Two-dimensional shape identification for the unsteady conduction problem

A transient heat conduction problem within an anisotropic domain is formulated. The variation of an arbitrary behavioural functional corresponding to the infinitesimal variation of structural domain is considered. The first-order sensitivity is presented using the material derivative concept and both direct and adjoint approaches. The results obtained are particularized for the specific form of the identification functional defined in the form of “distance” between temperature of the identified body and the measured temperature of the real structure. Stationarity conditions are derived. Numerical examples of internal boundary identification are presented.