INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Int. J. Numer. Meth. Engng 2002; 55:293–316 (DOI: 10.1002/nme.497) A new variable-order singular boundary element for two-dimensional stress analysis K. M. Lim 1; ∗; † , K. H. Lee 1; 2 , A. A. O. Tay 1; 3 and W. Zhou 1; 2 1 Department of Mechanical Engineering; National University of Singapore; Singapore 2 Center for Advanced Computations in Engineering Science; National University of Singapore; Singapore 3 Center for IC Failure Analysis and Reliability; National University of Singapore; Singapore SUMMARY A new variable-order singular boundary element for two-dimensional stress analysis is developed. This element is an extension of the basic three-node quadratic boundary element with the shape functions enriched with variable-order singular displacement and traction elds which are obtained from an asymp- totic singularity analysis. Both the variable order of the singularity and the polar prole of the singular elds are incorporated into the singular element to enhance its accuracy. The enriched shape functions are also formulated such that the stress intensity factors appear as nodal unknowns at the singular node thereby enabling direct calculation instead of through indirect extrapolation or contour-integral meth- ods. Numerical examples involving crack, notch and corner problems in homogeneous materials and bimaterial systems show the singular element’s great versatility and accuracy in solving a wide range of problems with various orders of singularities. The stress intensity factors which are obtained agree very well with those reported in the literature. Copyright ? 2002 John Wiley & Sons, Ltd. KEY WORDS: variable-order stress singularity; boundary element method; stress intensity factor 1. INTRODUCTION This paper describes the development of a new variable-order singular boundary element for two-dimensional stress analysis involving various orders of stress singularities. The present element is specially formulated for two-dimensional multi-domain problems in linear elasticity. This element incorporates the results of an asymptotic singularity analysis using complex stress functions, which provides both the correct singularity order and the proper polar description of the stress and displacement proles in the singularity region. Singular stress elds arise from linear elasticity problems, where discontinuities in geometry or boundary conditions are present. Problems involving sharp corners, cracks and wedges in multi-material domains usually exhibit such stress elds. Many researchers have studied and ∗ Correspondence to: K. M. Lim, Department of Mechanical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Singapore. † E-mail: limkm@nus.edu.sg Received 19 February 2001 Copyright ? 2002 John Wiley & Sons, Ltd. Revised 18 September 2001