Integral Equations of Plane Elasticity in Domains with Peak

Abstract

Boundary integral equations provide an effective tool in the study and solution of boundary value problems in elasticity theory. Boundary value problems for the Lamé system can be reduced to a system of integral equations for which one gets results similar to those given in the previous chapters. In order to describe the stress and strain state of a body in plane elasticity, one uses the displacement vector u(x, y) = (u₁(x, y), u₂(x, y)) and the stress tensor with components σ _xx , σ _yy and τ _xy , which are considered as functions of the complex variables z=x + iy and $\bar z = x - iy$. Here x and y are Cartesian coordinates of the initial position of points of an elastic body, whose displacement is the vector u(z, $\bar z$).