Body Force Analogy for Transient Thermal Stresses

A body-force analogy for transient thermal stresses in linear elastic solids is presented. The analogy is derived in the framework of the stress equations of motion and the corresponding stress-based characterization of initial boundary-value problems of elasticity. The latter framework was introduced by Professor Jozef Ignaczak, to whom the present contribution is dedicated. Starting from Ignaczak's stress-based formulation, we subsequently derive a body-force analogy by studying conditions, under which a certain time-dependent volume integral, being positive in case of non-vanishing stresses, and vanishing otherwise, becomes zero. These conditions lead us to the formulation of a boundary-value problem, which must be satisfied by the auxiliary body-forces, surface tractions and kinematic boundary conditions, in order that the stresses in the auxiliary isothermal problem and in the thermal stress problem do coincide. As a numerical example, Finite Element Computations for a beam-type structure are presented.