Some remarks about a worst-case problem for the torsional response of a plate (Q6144005)

Summary: We consider an optimization problem aiming to improve the torsional performance of rectangular plates modeling bridges. The involved functional is the gap function, namely, the maximum difference of displacements between the two free edges of the plate. We compute the explicit expression of the gap function for some forces that appear to be the most prone to generate torsional instability in the structure and we exploit it to partially prove a conjecture stated in [\textit{P. R. S. Antunes} and \textit{F. Gazzola}, ZAMM, Z. Angew. Math. Mech. 98, No. 11, 1974--1991 (2018; Zbl 07803554)] about a worst-case problem. For the entire collection see [Zbl 1504.74002].