Inserted: 20 apr 2018
Last Updated: 20 apr 2018
In this paper we study the optimal reinforcement of an elastic membrane, fixed at its boundary, by means of a connected one-dimensional structure. We show the existence of an optimal solution that may present multiplicities, that is regions where the optimal structure overlaps. Some numerical simulations are shown to confirm this issue and to illustrate the complexity of the optimal structures when their total length becomes large.
Keywords: reinforcement, Crack identification, relaxed solution