Thermoelastic state of a medium,containing a thermally insulated ellipsoidal cavity,when subjected to a uniform heat flow

This article examines a problem of static thermoelasticity for an isotropic medium with an ellipsoidal cavity. The orientation of the cavity relative to the heat flow is assumed to be arbitrary. The solution of the problem is constructed in closed form and is expressed through incomplete elliptic integrals of the first and second kinds. In cases when the ellipsoid degenerates into a spheroid or sphere, the stress-strain state can be written in elementary functions of the ellipsoidal coordinate.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 19, pp. 46–50, 1988.