The construction of free–free flexibility matrices as generalized stiffness inverses

Felippa, Carlos A.; Park, K. C.; Filho, Mauro Rezende

doi:10.1016/s0045-7949(98)00068-6

Cited by 45 publications

(25 citation statements)

References 5 publications

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“…Consequently, the derivative of the residual flexibility of the free-free substructure is not available. In this situation, the rigid body modes, which contribute to the zero-frequency modes, are employed (Felippa et al 1998). The detailed procedures on how to calculate the residual flexibility and the first-order derivatives of the free-free substructures can be found in Appendix.…”

Section: Eigenvalue Derivatives With the Substructuring Methodsmentioning

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

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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: Eigenvalue Derivatives With the Substructuring Methodsmentioning

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

View full text Add to dashboard Cite

show abstract

“…(55)). In substructure-based model updating, the elemental parameters of the analytical FE model are iteratively adjusted to minimize the discrepancy between the analytical substructural flexibility and that extracted from global data [18].…”

Section: The Projection Matrix To Extract Free-free Flexibility For Mmentioning

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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“…The free-free flexibility has been introduced in previous papers [11,12], but these have primarily focused on theoretical and "system level use" considerations. Four practical aspects are studied here in more detail at the individual substructure level:…”

Section: Motivationmentioning

confidence: 99%

“…This article only considers that case. The real-unsymmetric case, which arises in nonconservative and corotational FEM models, is briefly discussed in [11].…”

Section: Definitionsmentioning

confidence: 99%

The construction of free–free flexibility matrices for multilevel structural analysis

Felippa

Park

2002

Computer Methods in Applied Mechanics and Engineering

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The construction of free–free flexibility matrices as generalized stiffness inverses

Cited by 45 publications

References 5 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

Substructuring Method in Structural Health Monitoring

The construction of free–free flexibility matrices for multilevel structural analysis

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