  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.
