Phillip BAUMANN successfully defended his PhD thesis ”Topological asymptotic expansion of shape functionals via adjoint based methods and nonsmooth analysis in structural optimisation” on 13 June 2024. His thesis exams asymptotic analysis in the context of topology optimisation and the stress minimisation via shape optimisation. The results of this thesis cover a nonsmooth framework to tackle stress-constrained problems in structural optimisation as well as the correlation to some well established theory in nonsmooth analysis. Additionally, he investigated various adjoint based techniques to compute topological sensitivities, which lead to a schematic computation of the complete topological asymptotic expansion for a given model problem. These expansions pave the ground for higher order numerical methodologies, including Newton-type algorithms.
The PhD reviewers were Antonio André NOVOTNY (National Laboratory of Scientific Computing, Brazil) and Samuel AMSTUTZ (Avignon Université, Department of Mathematics, France).