Elasticity and Plasticity Problem for a Square Plate Weakened by a Hole with Partially Unknown Boundary

Abstract

We consider an elasticity and plasticity problem for a square plate weakened by a square hole with rounded vertices. The plasticity region contains only the unknown rounded part of the hole contour and is not spread inside the plate. We contract the solutions and obtain the equation of the unknown part of the hole contour when the normal displacement is constant on the linear parts of the boundary and there is no normal stress on the unknown part of the hole contour.