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Explicit benchmark solution for topology optimization of variable-thickness plates

Kyaw Ye Ko and Yury Solyaev

Vol. 11 (2023), No. 3, 381–392
Abstract

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.

Keywords
topology optimization, variable-thickness plates, rib-stiffened plates, analytical validation, benchmark problem
Mathematical Subject Classification
Primary: 74K10, 74K20, 74P05, 74P10
Milestones
Received: 27 December 2022
Revised: 20 February 2023
Accepted: 21 March 2023
Published: 15 November 2023

Communicated by Francesco dell'Isola
Authors
Kyaw Ye Ko
Moscow Aviation Institute
Russia
Yury Solyaev
Moscow Aviation Institute
Russia