Orateur
Description
This presentation focuses on shape optimization in thermoelasticity, motivated by the design of engine components subjected to thermal stresses.
First, I will discuss a linear framework in which the objective function—a von Mises norm under volume constraint—is analyzed using shape calculus and an adjoint state. This calculation involves a subtlety related to the boundary condition of the thermal adjoint, which becomes non-trivial as soon as the criterion weights the final time point. The framework is then extended to include a robust criterion, where temperature is modeled by a random field and the criterion becomes an expectation; thanks to the quadratic structure of the functional, this can be calculated exactly using a two-point correlation.
In a second step, the assumption of linearity is abandoned for temperature-dependent material parameters. This introduces reaction terms and tangent tensors into the sensitivity analysis, and, most importantly, a stronger coupling between the two adjoint states, which were previously independent. These new challenges are illustrated by numerical results on two test cases.