Two-dimensional polynomial eigenstrain formulation of boundary integral equation with numerical verification

• Published in: Applied mathematics and mechanics Vol. 32; no. 5; pp. 551 - 562
• Main Author: 马杭 郭钊 秦庆华
• Format: Journal Article
• Language: English
• Published: Heidelberg Shanghai University Press 01.05.2011; Department of Mechanics, College of Sciences, Shanghai University, Shanghai 200444, P. R. China%Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P. R. China%School of Engineering, Australian National University, Canberra, ACT 0200, Australia
• Subjects: Algorithms; Applications of Mathematics; Boundaries; Boundary element method; Classical Mechanics; Fluid- and Aerodynamics; Inhomogeneities; Integral equations; Mathematical analysis; Mathematical Modeling and Industrial Mathematics; Mathematical models; Mathematics; Mathematics and Statistics; Partial Differential Equations; Two dimensional; Eshelby tensor; O241; 74S05; 74S15; polynomial; boundary integral equation (BIE); inhomogeneity Berlin Heidelberg; eigenstrain; inhomogeneity
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-011-1437-x

The low-order polynomial-distributed eigenstrain formulation of the boundary integral equation （BIE） and the corresponding definition of the Eshelby tensors are proposed for the elliptical inhomogeneities in two-dimensional elastic media. Taking the results of the traditional subdomain boundary element method （BEM） as the control, the effectiveness of the present algorithm is verified for the elastic media with a single elliptical inhomogeneity. With the present computational model and algorithm, significant improvements are achieved in terms of the efficiency as compared with the traditional BEM and the accuracy as compared with the constant eigenstrain formulation of the BIE.