensive results indicate a considerable reduction in problem size and solution time without significant loss of accuracy in stresses, displacements and slopes.