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POST‐COLLAPSE BIFURCATION ANALYSIS OF SHELLS OF REVOLUTION BY THE ACCUMULATED ARC‐LENGTH METHOD
Author(s) -
TENG J. G.,
LOU Y. F.
Publication year - 1997
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19970715)40:13<2369::aid-nme168>3.0.co;2-8
Subject(s) - bifurcation , rotational symmetry , arc length , deflection (physics) , arc (geometry) , bifurcation theory , finite element method , mathematics , buckling , mechanics , structural engineering , geometry , engineering , physics , classical mechanics , nonlinear system , quantum mechanics
Shells of revolution subject to axisymmetric loads often fail by non‐symmetric bifurcation buckling after non‐linear axisymmetric deformations. A number of computer programmes have been developed in the past decades for these problems, but none of them is capable of bifurcation analysis on the descending branch of the primary load–deflection path following axisymmetric collapse/snap‐through. This paper presents the first finite element formulation of post‐collapse bifurcation analysis of axisymmetric shells in which a modified arc‐length method, the accumulated arc‐length method, is developed to effect a new automatic bifurcation solution procedure. Numerical examples are presented to demonstrate the validity and capability of the formulation as well as the practical importance of post‐collapse bifurcation analysis. The accumulated arc‐length method proposed here can also be applied to the post‐collapse bifurcation analysis of other structural forms. © 1997 by John Wiley & Sons, Ltd.