Influences of surface on the interaction between holes or edge

The effects of surface energy on the interaction between holes or edge are investigated. Three typical problems are discussed: (1) an infinite plate containing two holes of unequal size subjected to an all-round tension, (2) a circle disc containing an eccentric hole subjected to uniform pressure on either external or internal surface, (3) a semi-infinite plate containing an unstressed circular hole subjected to a uniform tension parallel to its straight edge. The problems are solved by series expansion in bipolar coordinates. The results show that the surface energy significantly affects the stress concentrations around the holes as the size of the holes shrinks to nanometers. Meanwhile, the interaction between the holes or edge influences the stress distribution around the holes or edge, which becomes evident as the holes or edge close to each other and is affected by the surface effect significantly.