Original scientific paper

https://doi.org/10.17559/TV-20160208123402

Similarity of structures based on matrix similarity

Ivica Kožar orcid.org/0000-0001-7017-6851 ; Faculty of Civil Engineering, University of Rijeka, Radmile Matejčić 3, 51000 Rijeka, Croatia
Tea Rukavina orcid.org/0000-0003-1492-5146 ; Faculty of Civil Engineering, University of Rijeka, Radmile Matejčić 3, 51000 Rijeka, Croatia
Neira Torić Malić ; Faculty of Civil Engineering, University of Rijeka, Radmile Matejčić 3, 51000 Rijeka, Croatia

Abstract

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.

Keywords

Levenberg-Marquardt method; matrix equivalence; similarity of structures; Smith normal form; structure scales; Sylvester equation

Hrčak ID:

174729

URI

https://hrcak.srce.hr/174729

Publication date:

10.2.2017.

Article data in other languages: croatian

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