Boundary element analysis of the stress intensity factors for the v-notched structures

In this paper a new way is proposed to determine thegeneralized stress intensity factors of the plane V-notch structures byboundary element method. Firstly, a small sector around the V-notch tip isdug out from the V-notch structure. Based on the assumption of an asymptoticstress field in the V-notch tip region, evaluation of stress singularitiesof the sector zone are transformed into an eigenvalue problem of theordinary differential equations. Then the solutions of the eigenvalueproblem provide the singularity orders and associated eigenvectors of theV-notch. Hence the displacements and tractions on the arc of the abovesector are expressed as the linear combination of the finite terms of theseries expansion with different singular orders. Secondly, the boundaryelement method is used to model the V-notch structure removed the smallsector, in which the boundary conditions along the arc edge from cutting thesector are expressed by the above linear combination. Consequently, thegeneralized stress intensity factors and the stress field of the V-notchedstructure are obtained through the boundary element analysis. Finally, twonumerical examples are given to show the effectiveness of the presentmethod.