Maximal monotone relations and the second derivatives of nonsmooth functions
Moreau's decomposition theorem revisited
Multi-phase structural optimization via a level set method
We consider the optimal distribution of several elastic materials in a fixed working domain. In order to optimize both the geometry and topology of the mixture we rely on the level set method for the description of the interfaces between the different phases. We discuss various approaches, based on Hadamard method of boundary variations, for computing shape derivatives which are the key ingredients for a steepest descent algorithm. The shape gradient obtained for a sharp interface involves jump...