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Topology optimization of binary structures under design-dependent fluid-structure interaction loads

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A current challenge for the structural topology optimization methods is the development of trustful techniques to account for different physics interactions. This paper devises a technique that considers separate physics analysis and optimization within the context of fluid-structure interaction (FSI) systems. Steady-state laminar flow and small structural displacements are assumed. We solve the compliance minimization problem subject to single or multiple volume constraints considering design-dependent FSI loads. For that, the TOBS (topology optimization of binary structures) method is applied. The TOBS approach uses binary {0,1} design variables, which can be advantageous when dealing with design-dependent physics interactions, e.g., in cases where fluid-structure boundaries are allowed to change during optimization. The COMSOL Multiphysics software is used to solve the fluid-structure equations and output the sensitivities using automatic differentiation. The TOBS optimizer provides a new set of {0,1} variables at every iteration. Numerical examples show smoothly converged solutions.

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The first author would like to thank the support of FAPESP (São Paulo Research Foundation), grants 2018/05797-8 and 2019/01685-3. The last author thanks the financial support of CNPq (National Council for Research and Development) under grant 302658/2018-1. All authors gratefully acknowledge the support from BG/Shell Brasil and FAPESP through the Research Centre for Gas Innovation - RCGI (Fapesp Proc. 2014/50279-4), hosted by the University of São Paulo, and the strategic importance of the support given by ANP (Brazil’s National Oil, Natural Gas and Biofuels Agency) through the R&D levy regulation.

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Correspondence to R. Picelli.

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Responsible Editor: Gengdong Cheng

Replication of results

A MATLAB code intended to reproduce the results presented here is available as supplementary material of this paper. More information on the data underpinning the results are available upon request by e-mail at An online repository with a demonstration code of the TOBS methods is available at, needed for running this paper’s supplementary code.

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Picelli, R., Ranjbarzadeh, S., Sivapuram, R. et al. Topology optimization of binary structures under design-dependent fluid-structure interaction loads. Struct Multidisc Optim 62, 2101–2116 (2020).

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