ASYMPTOTIC-BEHAVIOR OF STRESS-STRAIN STATE IN THE VICINITY OF SHARP DEFECTS IN AN ELASTIC BODY

The present paper deals with asymptotic representations of solutions to plane and three-dimensional elasticity problems in a neighbourhood of the tip of a sharp inclusion. In a two-dimensional case results are analysed for different kinds of cusp-shaped inclusions and for a thin angular one. With regard to the equations of three-dimensional elasticity, the stress-strain behaviour in the vicinity of cusp-shaped elastic and rigid inclusions have been studied. The dependence of results on the geometry of a cusp (in relation to the integral Diny condition) is emphasized, and a boundary layer effect in a neighbour of a irregular point on the boundary is studied.