Determination of stress intensity factors of V-notch structures by characteristic analysis coupled with isogeometric boundary element method

Abstract

To describe the physical fields of the V-notch structure accurately, the structure is first divided into two parts, the notch tip sector containing singular stress field and the non-singular remained part. A twofold procedure is then carried out to obtain the stress intensity factors: (I) the asymptotic expansions are introduced to describe physical fields of the singular region and transform the elastic governing equation to the characteristic ordinary differential equations. The interpolating matrix method is then implemented to provide stress singular orders and related characteristic angular functions of this singular area. (II) The boundary integral equation for the left part is then discretized by the non-uniform rational B-splines (NURBS) elements and is solved under the isogeometric framework. The amplitudes of the asymptotic expansions in process (I) are calculated by coupling procedures (I) and (II) through utilizing the interfacial continuity conditions. The stress intensity factors are finally obtained and compared with the referenced results for both symmetric and inclined V-notch structures. Benefiting from the isogeometric analysis, satisfied results can be provided by discretizing the artificial arc boundary between the singular and non-singular parts with fewer NURBS elements. This method can also be integrated with the preprocessing of computer aided design (CAD) conveniently.