Efficient Dynamic Reanalysis of Structures
Publication: Journal of Structural Engineering
Volume 133, Issue 3
Abstract
The combined approximations approach, developed originally for linear static reanalysis, is used for dynamic reanalysis of structures. The approach is based on the integration of several concepts and methods, including series expansion, reduced basis, matrix factorization, and Gram-Schmidt orthogonalizations. The advantage is that efficient local approximations and accurate global approximations are combined to achieve an effective solution procedure. Considering modal analysis, the computational effort involved in reanalysis is significantly reduced. However, the accuracy of the higher mode shapes might be insufficient. A procedure intended to improve the accuracy of the results is developed. A reduced eigenproblem is introduced, and a method for determining the basis vectors is presented. Improved basis vectors, using the concepts of shifts and Gram-Schmidt orthogonalizations, are developed, and eigenproblem reanalysis by combined approximations using inverse iteration with shifts is introduced. Numerical examples demonstrate the quality of the results. It is shown that high accuracy is achieved efficiently for various types of changes in the structure.
Get full access to this article
View all available purchase options and get full access to this article.
References
Abu Kassim, A. M., and Topping, B. H. V. (1987). “Static reanalysis: Areview.” J. Struct. Eng., 113(5), 1029–1045.
Arora, J. S. (1976). “Survey of structural reanalysis techniques.” J. Struct. Div., 102(4), 783–802.
Barthelemy, J-F. M., and Haftka, R. T. (1993). “Approximation concepts for optimum structural design—A review.” Struct. Optim., 5, 129–144.
Bathe, K. J. (1996). Finite Element Procedures, Prentice-Hall, N.J.
Chen, S. H., et al. (2000). “Comparison of several eigenvalue reanalysis methods for modified structures.” Struct. Multidiscip. Optim., 20, 253–259.
Chen, S. H., and Yang, X. W. (2000). “Extended Kirsch combined method for eigenvalue reanalysis.” AIAA J., 38, 927–930.
Chopra, A. K. (2001). Dynamics of Structures, Prentice-Hall N.J.
Kirsch, U. (2002). Design-oriented analysis of structures, Kluwer Academic, Dordrecht.
Kirsch, U. (2003a). “Design-oriented analysis of structures—Unified approach.” J. Eng. Mech., 129(3), 264–272.
Kirsch, U. (2003b). “A unified reanalysis approach for structural analysis, design, and optimization.” Struct. Multidiscip. Optim., 25, 67–85.
Kirsch, U. (2003c). “Approximate vibration reanalysis of structures.” AIAA J., 41, 504–511.
Kirsch, U., and Bogomolni, M. (2004a). “Procedures for approximate eigenproblem reanalysis of structures.” Int. J. Numer. Methods Eng., 60, 1969–1986.
Kirsch, U., and Bogomolni, M. (2004b), “Error evaluation in approximate reanalysis of structures.” Struct. Multidiscip. Optim., 28, 77–86.
Rong, F., et al., (2003). “Structural modal reanalysis for topological modificsatioms with extended Kirsch method.” Comput. Methods Appl. Mech. Eng., 192, 697–707.
Somerville, P., et al. (1997). “Development of ground motion time histories for Phase 2 of the FEMA/SAC steel project.” Report No. SAC/BD-97/04.
Venkataraman, S., and Haftka, R. T. (2004). “Structural optimization complexity: What has Moore’s law done for us.” Struct. Multidiscip. Optim., 28, 375–387.
Wilkinson, W. (1965). The Algebraic Eigenvalue Problem, Oxford University Press, Oxford.
Information & Authors
Information
Published In
Copyright
© 2007 ASCE.
History
Received: Feb 3, 2005
Accepted: Sep 29, 2006
Published online: Mar 1, 2007
Published in print: Mar 2007
Notes
Note. Associate Editor: Abhinav Gupta
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.