Improved substructuring method for eigensolutions of large-scale structures

Weng, Shun; Xia, Yong; Xu, You Lin; Zhou, Xiao Qing; Zhu, Hong

doi:10.1016/j.jsv.2009.01.015

Cited by 50 publications

(58 citation statements)

References 22 publications

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“…In that case, the transformation among these matrices will take more computation resources. This phenomenon has also been observed in calculation of the eigensolutions (Weng et al 2009). The trade-off between the number of the substructures and the size of each substructure needs further studies.…”

Section: Example 2: a Highway Bridgesupporting

confidence: 67%

“…(2), the primitive matrices and require calculating the complete eigensolutions of all substructures, which is time-consuming. The complete modes of each substructure are partitioned into the master part and the slave part (Weng et al 2009). The first a few eigenmodes in each substructure are retained as the 'master' modes, while the residual higher eigenmodes are discarded as the 'slave' modes and compensated by the first-order residual flexibility.…”

Section: Basic Theorymentioning

confidence: 99%

See 1 more Smart Citation

Calculation of eigenvalue and eigenvector derivatives with the improved Kron's substructuring method

Xia¹,

Weng²,

Xu³

et al. 2010

Structural Engineering and Mechanics

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Abstract. For large-scale structures, the calculation of the eigensolution and the eigensensitivity is usually very time-consuming. This paper develops the Kron's substructuring method to compute the firstorder derivatives of the eigenvalues and eigenvectors with respect to the structural parameters. The global structure is divided into several substructures. The eigensensitivity of the substructures are calculated via the conventional manner, and then assembled into the eigensensitivity of the global structure by performing some constraints on the derivative matrices of the substructures. With the proposed substructuring method, the eigenvalue and eigenvector derivatives with respect to an elemental parameter are computed within the substructure solely which contains the element, while the derivative matrices of all other substructures with respect to the parameter are zero. Consequently this can reduce the computation cost significantly. The proposed substructuring method is applied to the GARTEUR AG-11 frame and a highway bridge, which is proved to be computationally efficient and accurate for calculation of the eigensensitivity. The influence of the master modes and the division formations are also discussed.

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Section: Example 2: a Highway Bridgesupporting

confidence: 67%

Section: Basic Theorymentioning

confidence: 99%

Calculation of eigenvalue and eigenvector derivatives with the improved Kron's substructuring method

Xia¹,

Weng²,

Xu³

et al. 2010

Structural Engineering and Mechanics

Self Cite

View full text Add to dashboard Cite

show abstract

“…In matrix C, each row contains two non-zero elements, 1 and -1, for a rigid connection. From the physical perspective, matrix C bears the displacement compatibility [4,19] …”

Section: Disassembly Of Global Flexibility With Full Dof Measurementmentioning

confidence: 99%

“…The substructuring approach is potentially efficient in the model updating of large-scale structures [4][5][6][7] and related applications [8][9][10]. In these studies, the global structure is divided into smaller and more manageable substructures.…”

Section: Introductionmentioning

confidence: 99%

Inverse substructure method for model updating of structures

Weng¹,

Xia²,

Zhou³

et al. 2012

Journal of Sound and Vibration

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Traditional model updating of large-scale structures is usually time-consuming because the global structural model needs to be repeatedly re-analyzed as a whole to match global measurements. This paper proposes a new substructural model updating method. The modal data measured on the global structure are disassembled to obtain the independent substructural dynamic flexibility matrices under force and displacement compatibility conditions. The method is extended to the case when the measurement is carried out at partial degrees-of-freedom of the structure. The extracted substructural flexibility matrices are then used as references for updating the corresponding substructural models. An orthogonal projector is employed on both the extracted substructural measurements and the substructural models to remove the rigid body modes of the free-free substructures. Compared with the traditional model updating at the global structure level, only the sub-models at the substructural level are re-analyzed in the proposed substructure-based model updating process, resulting in a rapid convergence of optimization.Moreover, only measurement on the local area corresponding to the concerned substructures is required, and those on other components can be avoided. The effectiveness and efficiency of the proposed substructuring method are verified through applications to a laboratory-tested frame structure and a large-scale 600 m tall Guangzhou New TV Tower. The present technique is referred to as the inverse substructuring model updating method as the measured global modal data are disassembled into the substructure level and then the updating is conducted on the substructures only. This differs from the substructuring model updating method previously This is the Pre-Published Version. 2 proposed by the authors, in which the model updating is still conducted in the global level and the numerical global modal data are assembled from those of substructures. That can be referred to as the forward substructuring model updating method.

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“…It has been proved that the substructuring methods are efficient in dealing with large-scale structures, as it takes the local area as an independent structure [4][5][6][7][8][9]. First, the global structure is divided rationally into several smaller substructures to make it much easier and faster to analyze the small substructures independently.…”

Section: Introductionmentioning

confidence: 99%

Substructuring Method in Structural Health Monitoring

Weng¹,

Zhu²,

Xia³

et al. 2017

Structural Health Monitoring - Measurement Methods and Practical Applications

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In sensitivity-based finite element model updating, the eigensolutions and eigensensitivities are calculated repeatedly, which is a time-consuming process for large-scale structures. In this chapter, a forward substructuring method and an inverse substructuring method are proposed to fulfill the model updating of large-scale structures. In the forward substructuring method, the analytical FE model of the global structure is divided into several independent substructures. The eigensolutions of each independent substructure are used to recover the eigensolutions and eigensensitivities of the global structure. Consequently, only some specific substructures are reanalyzed in model updating and assembled with other untouched substructures to recover the eigensolutions and eigensensitivities of the global structure. In the inverse substructuring method, the experimental modal data of the global structure are disassembled into substructural flexibility. Afterwards, each substructure is treated as an independent structure to reproduce its flexibility through a model-updating process. Employing the substructuring method, the model updating of a substructure can be conducted by measuring the local area of the concerned substructure solely. Finally, application of the proposed methods to a laboratory tested frame structure reveals that the forward and inverse substructuring methods are effective in model updating and damage identification.

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Improved substructuring method for eigensolutions of large-scale structures

Cited by 50 publications

References 22 publications

Calculation of eigenvalue and eigenvector derivatives with the improved Kron's substructuring method

Calculation of eigenvalue and eigenvector derivatives with the improved Kron's substructuring method

Inverse substructure method for model updating of structures

Substructuring Method in Structural Health Monitoring

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