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A Minimaxmax Problem for Improving the Torsional Stability of Rectangular Plates

  • Elvise Berchio
  • Davide Buoso
  • Filippo Gazzola
  • Davide Zucco
Article

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 

Mathematics Subject Classification

35J40 35P15 74K20 

Notes

Acknowledgements

The authors are grateful to J. B. Kennedy for his kind revision of the use of the English Language within the present paper. Elvise Berchio, Davide Buoso and Davide Zucco are partially supported by the Research Project FIR (Futuro in Ricerca) 2013 Geometrical and qualitative aspects of PDEs. Filippo Gazzola is partially supported by the PRIN project Equazioni alle derivate parziali di tipo ellittico e parabolico: aspetti geometrici, disuguaglianze collegate, e applicazioni. Elvise Berchio, Davide Buoso, Filippo Gazzola and Davide Zucco are members of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM).

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Politecnico di TorinoTurinItaly
  2. 2.Universidade de LisboaLisbonPortugal
  3. 3.Politecnico di MilanoMilanItaly
  4. 4.Università di TorinoTurinItaly

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