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Structural Engineering and Mechanics Volume 36, Number 1, September10 2010 , pages 37-55 DOI: https://doi.org/10.12989/sem.2010.36.1.037 |
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Calculation of eigenvalue and eigenvector derivatives with the improved Kron |
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Yong Xia, Shun Weng, You-Lin Xu and Hong-Ping Zhu
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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. | ||
| Key Words | ||
| substructuring method; eigensolution; eigensensitivity; model updating. | ||
| Address | ||
| Yong Xia: Department of Civil & Structural Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong Shun Weng: Department of Civil & Structural Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong You-Lin Xu: Department of Civil & Structural Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong Hong-Ping Zhu: School of Civil Engineering & Mechanics, Huazhong University of Science and Technology, Wuhan, Hubei, P.R. China | ||