Numerical solution of elastic inclusion problem using complex variable boundary integral equation

Abstract

Based on a complex variable boundary integral equation (CVBIE) suggested previously, this paper provides a numerical solution for the elastic inclusion problem using CVBIE. A dissimilar elastic inclusion is embedded in the infinite matrix. The original problem is decomposed into two problems. One is an interior boundary value problem (BVP) for the elastic inclusion, while the other is an exterior BVP for the matrix with notch. Both problems are connected by conventional boundary integral equations (BIEs) in complex variables. After performing discretization for the coupled BIEs, the inverse matrix technique is suggested to solve the relevant algebraic equations. Based on the properties of some integral operators, three ways for the inverse matrix technique are suggested. Several numerical examples are carried out to prove the efficiency of the suggested method.

Numerical solution for the degenerate scale problem in plane elasticity using null field CVBIE

“…1). Previously, a CVBIE (complex variable boundary integral equation) for the exterior region was suggested [18,19]. After dropping the free term in the usual CVBIE, and assuming the null field point t o to be inside the contour Γ, or t o A Γ o (Fig.…”

“…This paper provides a numerical solution for the degenerate scale problem in plane elasticity, which is based on the usage of the null field complex variable boundary integral equation (CVBIE) [18,19]. Comparing with the usual real BIE, the CVBIE has a particular Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/enganabound advantage in derivation.…”

An Innovative Solution in Closed Form and Numerical Analysis for Dissimilar Elliptical Inclusion in Plane Elasticity

“…The analytical continuation method together with an alternating technique was used in the derivation. Based on a complex variable boundary integral equation (CVBIE), a dissimilar inclusion problem was solved [Chen, 2012]. After performing discretization for the coupled BIEs, the inverse matrix technique is suggested to solve the relevant algebraic equations.…”