Structure Design of a Piezoelectric Composite Disk for Control of Thermal Stress

In order to realize a plan for a hypersonic aircraft, development of a smart heat-resisting plate possible to control a thermal stress has been required because the safety of structural members must be secured even if they are exposed to a severe thermal loading beyond an estimated load. In view of such a background, this paper deals with a control problem of a thermal stress in a multilayer composite circular disk consisting of a structural layer and piezoceramic layers with concentrically arranged electrodes. When a heating temperature distribution acts on the structural layer surface, the maximum thermal stress in the structural layer can be suppressed by applying appropriate voltages to the electrodes. This thermo-elastic problem has been theoretically analyzed by employing the potential function techniques. Utilizing the analytical results, the nonlinear optimization problem for determining the applied voltages is transformed into a linear programming problem and then the optimum solution is successfully obtained. Based on the obtained solutions, the structure of a composite disk has been designed in order to demonstrate the function of stress control to the fullest extent possible. Finally, numerical results for the stresses before and after applying the determined voltages as well as for the structure design of the composite disk and the suppression ratio of the maximum thermal stress are shown in graphical and tabular forms. It is seen from the numerical results that the maximum thermal stress can be reduced by about 34% when the structure of the composite disk is designed optimally.