Optimal control of thermal and mechanical loads in activation processes of mechanical components

This paper develops a mathematical framework that aims to control the temperature and rotational speed in the activation process of a gas turbine in an optimal way. These controls influence the deformation and the stress in the component due to centripetal loads and transient thermal stress. An optimal control problem is formulated as the minimization of maximal von Mises stress over a given time and over the whole component. To find a solution for this, we need to solve the linear thermoelasticity and the heat equations using the finite element method. The results for the optimal control as functions of the rotation speed and external gas temperature over time are computed by sequential quadratic programming, where gradients are computed using finite differences.The overall outcome reveals a significant reduction of approximately 10\%, from $830 \frac{N}{mm^2}$ to $750 \frac{N}{mm^2}$, in von Mises stress by controlling two parameters, along with the temporal separation of physical control phenomena.