Similarity of structures based on matrix similarity
The paper presents a numerical procedure for relating the behaviour of two different structures, i.e. determining a scale between two structures. This novel solution is based on the notion of matrix similarity and linear transformations, with the restriction that the scale between structures is dete...
Main Authors: | , , |
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Format: | Article |
Language: | English |
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Faculty of Mechanical Engineering in Slavonski Brod, Faculty of Electrical Engineering in Osijek, Faculty of Civil Engineering in Osijek
2017-01-01
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Series: | Tehnički Vjesnik |
Subjects: | |
Online Access: | https://hrcak.srce.hr/file/257879 |
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author | Ivica Kožar Tea Rukavina Neira Torić Malić |
author_facet | Ivica Kožar Tea Rukavina Neira Torić Malić |
author_sort | Ivica Kožar |
collection | DOAJ |
description | The paper presents a numerical procedure for relating the behaviour of two different structures, i.e. determining a scale between two structures. This novel solution is based on the notion of matrix similarity and linear transformations, with the restriction that the scale between structures is determined only after structural discretization, and that both structures have to be in the elastic regime. The structure scale can be determined in loading space or displacement space (i.e. structure forces or displacements are put into relation) where the scaling of the static structure model is based on the matrix equivalence principle, and scaling of the dynamic structure model is based on the Smith normal form. The structure scale in operator space (structure stiffness or flexibility matrices are put into relation) should be based on the Sylvester matrix equation. However, that approach is not practical and is replaced with the Levenberg-Marquardt method for obtaining only approximately equivalent stiffness matrices. Numerical examples illustrate the proposed novel approach. |
first_indexed | 2024-04-24T09:30:04Z |
format | Article |
id | doaj.art-938917b4435d4a15af988372093045d5 |
institution | Directory Open Access Journal |
issn | 1330-3651 1848-6339 |
language | English |
last_indexed | 2024-04-24T09:30:04Z |
publishDate | 2017-01-01 |
publisher | Faculty of Mechanical Engineering in Slavonski Brod, Faculty of Electrical Engineering in Osijek, Faculty of Civil Engineering in Osijek |
record_format | Article |
series | Tehnički Vjesnik |
spelling | doaj.art-938917b4435d4a15af988372093045d52024-04-15T14:02:15ZengFaculty of Mechanical Engineering in Slavonski Brod, Faculty of Electrical Engineering in Osijek, Faculty of Civil Engineering in OsijekTehnički Vjesnik1330-36511848-63392017-01-0124123924610.17559/TV-20160208123402Similarity of structures based on matrix similarityIvica Kožar0Tea Rukavina1Neira Torić Malić2Faculty of Civil Engineering, University of Rijeka, Radmile Matejčić 3, 51000 Rijeka, CroatiaFaculty of Civil Engineering, University of Rijeka, Radmile Matejčić 3, 51000 Rijeka, CroatiaFaculty of Civil Engineering, University of Rijeka, Radmile Matejčić 3, 51000 Rijeka, CroatiaThe paper presents a numerical procedure for relating the behaviour of two different structures, i.e. determining a scale between two structures. This novel solution is based on the notion of matrix similarity and linear transformations, with the restriction that the scale between structures is determined only after structural discretization, and that both structures have to be in the elastic regime. The structure scale can be determined in loading space or displacement space (i.e. structure forces or displacements are put into relation) where the scaling of the static structure model is based on the matrix equivalence principle, and scaling of the dynamic structure model is based on the Smith normal form. The structure scale in operator space (structure stiffness or flexibility matrices are put into relation) should be based on the Sylvester matrix equation. However, that approach is not practical and is replaced with the Levenberg-Marquardt method for obtaining only approximately equivalent stiffness matrices. Numerical examples illustrate the proposed novel approach.https://hrcak.srce.hr/file/257879Levenberg-Marquardt methodmatrix equivalencesimilarity of structuresSmith normal formstructure scalesSylvester equation |
spellingShingle | Ivica Kožar Tea Rukavina Neira Torić Malić Similarity of structures based on matrix similarity Tehnički Vjesnik Levenberg-Marquardt method matrix equivalence similarity of structures Smith normal form structure scales Sylvester equation |
title | Similarity of structures based on matrix similarity |
title_full | Similarity of structures based on matrix similarity |
title_fullStr | Similarity of structures based on matrix similarity |
title_full_unstemmed | Similarity of structures based on matrix similarity |
title_short | Similarity of structures based on matrix similarity |
title_sort | similarity of structures based on matrix similarity |
topic | Levenberg-Marquardt method matrix equivalence similarity of structures Smith normal form structure scales Sylvester equation |
url | https://hrcak.srce.hr/file/257879 |
work_keys_str_mv | AT ivicakozar similarityofstructuresbasedonmatrixsimilarity AT tearukavina similarityofstructuresbasedonmatrixsimilarity AT neiratoricmalic similarityofstructuresbasedonmatrixsimilarity |