On an inverse thermo-elasticity problem for an infinite medium containing a cavity of unknown shape

Abstract

The static inverse thermoelastic problem for an infinite elastic isotropic medium containing a cavity of unknown shape, under three-axes tension and given constant values of the pressure and the temperature on the cavity surface, is considered. The shape of a cavity is sought subject to the condition that certain stress components are uniform on the cavity surface. It is shown that ellipsoidal shapes furnish a solution of this inverse thermo-elasticity problem. Nonlinear equations for determining the geometric cavity parameters, which lead to an equal-stress state along the cavity surface, are obtained. Results of other authors for force loading only are obtained as special cases. Numerical investigations have been carried out and correlations between values of the force and temperature loadings and geometrical parameters for an equal-stress cavity surface are studied. The stress values on the equal-stress cavity surface under force and temperature loadings are investigated.

Inverse Reconstruction of Thermal and Mechanical Boundary Conditions in Coupled Nonlinear Thermo-Elastic Problems

“…Kirilyuk et al [2007] focused on the thermo-elastic inverse problems containing a cavity of unknown shape in the domain. In another study, Kirilyuk and Levchuk [2008] considered the static ITEP for an infinite elastic isotropic medium containing a cavity of unknown shape, under three-axial tension. Some researches on inverse problems are related to hollow cylinders.…”