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 and 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.
A Minimaxmax Problem for Improving the Torsional Stability of Rectangular Plates / Berchio, Elvise; Buoso, Davide; Gazzola, Filippo; Zucco, Davide. - In: JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS. - ISSN 0022-3239. - STAMPA. - 177:1(2018), pp. 64-92. [10.1007/s10957-018-1261-1]
|Titolo:||A Minimaxmax Problem for Improving the Torsional Stability of Rectangular Plates|
|Data di pubblicazione:||2018|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1007/s10957-018-1261-1|
|Appare nelle tipologie:||1.1 Articolo in rivista|