Branch Switching in Bifurcation of Structures

Computational Mechanics

Ramm

2000

The postbuckling behavior of an axially compressed circular cylindrical shell is exceedingly complicated due to an in®nite number of closely spaced postbuckling branches and bifurcation points. The minimum strength existing in the deep bottom of the postbuckling region may serve as a design limit. The primary concern in this present paper is to compute this stable postbuckling equilibrium solution by two different approaches: One is to repeat the procedures of tracing unstable branches, pinpointing bifurcation points and branch-switching in order to carefully approach to the target. The other is to trigger a static jump to the target by two-parametric loading. As a numerical example, a perfect circular cylindrical panel is analyzed to show that a direct jump from the undeformed state to a stable postbuckling solution is possible with a proper choice of the load perturbation.

“…For details including the linearized equations and individual solution procedures, the previous works [21,22,23,24,28] of the authors may be referred to.…”

Section: Computational Bifurcation Theorymentioning

confidence: 99%

“…2), line search is recommended [21,22,23] to ®nd a stationary point of the potential in the direction of the critical eigenvector h:…”

Section: Branch-switchingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Static path jumping to attain postbuckling equilibria of a compressed circular cylinder

Computational Mechanics

Ramm

2000

“…For local branch-switching at a ÿxed load level p = p A , line search is recommended [1][2][3] to ÿnd a stationary point of the potential in the direction of the critical eigenvector q m ( ∼ = Â s ). The nodal displacement ÿeld is assumed to be with an arc-length in line search direction.…”

Section: Branch-switchingmentioning

confidence: 99%

“…The computational procedures, which are indispensable in the non-linear bifurcation analysis, are those for tracing the non-linear equilibrium response, inspecting and pinpointing the bifurcation point and also branch-switching [1][2][3][4]. The path-tracing procedure, based upon arc-length control, is today well established and its details need not be mentioned in this present paper.…”

Section: Introductionmentioning

confidence: 98%

Eigenvector‐free indicator, pinpointing and branch‐switching for bifurcation

Commun. Numer. Meth. Engng.

2003

SUMMARYThe authors have already proposed in their previous papers an innovative eigenanalysis-free idea to extract the buckling mode for bifurcation instability from the LDL T -decomposed sti ness matrix. The present study ÿrst outlines this basic idea very brie y for a review purpose. The idea will then be applied to eigenvector-free procedures for identifying and pinpointing the stability point and branchswitching for post-bifurcation analysis. Numerical examples will examine the versatility and robustness of the proposed eigenvector-free procedures in computational bifurcation theory. It is illustrated that the proposed procedures are robust enough for multiple as well as simple bifurcation.

The buckling mode extracted from the LDL^T‐decomposed large‐order stiffness matrix

Commun. Numer. Meth. Engng.

2002

Self Cite

SUMMARYThe present study proposes an innovated eigenanalysis-free idea to extract the buckling mode only from the LDL T -decomposed sti ness matrix in large-scale bifurcation analysis. The computational cost for extracting the critical eigenvector is negligible, because the decomposition of the sti ness matrix will continually be repeated during path-tracing to solve the sti ness equations. A numerical example is computed to illustrate that the proposed idea is tough enough even for multiple bifurcation.