We are interested in optimizing the compliance of an elastic structure when the applied forces are partially unknown or submitted to perturbations, the so-called "robust compliance".
For linear elasticity,the compliance is a solution to a minimizing problem of the energy. The robust compliance is then a min-max, the minimum beeing taken amongst the possible displacements and the maximum amongst the perturbations. We show that this problem is well-posed and easy to compute.
We then show that the problem is relatively easy to differentiate with respect to the domain and to compute the steepest direction of descent.
The levelset algorithm is then applied and many examples will explain the different mathematical and technical difficulties one faces when one
tries to tackle this problem.