Skip to main content

Abstract

A general and powerful method of finding numerical solutions of dynamic time-dependent problems in mechanics is based on the reduction to ordinary differential equations of the partial differential equations describing the problem. This reduction can be effected by means of finite-element or finite-difference methods, the partial differential equations being semidiscretized in space and the resulting ordinary differential equations then integrated in time.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bathe, K.J.; Sonnad, V. On effective implicit time integration in analysis of fluid-structure problems. Int. J. Numer. eths. Eng. (1980), 943-948.

    Google Scholar 

  2. Belytschko, T; Schoeberle, D.F. On the unconditional stability of an implicit algorithm for nonlinear structural dynamics. J. Appl. Mack. 72 (1975), 865–869.

    Article  Google Scholar 

  3. Belytschko, T.; Kennedy, Ü.M.; Schoeberle, D.F. On finite element and difference formulations of transient fluid-structure problems. Proc. Conf. Comput. Meths. in Nuclear Eng., Charleston 2 (1975), 39–52.

    Google Scholar 

  4. Belytschko, T.; Mullen, R. Stability of explicit-implicit mesh partitions in time integration. Int. J. Numan. Meths. Eng. 12 (1978), 1575–1586.

    Article  Google Scholar 

  5. Belytschko, T.; Yen, J.; Mullen, R. Mixed methods for time integration. Comp. Meths. Appl. Mech. Eng. 17/18 (1979), 259–275.

    Article  Google Scholar 

  6. Belytschko, T. Fluid-structure interaction. Computers and Structures 12 (1980), 459–469.

    Article  Google Scholar 

  7. Belytschko, T. Partitioned and adaptive algorithms for explicit time integration. Nonlinear Finite Element Analytis in Structural Mechanics. Edited by Wunderlich, W., et. al., (1980), 572-584.

    Google Scholar 

  8. Felippa, C.A.; Park, K.C. Computational aspects of time integration procedures in structural dynamics. J. Appl. Mech. 45 (1978), 595–602.

    Article  Google Scholar 

  9. Felippa, C.A.; Park, K.C. Staggered transient analysis procedures for coupled mechanical systems: formulation. Comp. Meths. Appl. Mech, Eng. 24 (1980), 6–111.

    Article  Google Scholar 

  10. Gallagher, R.H.; Oden, J.T.; Taylor, C; Zienkiewicz, O.C Finite Elemets in Fluids, Vol. 1, 2, John Wiley & Sons, London, (1975).

    Google Scholar 

  11. Hughes, T.J.R.; Liu W.K. Implicit-explicit finite elements in transient analysis: stability theory. J. Appl. Mech. 45 (1978), 371–374.

    Article  Google Scholar 

  12. Hughes, T.J.R.; Liu, W.K. Implicit-explicit finite elements in transient analysis: implementation and numerical examples. J. Appl. Mech. 45 (1978), 375–378.

    Article  Google Scholar 

  13. Hughes, T.J.R.; Pister, K.S.; Taylor, R.L. Implicit-explicit finite elements in nonlinear transient analysis. Comp. Meths. Appl. Mech. 17/18 (1979), 159–182.

    Article  Google Scholar 

  14. Hughes, T.J.R.; Stephenson R.S. Convergence of implicit-explicit finite elements in nonlinear transient analysis. Int. J. Eng. Sci., in press.

    Google Scholar 

  15. Hughes, T.J.R. Implicit-explicit finite element techniques for symmetric and nonsymmetric systems. Numerical Methods for Non-Linear Problems. Edited by Taylor, C., et. al., Pineridge Press, Swansea, (1980), 127–139.

    Google Scholar 

  16. Key, S.W.; Krieg, R.D. Comparison of finite element and finite difference methods, Numerical and Computer methods in Structural Analysis. Edited by Fenves, S.J., et. al., Academic Press, New York, (1973), 337–352.

    Google Scholar 

  17. Neishlos, H.; Israeli, M.; Kivity, Y. Stability of some explicit difference schemes for fluid-structure interaction problems. Computers and Structures 13 (1981), 97–101.

    Article  Google Scholar 

  18. Neishlos, H.; Israeli, M.; Kivity, Y. A coupling algorithm forfluid and structure with different time steps. Numerical Methods for Coupled Problems. Edited by Hinton, E., et. al., Pineridge Press, Swansea, (1981), 313–320.

    Google Scholar 

  19. Neishlos, H. The stability of explicit difference schemes for solving the problem of interaction between a compressible fluid and an elastic shell. Report No. 1345, CSIR-NRIMS, Pretoria, (1981).

    Google Scholar 

  20. Park, K.C.; Felippa, C.A. Computational aspects of time integration procedures in structural dynamics. J. Appl. Mech. 45 (1978), 595–611.

    Article  Google Scholar 

  21. Park, K.C. Partitioned analysis procedures for coupled-fields problems: stability analysis. J. Appl. Mech. 47 (1980), 320–326.

    Google Scholar 

  22. Park, K.C. An improved semi-implicit algorithm for structural dynamics. Numerical Methods for Coupled Problems. Edited by Hinton, E., et. al., Pineridge Press, Swansea, (1981), 416–417.

    Google Scholar 

  23. Wright, J.P. Mixed time integration schemes. Computers and Structures 10 (1979), 235–238.

    Article  Google Scholar 

  24. Zienkiewicz, O.C. The finite Element Method. McGraw-Hill, London, 1977.

    Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1983 Springer Basel AG

About this chapter

Cite this chapter

Neishlos, H. (1983). Finite-Element Mesh Partitioning for Time Integration of Transient Problems. In: Laurie, D.P. (eds) Numerical Solution of Partial Differential Equations: Theory, Tools and Case Studies. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 66. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6262-2_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-6262-2_8

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-6264-6

  • Online ISBN: 978-3-0348-6262-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics