A Minimaxmax Problem for Improving the Torsional Stability of Rectangular Plates

Elvise Berchio (), Davide Buoso (), Filippo Gazzola () and Davide Zucco ()
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Elvise Berchio: Politecnico di Torino
Davide Buoso: Universidade de Lisboa
Filippo Gazzola: Politecnico di Milano
Davide Zucco: Università di Torino

Journal of Optimization Theory and Applications, 2018, vol. 177, issue 1, No 3, 64-92

Abstract: Abstract 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.

Keywords: Shape optimization; Worst-case optimization; Torsional instability; Plates; Bridges; 35J40; 35P15; 74K20 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10957-018-1261-1

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