Calculus of Variations and Geometric Measure Theory

G. Alberti - G. Buttazzo - S. Guarino Lo Bianco - E. Oudet

Optimal reinforcing networks for elastic membranes

created by buttazzo on 20 Apr 2018
modified by alberti on 21 May 2019


Accepted Paper

Inserted: 20 apr 2018
Last Updated: 21 may 2019

Journal: Networks and Heterogeneous Media
Year: 2019

ArXiv: 1904.01905 PDF


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.

Keywords: Optimal Networks, reinforcement, relaxed solution, elastic membranes