Shape optimization is indispensable for designing and constructing industrial components. Many problems that arise in application, particularly in structural mechanics and in the optimal control of distributed parameter systems, can be formulated as the minimization of functionals which are defined over a class of admissible domains.

Shape optimization problems can be solved by means of gradient based minimization algorithms, which involve the shape functionals’ derivative with respect to the domain under consideration. The computation of the shape gradient and the implementation of appropriate numerical optimization algorithms is meanwhile well understood, provided that the state equation’s input data are given exactly. In practice, however, input data for numerical simulations in engineering are often not exactly known. One must thus address how to account for uncertain input data in the state equation.

This project is concered with shape optimization under uncertainty. The uncertainty might be caused by different sources like uncertain geometric entities, uncertain loads, or uncertain material parameters.