New superelements for singular derivative problems of arbitrary order

The paper describes a new method for development of singular elements through optimal positioning of o set 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 di erent forms of singular stress eld in a bimaterial joint in a three-point-bend test. Numerical solutions for the singular elds existing at both ends of the material interface compare favourably with those obtained with the more usual re ned mesh approach.