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Some solutions of minimaxmax problems for the torsional displacements of rectangular plates
Author(s) -
Antunes Pedro R.S.,
Gazzola Filippo
Publication year - 2018
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201800065
Subject(s) - function (biology) , structural engineering , line (geometry) , geometry , mathematics , mathematical analysis , engineering , evolutionary biology , biology
We consider an optimal shape problem aiming to reduce the torsional displacements of a partially hinged rectangular plate. The cost functional is the gap function , namely the maximum difference of displacements between the two free edges of the plate. We seek optimal shapes for reinforcements in order to minimize the gap function. This leads to a minimaxmax problem that we address both theoretically and numerically in some particular situations. Our results are in line with the expected behavior of bridges and they also give some hints for designs of future bridges.