New superelements for singular derivative problems of arbitrary order

The paper describes a new method for development of singular elements through optimal positioning of offset mid-side nodes using adjacent six- and eight-noded isoparametric elements. By joining the two elements to form a superelement, an attempt to rectify a known problem with existing approaches proves successful. Calculations are made to optimize the mid-side node positions and the relative size of the two elements for a wide range of singular orders. By way of example, the approach is applied to two different forms of singular stress field in a bimaterial joint in a three-point-bend test. Numerical solutions for the singular fields existing at both ends of the material interface compare favourably with those obtained with the more usual refined mesh approach. Copyright (C) 2001 John Wiley & Sons, Ltd.