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Abstract
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We propose a variant of benchmark problem for the topology optimization (TO)
method applied to variable-thickness plates. This method can be applied for the
design of rib-stiffened structures and it is important to have some kind of test
solutions that can be used to make an assessment on the efficiency of numerical
optimization algorithms. In the present study we show that such test problems can
be formulated for a square simply supported plate loaded by an eccentric
transverse load. TO solutions for such problems contain several straight ribs,
whose orientation depends on the relative shift of the loaded point from
the center of the plate. By using the corresponding beam-type model (in
which we retain only the ribs and neglect the influence of the face sheet
of plate), we show that similar unique optimal solutions for the ribs can
be obtained analytically so that numerical TO solutions can be validated.
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Keywords
topology optimization, variable-thickness plates,
rib-stiffened plates, analytical validation, benchmark
problem
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Mathematical Subject Classification
Primary: 74K10, 74K20, 74P05, 74P10
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Milestones
Received: 27 December 2022
Revised: 20 February 2023
Accepted: 21 March 2023
Published: 15 November 2023
Communicated by Francesco dell'Isola
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| © 2023 MSP (Mathematical Sciences
Publishers). |
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