Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Bypass, homotopy path and local iteration to compute the stability point

  • Published : 1997.09.25
⟨ Previous Next ⟩

Abstract

In nonlinear finite element stability analysis of structures, the foremost necessary procedure is the computation to precisely locate a singular equilibrium point, at which the instability occurs. The present study describes global and local procedures for the computation of stability points including bifurcation points and limit points. The starting point, at which the procedure will be initiated, may be close to or arbitrarily far away from the target point. It may also be an equilibrium point or non-equilibrium point. Apart from the usual equilibrium path, bypass and homotopy path are proposed as the global path to the stability point. A local iterative method is necessary, when it is inspected that the computed path point is sufficiently close to the stability point.

Keywords

References

  1. Okazawa, S. and Fujii, F. (1996), "Global and local procedures to compute the stability points", Proceedings of the 3rd Asian-Pacific Conference on Computational Mechanics, 1, 455-460, Seoul
  2. Fujii, F., Choong, K.K. and Kitagawa, T. (1992), "Branch-switching in multi-bifurcation of structures", in "Computing methods in applied sciences and engineering", Nova Science publishers inc., N.Y. edited by Glowinski, R, 457-466, 1992, Paris.
  3. Fujii, F. and Choong, K.K. (1992), "Branch-switching in bifurcation of structures", Journal of Engineering Mechanics, ASCE, 118, 1578-1596. https://doi.org/10.1061/(ASCE)0733-9399(1992)118:8(1578)
  4. Fujii, F. (1994), "Bifurcation and path-switching in nonlinear elasticity", Invited lecture, extended abstracts, 1246-1247, 3rd WCCM (World Congress on Computational Mechanics), Makuhari, Japan.
  5. Fujii, F. and Okazawa, S. (1994), "Multi-bifurcation models in nonlinear elasticity", Proceedings of the COMSAGE94 (International Conference on Computational Methods in Structural and Geotechnical Engineering), 11, 583-588, edited by Lee, P, Translation & Printing Services Ltd., Hong Kong.
  6. Fujii, F. and Ramm, E. (1995), "Computational bifurcation theory-path-tracing, pinpointing and path-switching-", invited address, ICSS95 (International Conference on Stability of Structures), Proceedings, 1, 177-191, Coimbatore, India.
  7. Fujii, F., Okazawa, S. and Gong, S.-X. (1995), "Computational stability theory-its strategy", Computational Mechanics' 95, edited by Atluri, S.N., Yagawa, G. and Cruse, T.A. (editors), Springer, 1, 1523-1528.
  8. Fujii, F. and Okazawa, S. (1997), "Pinpointing bifurcation points and branch-switching", Journal of Engineering Mechanics, ASCE, 123, 179-189. https://doi.org/10.1061/(ASCE)0733-9399(1997)123:3(179)
  9. Fujii, F., Ikeda, K. and Okazawa, S. (1997), "Modified stiffness iteration to compute the multiple bifurcation point", ICCSS 97, IASS International Colloquium on Computation of Shell and Spatial Structures, Taipei, Taiwan, Nov. 5-7.
  10. Noguchi, H. and Hisada, T. (1994), "Development of a new branch-switching algorithm in nonlinear FEM using scaled corrector", JSME, International Journal, 37(3).
  11. Wagner, W. and Wriggers, P. (1988), "A simple method for the calculation of postctiritcal branches", Engineering Computation, 5, 103. https://doi.org/10.1108/eb023727
  12. Wriggers, P., Wagner, W. and Miehe, C. (1988), "A quadratically convergent procedure for calculation of stability points in finite element analysis", Computer Methods in Applied Mechanics and Engineering, 70, 329-347. https://doi.org/10.1016/0045-7825(88)90024-2
  13. Wriggers, P. and Simo, J.C. (1990), "General procedure for the direct computation of Luring and bifurcation points", International Journal for Numerical Methods in Engineering, 30, 155-176. https://doi.org/10.1002/nme.1620300110

Cited by

  1. Postbuckling strength of an axially compressed elastic circular cylinder with all symmetry broken vol.11, pp.2, 2001, https://doi.org/10.12989/sem.2001.11.2.199
  2. A robust continuation method to pass limit-point instability vol.47, pp.11, 2011, https://doi.org/10.1016/j.finel.2011.05.012
  3. On the local stability condition in the planar beam finite element vol.12, pp.5, 2001, https://doi.org/10.12989/sem.2001.12.5.507