Control of thermal stresses in axissymmetric problems of fractional thermoelasticity for an infinite cylindrical domain

Abstract

In this paper, we study a control problem of thermal stresses in an infinite cylindrical body. The temperature distribution is defined by the time-fractional heat conduction equation with the Caputo derivative of the order 0 < a <= 2. The problem is formulated for axisymmetric case. The sought-for heat source function is treated as a control of stress and displacement components. For this purpose, we find the control function which guarantees the distribution of the stress component in some section of a body and at some time at a prescribed level. Integral transform technique is applied to obtain the desired control function, stresses, and displacement components. Numerical results are illustrated graphically.