SEPARATION OF VARIABLES IN THE INVERSE AXISYMMETRIC PROBLEM OF ELASTICITY.

The inverse problem of elasticity for a multiply connected homogeneous and isotropic space S with cavities, loaded at infinity by forces consists in determining the shape of the smooth boundary of the closed nonintersecting cavities, that minimize the maximum density (over the domain) of the integral of the strain energy of dispersion, i. e. , the local Mises criterion. The optimal boundary in this sense makes it possible to increase the acting load to the maximum possible limit, at which plasticity does not arise at any point of S. In this paper we give a method of determining the boundary for the case of two identical cavities, and with force and geometrical symmetry of the problem with respect to the axis of the cylindrical (z, r, theta ) system.