One dimensional optimal reinforcements of elastic structures

grenoble
[MATH]Mathematics [math]
mathalp colloquium 2018
colloquium mathalp 2018
elastic structures
dimensional optimal reinforcements

Appears in collection : Colloquiums MathAlp

In this talk 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.