This content is not included in your SAE MOBILUS subscription, or you are not logged in.
A Comparison of Mode-Acceleration and Ritz Vector Reduced Basis Procedures in Transient Analysis
ISSN: 0148-7191, e-ISSN: 2688-3627
Published April 01, 1988 by SAE International in United States
Annotation ability available
Reduced basis techniques and the method of mode-acceleration are applied to transient analysis of simple beam and truss structures. It is noted that the method of mode-acceleration effectively recovers the first Ritz vector used in Ritz procedures. The theoretical basis for Lanczos algorithms that generate Ritz vectors is explained. Both mode-acceleration and Ritz procedures are found, generally, to be more accurate than mode-displacement in calculation of transient shear stresses, moments and normal stresses. Reanalysis using Ritz vectors is discussed following Kitis and Pilkey  and Noor and Lowder .
CitationDrucker, D., Lou, M., Wang, S., and Kline, K., "A Comparison of Mode-Acceleration and Ritz Vector Reduced Basis Procedures in Transient Analysis," SAE Technical Paper 880908, 1988, https://doi.org/10.4271/880908.
- Kline K. A. “Dynamic Analysis Using a Reduced Basis of Exact Modes and Ritz Vectors” AIAA Journal 24 2022 2029 1986
- Wilson E. L. Yuan M. W. Dickens J. M. “Dynamic Analysis by Direct Superposition of Ritz Vectors” Earthquake Eng. Struct. Dyn. 10 813 821 1982
- Bayo E. P. Wilson E. L. “Use of Ritz Vectors in Wave Propagation and Foundation Response,” Earthquake Eng. Struct. Dyn. 12 499 505 1984
- Nour-Omid B. Clough R. W. “Dynamic Analysis of Structures Using Lanczos Co-ordinates,” Earthquake Eng. Struct. Dyn. 12 565 577 1984
- Parlett B. N. The Symmetric Eigenvalue Problem Prentice-Hall Englewood Cliffs, NJ 1980
- Golub G. H. Van Loan C. F. Matrix Computations Johns Hopkins University Press Baltimore, MD 1983
- Paige C. C. “Computational Variants of the Lanczos Method for the Eigenproblem,” J. Inst. Maths. Applics. 10 373 381 1972
- Cornwell R. E. Craig R. R. Jr., Johnson C. P. “On the Application of the Mode-Acceleration Method to Structural Engineering Problems” Earthquake Eng. Struct. Dyn. 11 679 688 1983
- Kitis L. Pilkey W. D. “Appendant Subsystem Design Using Ritz Vectors” 21 28 Reanalysis of Structural Dynamic Models Wang B. P. 76 Amer. Soc. Mech. Engr. 1986
- Noor A. K. Lowder H. E. “Aprroximate Techniques of Structural Reanalysis” Computers and Structures 4 801 812 1974
- Haug E. J. Arora J. S. Applied Optimal Design John Wiley and Sons New York 1979