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Quick and Highly Efficient Modal Analysis Method Based on the Reanalysis Technique for Large Complex Structure and Topology Optimization

School of Automobile and Mechanical Engineering, Changsha University of Science and Technology, Changsha 410114, P. R. China

E-mail Address: hezhengde8@163.com

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Bin Xu

Institute of Vibration Engineering, Northwestern Polytechnical University, Xi’an 710072, P. R. China

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https://doi.org/10.1142/S0219876218501347Cited by:4 (Source: Crossref)

Abstract

Modal analysis is widely used to investigate the dynamic characteristics of large and complex structures. For finite element models, iterative solvers are needed to precisely calculate eigenpairs or frequency and vibration mode. However, in cases such as large-scale analysis or reanalysis studies, or optimization design of a huge structure, computational cost may become too time consuming. This paper focuses on the quick structural modal analysis based on the reanalysis technique for large complex structures. Based on the stiffness and mass matrix of the analytical structures, a high precision and efficiency eigensolution is generated by the proposed modal analysis method (the Pseudo Random Independent and Coupling Inverse Iteration (PRICII) method), which combines the pseudo random number initialization, ICII (Independent and Coupling Inverse Iteration) strategy with the double Rayleigh–Ritz analysis. By comparing with the Subspace iteration method, Lanczos method, etc. the large-scale numerical examples show that the actual computational savings of the proposed method are usually higher than 75% with sufficient precision. Also, its applications in topology optimization are greatly effective.

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References

Amir, O., Sigmund, O., Lazarov, B. S. et al. [2012] “ Efficient reanalysis techniques for robust topology optimization,” Comput. Methods Appl. Mech. Eng. 245–246: 217–231. Web of Science, Google Scholar
Bathe, K. J. [2013] “ The subspace iteration method — Revisited,” Comput. Struct. 126, 177–183. Web of Science, Google Scholar
Bathe, K. J. [2014] Finite Element Procedure, 2nd Edition (Prentice Hall, Watertown, MA). Google Scholar
Cacciola, P. and Muscolino, G. [2011] “ Reanalysis techniques in stochastic analysis of linear structures under stationary multi-correlated input,” Probabilist. Eng. Mech. 26, 92–100. Web of Science, Google Scholar
Chen, S. H., Ma, L. and Meng, G. W. [2008] “ Dynamic response reanalysis for modified structures under arbitrary excitation using epsilon-algorithm,” Comput. Struct. 86, 2095–2101. Web of Science, Google Scholar
Chen, W. H., Lu, Z. R., Lin, W. et al. [2011] “ Theoretical and experimental modal analysis of the Guangzhou New TV Tower,” Eng. Struct. 33, 3628–3646. Web of Science, Google Scholar
Chen, S. H., Ma, L., Meng, G. W. et al. [2009] “ An efficient method for evaluating the natural frequencies of structures with uncertain-but-bounded parameters,” Comput. Struct. 87, 582–590. Web of Science, Google Scholar
Fang, Z., Liu, X., Fan, X. et al. [2007] “ Design and research of large-span steel structure for the National Stadium,” J. Build. Struct. 28(2), 1–16 (in Chinese). Google Scholar
Gao, G., Wang, H. and Li, G. [2013] “ An adaptive time-based global method for dynamic reanalysis,” Struct. Multidisc. Optim. 48, 355–365. Web of Science, Google Scholar
He, J. J. and Xu, B. B. [2017] “ Quick pseudo-random topology optimization design based on triangle element,” J. Vibroeng. 19(4), 2822–2843. Web of Science, Google Scholar
He, X. Y. and Jiang, Y. [2018] “ Review of hybrid electric systems for construction machinery,” Automat. Constr. 92, 286–296. Web of Science, Google Scholar
Huang, G., Wang, H., Wang, G. et al. [2017] “ Closed loop geometry based optimization by integrating subdivision, reanalysis and metaheuristic searching techniques,” Comput. Struct. 182, 459–474. Web of Science, Google Scholar
Jun, J., Zi, H. X. and Xu, C. B. [2015] “ Structural modal reanalysis for large, simultaneous and multiple type modifications,” Mech. Syst. Signal Process. 62–63, 207–217. Web of Science, Google Scholar
Kashiwagi, M. [2009] “ A numerical method for eigensolution of locally modified systems based on the inverse power method,” Finite Elem. Anal. Des. 45, 113–120. Web of Science, Google Scholar
Kaveh, A. and Fazli, H. [2011] “ Approximate eigensolution of locally modified regular structures using a substructuring technique,” Comput. Struct. 89, 529–537. Web of Science, Google Scholar
Kirsch, U. and Bogomolni, M. [2007] “ Nonlinear and dynamic structural analysis using combined approximations,” Comput. Struct. 85(10), 566–578. Web of Science, Google Scholar
Kirsch, U. [2008] Reanalysis of Structures — A Unified Approach for Linear, Nonlinear, Static and Dynamic Systems (Springer, Dordrecht). Google Scholar
Ma, L., Chen, S. H. and Meng, G. W. [2009] “ Combined approximation for reanalysis of complex eigenvalues,” Comput. Struct. 87, 502–506. Web of Science, Google Scholar
Massa, F., Tison, T. and Lallemand, B. [2011] “ Structural modal reanalysis methods using homotopy perturbation and projection techniques,” Comput. Methods Appl. Mech. Eng. 200, 2971–2982. Web of Science, Google Scholar
Massa, F., Lallemand, B. and Tison, T. [2015] “ Multi-level homotopy perturbation and projection techniques for the reanalysis of quadratic eigenvalue problems: The application of stability analysis,” Mech. Syst. Signal Process. 52–53, 88–104. Web of Science, Google Scholar
Yanlin, G. and Yili, H. [2008] “ Analysis on earthquake response and aseismic load-carrying capability of New CCTV Building,” J. Build. Struct. 29(3), 10–23 (in Chinese). Google Scholar