Optimal reinforcing networks for elastic membranes
Giovanni Alberti, Giuseppe Buttazzo, Serena Guarino Lo Bianco, Édouard Oudet, ,Dipartimento di Matematica e an, 80126 Napoli, Italy, ,Laboratoire Jean Kuntzmann, Université Grenoble Alpes, 38041 Grenoble, France · Networks and Heterogeneous Media · 2019
In this paper we study the optimal reinforcement of an elastic membrane, fixed at its boundary, by means of a network (connected one-dimensional structure), that has to be found in a suitable admissible class. We show the existence of an optimal network, and observe that such network carries a multiplicity that in principle can be strictly larger than one. Some numerical simulations are shown to confirm this issue and to illustrate the complexity of the optimal network when the total length becomes large.