Skip to main content
SpringerLink
Log in

An Adaptive Dynamic Relaxation Method for Static Problems

  • Conference paper
Computational Mechanics ’86

Abstract

The present paper re-defines the parameters of the dynamic relaxation method for static problems and examines how they affect the rate of convergence of the method. A new adaptive scheme is used to improve the efficiency and accuracy of the method. The scheme involves using the current residual vector to update the lower frequency limit during integration and to improve the accuracy of the converged solution. The new approach compares favorably with the results of a previously proposed adaptive method.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Tong, P. and Rossettos J., ‘Finite Element Methodș MIT Press, 1977.

    Google Scholar 

  2. Tong, P., ‘on the Numerical Problems of Finite Element Methods,’ Computer Aided Engineering, 539–559, Ed. by G. M. Gladwell, Univ. of Waterloo, Canada, 1971.

    Google Scholar 

  3. Underwood, P., ‘An Adaptive Dynamic Relaxation Method for Linear and Nonlinear Analyses,’ Lockheed Report.

    Google Scholar 

  4. Bunce, J. W., ‘A Note on the Estimation of Critical Damping in Dynamic Relaxation,’ Int. J. for Num. Meth. in Eng., Vol. 4, 301–304, 1972.

    Article  MathSciNet  Google Scholar 

  5. Wood, W. L., ‘Note on Dynamic Relaxation,’ Int. J. for Num. Meth. in Eng., Vol. 3, 145–147, 1971.

    Article  MATH  Google Scholar 

  6. Park, K. C., ‘Practical Aspects of Numerical Time Integration,’ Computers and Structures, Vol. 7, 343–353, 1977.

    Article  MATH  Google Scholar 

  7. Leech, J. W., Hsu, P. T. and Mack, E. W., ‘Stability of a Finite Difference Method for Solving Matrix Equations,’ AIAA J., Vol. 3, 2172–2173, 1965.

    Article  MATH  Google Scholar 

  8. Tong, P., ‘Automobile Crash Dynamics and Numerical Integration Methods,’ presented at Symposium on Frontier in Applied Mechanics, University of Calif, at San Diego, July 1984.

    Google Scholar 

  9. Frankel, S., ‘Convergence Rates of Iterative Treatments of Partial Differential Equations,’ Math. Tables - National Res. Council, Washington, Vol. 4, 65–75, 1950.

    Article  MathSciNet  Google Scholar 

  10. Isaacson, H. B., and Keller, H. B.,’Analysis of Numerical Methods,’ John Wiley & Sons, London 1966.

    MATH  Google Scholar 

  11. Irons, B. M. and Treharne, G., ‘A Bound Theorem in Eigenvalues and Its Practical Applications,’ Proc. of the Third Conf. on Matrix Methods in Structural Mechanics, Wright- Patterson, AFB, Ohio, 1971, AFFDL-TR-71–160.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Transportation Systems Center, DOT, Cambridge, MA, 02142, USA

    Pin Tong

Authors
  1. Pin Tong
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Nuclear Engineering, The University of Tokyo, 3-1, Hongo 7-chome, Bunkyo-ku, Tokyo 113, Japan

    Genki Yagawa

  2. Center for the Advancement of Computational Mechanics, School of Civil Engineering, Georgia Institute of Technology, 225, North Avenue, Atlanta, GA, 30332, USA

    Satya N. Atluri

Rights and permissions

Reprints and permissions

Copyright information

© 1986 Springer Japan

About this paper

Cite this paper

Tong, P. (1986). An Adaptive Dynamic Relaxation Method for Static Problems. In: Yagawa, G., Atluri, S.N. (eds) Computational Mechanics ’86. Springer, Tokyo. https://doi.org/10.1007/978-4-431-68042-0_43

Download citation

  • DOI: https://doi.org/10.1007/978-4-431-68042-0_43

  • Publisher Name: Springer, Tokyo

  • Print ISBN: 978-4-431-68044-4

  • Online ISBN: 978-4-431-68042-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation