Analysis of singular stress field around the inclusion corner tip

Abstract

The plane problem of an infinite plate containing an inclusion is considered. The singular stress field around the inclusion corner tip is expressed as a sum of two independent types: a symmetric type with a stress singularity 1 r 1−λ1 and a skew-symmetric type with a stress singularity 1 r 1−λ2 . The intensities of the symmetric and skew-symmetric singular stress fields are defined in terms of constants K Iλ 1 and K II, λ2 , respectively. The body force method is used to calculate the values of K I, λ1 and K II, λ2 . In numerical analysis, basic density functions of the body forces are introduced to characterize the stress singularity at the inclusion corner. The advantages of this technique are the high accuracy of results, due to the smoothness of the unknown weight functions, and the presence of the direct relation between the values of K I, λ1 , K II, λ2 and the values of unknown weight functions at the corner tip.