Zonal free element method for free and forced vibration analysis of two- and three-dimensional structures

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Autoren

  • Bin Li
  • Jing da Li
  • Hua yu Liu
  • Miao Cui
  • Jun Lv
  • Bing bing Xu
  • Xiao wei Gao

Organisationseinheiten

Externe Organisationen

  • Dalian University of Technology
Forschungs-netzwerk anzeigen

Details

OriginalspracheEnglisch
Aufsatznummer107400
Seitenumfang16
FachzeitschriftComputers and Structures
Jahrgang299
Frühes Online-Datum9 Mai 2024
PublikationsstatusVeröffentlicht - 1 Aug. 2024

Abstract

This paper presents a new numerical method called the zonal free element method (ZFREM) for the free and forced vibration analysis of elastodynamic problems. In this approach, a complex computational domain is divided into some simple zones and generates a series of regularly arranged nodes in each zone, which can improve the accuracy during the analysis of complex models. The distinguishing feature of the ZFREM is that an independent isoparametric element is formed by only one freely chosen surrounding node at each configuration node. In this method, the mass term exists only in the internal nodes, which can accelerate the assembly of the final system equations. Building upon this foundation, the present study developed the Krylov reduced dimensional iterative method, which approximates the solution of the equation system by constructing a lower-dimensional subspace. This approach avoids the complex equation transformations involved in traditional algorithms for solving eigenvalue problems, thereby further enhancing computational efficiency. Moreover, to tackle damped vibration problems encountered in engineering applications, the proposed method is further extended to solve the non-linear forced vibration problems. The accuracy and effectiveness of the method are verified by numerical examples of free and forced vibration problems.

ASJC Scopus Sachgebiete

Zitieren

Zonal free element method for free and forced vibration analysis of two- and three-dimensional structures. / Li, Bin; Li, Jing da; Liu, Hua yu et al.
in: Computers and Structures, Jahrgang 299, 107400, 01.08.2024.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Li B, Li JD, Liu HY, Cui M, Lv J, Xu BB et al. Zonal free element method for free and forced vibration analysis of two- and three-dimensional structures. Computers and Structures. 2024 Aug 1;299:107400. Epub 2024 Mai 9. doi: 10.1016/j.compstruc.2024.107400
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title = "Zonal free element method for free and forced vibration analysis of two- and three-dimensional structures",
abstract = "This paper presents a new numerical method called the zonal free element method (ZFREM) for the free and forced vibration analysis of elastodynamic problems. In this approach, a complex computational domain is divided into some simple zones and generates a series of regularly arranged nodes in each zone, which can improve the accuracy during the analysis of complex models. The distinguishing feature of the ZFREM is that an independent isoparametric element is formed by only one freely chosen surrounding node at each configuration node. In this method, the mass term exists only in the internal nodes, which can accelerate the assembly of the final system equations. Building upon this foundation, the present study developed the Krylov reduced dimensional iterative method, which approximates the solution of the equation system by constructing a lower-dimensional subspace. This approach avoids the complex equation transformations involved in traditional algorithms for solving eigenvalue problems, thereby further enhancing computational efficiency. Moreover, to tackle damped vibration problems encountered in engineering applications, the proposed method is further extended to solve the non-linear forced vibration problems. The accuracy and effectiveness of the method are verified by numerical examples of free and forced vibration problems.",
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T1 - Zonal free element method for free and forced vibration analysis of two- and three-dimensional structures

AU - Li, Bin

AU - Li, Jing da

AU - Liu, Hua yu

AU - Cui, Miao

AU - Lv, Jun

AU - Xu, Bing bing

AU - Gao, Xiao wei

PY - 2024/8/1

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N2 - This paper presents a new numerical method called the zonal free element method (ZFREM) for the free and forced vibration analysis of elastodynamic problems. In this approach, a complex computational domain is divided into some simple zones and generates a series of regularly arranged nodes in each zone, which can improve the accuracy during the analysis of complex models. The distinguishing feature of the ZFREM is that an independent isoparametric element is formed by only one freely chosen surrounding node at each configuration node. In this method, the mass term exists only in the internal nodes, which can accelerate the assembly of the final system equations. Building upon this foundation, the present study developed the Krylov reduced dimensional iterative method, which approximates the solution of the equation system by constructing a lower-dimensional subspace. This approach avoids the complex equation transformations involved in traditional algorithms for solving eigenvalue problems, thereby further enhancing computational efficiency. Moreover, to tackle damped vibration problems encountered in engineering applications, the proposed method is further extended to solve the non-linear forced vibration problems. The accuracy and effectiveness of the method are verified by numerical examples of free and forced vibration problems.

AB - This paper presents a new numerical method called the zonal free element method (ZFREM) for the free and forced vibration analysis of elastodynamic problems. In this approach, a complex computational domain is divided into some simple zones and generates a series of regularly arranged nodes in each zone, which can improve the accuracy during the analysis of complex models. The distinguishing feature of the ZFREM is that an independent isoparametric element is formed by only one freely chosen surrounding node at each configuration node. In this method, the mass term exists only in the internal nodes, which can accelerate the assembly of the final system equations. Building upon this foundation, the present study developed the Krylov reduced dimensional iterative method, which approximates the solution of the equation system by constructing a lower-dimensional subspace. This approach avoids the complex equation transformations involved in traditional algorithms for solving eigenvalue problems, thereby further enhancing computational efficiency. Moreover, to tackle damped vibration problems encountered in engineering applications, the proposed method is further extended to solve the non-linear forced vibration problems. The accuracy and effectiveness of the method are verified by numerical examples of free and forced vibration problems.

KW - Free and forced Vibration

KW - Meshless method

KW - Non-linear forced vibration

KW - Zonal free element method

KW - Zone mapping

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