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...

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Main Authors: Ivica Kožar, Tea Rukavina, Neira Torić Malić
Format: Article
Language:English
Published: Faculty of Mechanical Engineering in Slavonski Brod, Faculty of Electrical Engineering in Osijek, Faculty of Civil Engineering in Osijek 2017-01-01
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.
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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