Influence of the Fractal Geometry on the Mechanical Resistance of Cantilever Beams Designed through Topology Optimization

In this work, the complex geometry of beams obtained from topology optimization is characterized through the fractal dimension (<i>F<sub>D</sub></i>). The fractal dimension is employed as an efficiency measure of the mass distribution in the beams, that is, the capacity of th...

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Autores principales:	Pablo Pavón-Domínguez, Guillermo Portillo-García, Alejandro Rincón-Casado, Lucía Rodríguez-Parada
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	fractal dimension topology optimization static analysis box-counting Michell’s beam Technology T Engineering (General). Civil engineering (General) TA1-2040 Biology (General) QH301-705.5 Physics QC1-999 Chemistry QD1-999
Acceso en línea:	https://doaj.org/article/19b3188756e84345a67bceaff3e01bd8
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id	oai:doaj.org-article:19b3188756e84345a67bceaff3e01bd8
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spelling	oai:doaj.org-article:19b3188756e84345a67bceaff3e01bd82021-11-25T16:31:20ZInfluence of the Fractal Geometry on the Mechanical Resistance of Cantilever Beams Designed through Topology Optimization10.3390/app1122105542076-3417https://doaj.org/article/19b3188756e84345a67bceaff3e01bd82021-11-01T00:00:00Zhttps://www.mdpi.com/2076-3417/11/22/10554https://doaj.org/toc/2076-3417In this work, the complex geometry of beams obtained from topology optimization is characterized through the fractal dimension (<i>F<sub>D</sub></i>). The fractal dimension is employed as an efficiency measure of the mass distribution in the beams, that is, the capacity of the optimized solutions to be efficiently distributed in the design space. Furthermore, the possible relationships between the fractal dimension and beams’ mechanical properties are explored. First, a set of theoretical beams are studied based on their well-known fractal dimension. A 3D fractal called Menger sponge is reproduced on a Michell’s beam (cantilever with a single force applied at the end). The programming codes that generate those beams are created in Matlab software, as are the algorithms for estimating the fractal dimension (box-counting method). Subsequently, identical beams are modelled in the software Inspire in order to apply the topology optimization and determine the mechanical parameters from the static analysis. Results indicate that the fractal dimension is affected by the design geometry and proposed optimized solutions. In addition, several relationships among fractal dimension and some mechanical resistance parameters could be established. The obtained relations depended on the objectives that were initially defined in the topology optimization.Pablo Pavón-DomínguezGuillermo Portillo-GarcíaAlejandro Rincón-CasadoLucía Rodríguez-ParadaMDPI AGarticlefractal dimensiontopology optimizationstatic analysisbox-countingMichell’s beamTechnologyTEngineering (General). Civil engineering (General)TA1-2040Biology (General)QH301-705.5PhysicsQC1-999ChemistryQD1-999ENApplied Sciences, Vol 11, Iss 10554, p 10554 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	fractal dimension topology optimization static analysis box-counting Michell’s beam Technology T Engineering (General). Civil engineering (General) TA1-2040 Biology (General) QH301-705.5 Physics QC1-999 Chemistry QD1-999
spellingShingle	fractal dimension topology optimization static analysis box-counting Michell’s beam Technology T Engineering (General). Civil engineering (General) TA1-2040 Biology (General) QH301-705.5 Physics QC1-999 Chemistry QD1-999 Pablo Pavón-Domínguez Guillermo Portillo-García Alejandro Rincón-Casado Lucía Rodríguez-Parada Influence of the Fractal Geometry on the Mechanical Resistance of Cantilever Beams Designed through Topology Optimization
description	In this work, the complex geometry of beams obtained from topology optimization is characterized through the fractal dimension (<i>F<sub>D</sub></i>). The fractal dimension is employed as an efficiency measure of the mass distribution in the beams, that is, the capacity of the optimized solutions to be efficiently distributed in the design space. Furthermore, the possible relationships between the fractal dimension and beams’ mechanical properties are explored. First, a set of theoretical beams are studied based on their well-known fractal dimension. A 3D fractal called Menger sponge is reproduced on a Michell’s beam (cantilever with a single force applied at the end). The programming codes that generate those beams are created in Matlab software, as are the algorithms for estimating the fractal dimension (box-counting method). Subsequently, identical beams are modelled in the software Inspire in order to apply the topology optimization and determine the mechanical parameters from the static analysis. Results indicate that the fractal dimension is affected by the design geometry and proposed optimized solutions. In addition, several relationships among fractal dimension and some mechanical resistance parameters could be established. The obtained relations depended on the objectives that were initially defined in the topology optimization.
format	article
author	Pablo Pavón-Domínguez Guillermo Portillo-García Alejandro Rincón-Casado Lucía Rodríguez-Parada
author_facet	Pablo Pavón-Domínguez Guillermo Portillo-García Alejandro Rincón-Casado Lucía Rodríguez-Parada
author_sort	Pablo Pavón-Domínguez
title	Influence of the Fractal Geometry on the Mechanical Resistance of Cantilever Beams Designed through Topology Optimization
title_short	Influence of the Fractal Geometry on the Mechanical Resistance of Cantilever Beams Designed through Topology Optimization
title_full	Influence of the Fractal Geometry on the Mechanical Resistance of Cantilever Beams Designed through Topology Optimization
title_fullStr	Influence of the Fractal Geometry on the Mechanical Resistance of Cantilever Beams Designed through Topology Optimization
title_full_unstemmed	Influence of the Fractal Geometry on the Mechanical Resistance of Cantilever Beams Designed through Topology Optimization
title_sort	influence of the fractal geometry on the mechanical resistance of cantilever beams designed through topology optimization
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/19b3188756e84345a67bceaff3e01bd8
work_keys_str_mv	AT pablopavondominguez influenceofthefractalgeometryonthemechanicalresistanceofcantileverbeamsdesignedthroughtopologyoptimization AT guillermoportillogarcia influenceofthefractalgeometryonthemechanicalresistanceofcantileverbeamsdesignedthroughtopologyoptimization AT alejandrorinconcasado influenceofthefractalgeometryonthemechanicalresistanceofcantileverbeamsdesignedthroughtopologyoptimization AT luciarodriguezparada influenceofthefractalgeometryonthemechanicalresistanceofcantileverbeamsdesignedthroughtopologyoptimization
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Influence of the Fractal Geometry on the Mechanical Resistance of Cantilever Beams Designed through Topology Optimization

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