Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

An adaptive control of spatial-temporal discretization error in finite element analysis of dynamic problems

  • Choi, Chang-Koon (Department of Civil Engineering, Korea Advanced Institute of Science and Technology) ;
  • Chung, Heung-Jin (Department of Civil Engineering, Korea Advanced Institute of Science and Technology)
  • Published : 1995.07.25
⟨ Previous Next ⟩

Abstract

The application of adaptive finite element method to dynamic problems is investigated. Both the kinetic and strain energy errors induced by space and time discretization were estimated in a consistent manner and controlled by the simultaneous use of the adaptive mesh generation and the automatic time stepping. Also an optimal ratio of spatial discretization error to temporal discretization error was discussed. In this study it was found that the best performance can be obtained when the specified spatial and temporal discretization errors have the same value. Numerical examples are carried out to verify the performance of the procedure.

Keywords

References

  1. Babuska, I. and Rheinboldt, W. (1979), "Adaptive approaches and reliability estimates in finite element analysis", Comput. Meths. Appl. Mech. Engrg., 17/18, 519-514. https://doi.org/10.1016/0045-7825(79)90042-2
  2. Bajer, C.I., Bogacz, R. and Bonthoux, X. (1991), "Adaptive space-time elements in the dynamic elastic-viscoplastic problem", Computers and Structures, 39, 415-423. https://doi.org/10.1016/0045-7949(91)90048-Q
  3. Bergan, P.G. and Mollestad, E. (1985), "An automatic time-stepping algorithm for dynamic problems", Comput. Meths. Appl. Mech. Engrg., 49, 299-318. https://doi.org/10.1016/0045-7825(85)90127-6
  4. Choi, C.K. and Park, Y.M. (1992), "An adaptive h-refinement using transition element for plate bending problems", Int. J. Numer. Methods Eng., 35, 145-163. https://doi.org/10.1002/nme.1620350110
  5. Choi, C.K. and Chung, H.J. (1994), "An adaptive procedure in finite element analysis of elastodynamic problems", Proceedings of International Conference on Computational Methods in Structural and Geotechnical Engineering, Hong Kong, December.
  6. Ewing, R.E. (1990), "A posteriori error estimation", Comput. Meths. Appl. Mech. Engrg., 82, 59-72. https://doi.org/10.1016/0045-7825(90)90158-I
  7. Hughes, J.R. (1987), The finite element method-linear static and dynamic finite element analysis, Prentice-Hall, Englewood Cliffs, NJ.
  8. Joo, K.J. and Wilson, E.L. (1988), "An adaptive finite element technique for structural dynamic analysis", Computers and Structures, 30, 1319-1339. https://doi.org/10.1016/0045-7949(88)90196-4
  9. Oden, J.T. and Reddy, J.N. (1976), An introduction to the mathematical theory of finite elements, Wiley, New York, 1976.
  10. Park, K.C. and Underwood, P.G. (1980), "A variable central difference method for structural dynamic analysis. Part 1-Theoretical aspects", Comput. Meths. Appl. Mech. Engrg., 22, .241-258. https://doi.org/10.1016/0045-7825(80)90087-0
  11. Probert, E.J., Hassan, O. and Morgan, K. (1991), "An adaptive finite element method for transient compressible flows with moving boundaries", Int. J. Numer. Methods Eng., 32, 751-765. https://doi.org/10.1002/nme.1620320407
  12. Probert, E.J.;Hassan, O., Peraire, J. and Morgan, K. (1991), "An adaptive finite element method for transient compressible flows", Int. J. Numer. Methods Eng., 32, 1145-1159. https://doi.org/10.1002/nme.1620320514
  13. Probert, E.J., Hassan, O., Morgan, K. and Peraire, J. (1992), "Adaptive explicit and implicit finite element method for transient thermal analysis", Int. J. Numer. Methods Eng., 35, 655-670. https://doi.org/10.1002/nme.1620350404
  14. Strang, G. and Fix, G.J. (1973), An analysis of the finite element method, Prentice-Hall, Englewood Cliffs, N. J.
  15. Wang, Y.C., Murti, V. and Valliappan, S. (1992), "Assessment of the accuracy of the Newmark method in transient analysis of wave propagation problems", Earthquake Eng. Struct. Dyn., 21, 987-1004. https://doi.org/10.1002/eqe.4290211104
  16. Wiberg, N.E. and Li, X.D. (1993), "A post-processing technique and a posteriori error estimate for the Newmark method in dynamic analysis", Earthquake Eng. Struct. Dyn., 22, 465-489. https://doi.org/10.1002/eqe.4290220602
  17. Zeng, L.F. and Wiberg, N.E. (1992), "Spatial mesh adaptation in semidiscrete finite element analysis of linear elastodynamic problems", Comput. Mech., 9, 315-332. https://doi.org/10.1007/BF00370012
  18. Zeng, L.F., Wiberg, N.E., Li, X.D. and Xie, Y.M. (1992), "A posteriori local error estimation and adaptive time stepping for Newmark integration in dynamic analysis", Earthquake Eng. Struct. Dyn., 21, 555-571. https://doi.org/10.1002/eqe.4290210701
  19. Zienkiweicz, O.C. and Xie, Y.M. (1991), "A simple estimator and adaptive time stepping procedure for dynamic analysis", Earthquake Eng. Struct. Dyn., 20, 871-887. https://doi.org/10.1002/eqe.4290200907
  20. Zienkiewicz, O.C. and Zhu, J.Z. (1987), "A simple error estimator and adaptive procedures for practical engineering analysis", Int. J. Numer. Methods Eng., 24, 337-357. https://doi.org/10.1002/nme.1620240206

Cited by

  1. Error estimates and adaptive finite element methods vol.18, pp.5/6, 2001, https://doi.org/10.1108/EUM0000000005788
  2. Adaptive superposition of finite element meshes in non-linear transient solid mechanics problems vol.72, pp.9, 2007, https://doi.org/10.1002/nme.2067
  3. An efficient adaptive strategy to master the global quality of viscoplastic analysis vol.78, pp.1-3, 2000, https://doi.org/10.1016/S0045-7949(00)00107-3
  4. Adaptive superposition of finite element meshes in elastodynamic problems vol.63, pp.11, 2005, https://doi.org/10.1002/nme.1331
  5. Error estimates and adaptive time stepping for various direct time integration methods vol.60, pp.6, 1996, https://doi.org/10.1016/0045-7949(95)00452-1
  6. An edge-based smoothed finite element method for adaptive analysis vol.39, pp.6, 2011, https://doi.org/10.12989/sem.2011.39.6.767