Calculus of Variations and Geometric Measure Theory

E. Berchio - D. Buoso - F. Gazzola - D. Zucco

A Minimaxmax Problem for Improving the Torsional Stability of Rectangular Plates

created by zucco on 11 Mar 2018


Published Paper

Inserted: 11 mar 2018
Last Updated: 11 mar 2018

Journal: JOTA
Year: 2018
Doi: 10.1007/s10957-018-1261-1

ArXiv: 1802.07230 PDF


We use a gap function in order to compare the torsional performances of different reinforced plates under the action of external forces. Then, we address a shape optimization problem, whose target is to minimize the torsional displacements of the plate: this leads us to set up a minimaxmax problem, which includes a new kind of worst-case optimization. Two kinds of reinforcements are considered: one aims at strengthening the plate, the other aims at weakening the action of the external forces. For both of them, we study the existence of optima within suitable classes of external forces and reinforcements. Our results are complemented with numerical experiments and with a number of open problems and conjectures.