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We use a gap function in order to compare the torsional performances ofdifferent reinforced plates under the action of external forces. Then, weaddress a shape optimization problem, whose target is to minimize the torsionaldisplacements of the plate: this leads us to set up a minimaxmax problem, whichincludes a new kind of worst-case optimization. Two kinds of reinforcements areconsidered: one aims at strengthening the plate, the other aims at weakeningthe action of the external forces. For both of them, we study the existence ofoptima within suitable classes of external forces and reinforcements. Ourresults are complemented with numerical experiments and with a number of openproblems and conjectures.

A Minimaxmax Problem for Improving the Torsional Stability of Rectangular Plates