A novel boundary element approach for solving the 2D elasticity problems Y.M. Zhang a,b,⇑ , Z.Y. Liu c , X.W. Gao b , V. Sladek d , J. Sladek d a Institute of Applied Mathematics, Shandong University of Technology, Zibo 255049, Shandong Province, PR China b State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, PR China c School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, PR China d Slovak Academy of Sciences, Institute of Construction and Architecture, 84503 Bratislava, Slovakia article info Keywords: BEM Elastic plane problem Exact geometrical element IBIE Nonsingular IBIE abstract The presentation is mainly devoted to the research on the regularized BEM formulations with indirect unknowns for two-dimensional (2D) elasticity problems. A novel regulariza- tion technique, in which regularized forms of the gradient equations without involving the direct calculation of CPV and HFP integrals are derived and shown to be independent of dis- placement equations, is pursued in this paper. After that, a numerically systematic scheme with generality is established by adopting quadratic Lagrange’s elements. Moreover, con- sidering the special geometric domain, such as circular or elliptic arcs, a new boundary geometric approximate technique, named as exact elements, is presented, and thus by the utilization of these elements the error of the results will arise mainly from the approx- imation of boundary quantities. Numerical examples show that a better precision and high computational efficiency can be achieved. Ó 2014 Elsevier Inc. All rights reserved. 1. Introduction The boundary element method (BEM) has become an efficient numerical method in solving practical engineering prob- lems. It is now not only available for many relevant linear problems of applied mechanics (e.g. elastostatics, elastodynamics, plate bending, etc.) but also for a number of nonlinear problems, such as elastoplasticity, etc. The main advantage of this method is the reduction of the dimension of boundary value problems. On the other hand, it is known as well that the stan- dard BEM formulations include singular integrals. Hence, the integrations should be performed very carefully and the overall accuracy of the BEM is largely dependent on the precision with which the various integrals, especially the singular integrals, are evaluated. Regularization, or singularity removal before numerical computation, can make the BEM an efficient and gen- erally well-conditioned numerical solution procedure [1–4]. For a better understanding of the proposed algorithm in this paper, a brief review of the other schemes employed to han- dle the singularity of the integrals is necessary and these proposed methods can be summarized on the whole as two cat- egories: the local and the global strategies. The local strategies are employed to calculate the singular integrals directly. They usually include, but are not limited to, analytical and semi-analytical one [5–8], new Gaussian quadrature [9], trans- formation method [10–12], the local regularization method [8,13,14], the interval subdivision [15,16] and finite-part integral [17,18], etc. The analytical algorithm needs enormous works of deduction and is generally considered more difficult for http://dx.doi.org/10.1016/j.amc.2014.01.071 0096-3003/Ó 2014 Elsevier Inc. All rights reserved. ⇑ Corresponding author at: Institute of Applied Mathematics, Shandong University of Technology, Zibo 255049, Shandong Province, PR China. E-mail address: zymfc@163.com (Y.M. Zhang). Applied Mathematics and Computation 232 (2014) 568–580 Contents lists available at ScienceDirect Applied Mathematics and Computation journal homepage: www.elsevier.com/locate/amc