2002
DOI: 10.1002/cnm.504
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The buckling mode extracted from the LDLT‐decomposed large‐order stiffness matrix

Abstract: 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.

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Cited by 17 publications
(7 citation statements)
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“…The other important properties of d j , t j and s j , are proved in the previous papers [8,[14][15][16][17] of the authors.…”
Section: Ldl T -Decomposed Stiffness Matrixmentioning
confidence: 81%
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“…The other important properties of d j , t j and s j , are proved in the previous papers [8,[14][15][16][17] of the authors.…”
Section: Ldl T -Decomposed Stiffness Matrixmentioning
confidence: 81%
“…It is noteworthy that L T in Equation (12) is already upper-triangulated and the computational cost necessary to solve Equation (12) for s j is negligible. The deÿned scalar and vectors, d j , t j and s j , will satisfy a lot of linear-algebraic properties, which were derived in the papers [8,[14][15][16][17]. Some important properties, which will be necessary later in the present paper, are:…”
Section: Ldl T -Decomposed Stiffness Matrixmentioning
confidence: 97%
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“…The eigenanalysis might be, however, a bottle neck in largescale nonlinear FEA and, if possible, the solution of eigenproblems should be avoided to accelerate the nonlinear analysis. For this purpose, the authors already proposed a computational procedure to extract the critical (multiple) eigenvector(s) from the LDL T -decomposed symmetric stiffness matrix K (N × N ) in the vicinity of a stability point [1][2][3][4][5][6][7][8][9][10]. Any eigensolver, for example, inverse iteration or subspace method, is not needed.…”
Section: Introductionmentioning
confidence: 99%