General Displacement and Traction BEM for Plane Couple-Stress Problems

In this paper, the general equations of plane strain problems are first summarized for three typical couple stress theories. Based on the constitutive relations, the general traction boundary integral equations (TBIEs) are then derived from the displacement BIEs (DBIEs) along with the explicit high-order fundamental solutions for the plane couple-stress problems. Then, the boundary element method (BEM) codes based on the DBIEs (DBEM) and TBIEs (TBEM) discretized by the collocation scheme are developed separately. Some typical elastic couple-stress problems are numerically studied. For crack problems, the displacement extrapolation formulas are derived for computing the stress and couple-stress intensity factors. Good agreements are observed between the results obtained by the DBEM and the TBEM. The high accuracy of the present BEM results is verified by comparing them with the analytical results.