ИСТИНА

The two-dimensional problem on a curvilinear nanohole in an infinite elastic body under arbitrary remote loading is solved. The shape of the hole is assumed to be weakly deviated from the circular one and the complementary surface stresses are acting at the boundary. The boundary conditions are formulated according to the generalized Laplace - Young law. The study is based on Gurtin - Murdoch surface elasticity model. Using Goursat - Kolosov complex potentials and the boundary perturbation technique, the solution of the problem is reduced to a singular integro-differential equation for any-order approximation. The algorithm of solving this integral equation is constructed in the form of a power series. Solutions of the integral equation and corresponding complex potentials are obtained for zero-order and firstorder approximations. The size effect in the form of the dependence of the stress distribution at the surface on the size of the hole is demonstrated.