THE SOLUTION OF PROBLEMS OF THE THEORY OF ELASTICITY FOR A PLANE WITHA DOUBLY SYMMETRICAL 2-CUSP CUT

The first fundamental and mixed problems of the theory of elasticity f or a plane with a doubly symmetric two-cusp cut at the boundary are so lved. By changing the parameter this cut can be deformed, bringing the edges together or separating them. The case of free edges and contact displacements in a small neighbourhood of the tip were investigated f or a family of cuts of this kind in [1-3]. The first fundamental probl em of the theory of elasticity with non-zero boundary stresses is redu ced to solving two Hilbert problems for the exterior of the unit circl e. A mixed problem when the normal stresses acting at the boundary of the opening ensure specified displacements along a vertical axis. This mixed problem is reduced to a singular Hilbert integral equation and after solving it is reduced to the first fundamental problem of the th eory of elasticity solved earlier.