Passing of instability points by applying a stabilized Newton–Raphson scheme to a finite element formulation: Comparison to arc-length method

Müller, Michael R.

doi:10.1007/s00466-006-0133-y

Cited by 6 publications

(54 citation statements)

References 15 publications

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“…Wright and Gaylord [31] and Felippa [5,6] examined such schemes, which were, e.g. summarized by Ramm [19], Wagner [26] and Müller [12,13]. Wright's and Felippa's works are of particular concern as they introduce stabilization by springs.…”

Section: Summary Of Procedures Documented So Farmentioning

confidence: 99%

“…In [13] the application of a stabilized Newton-Raphson scheme was suggested for the tracing of solution paths, which allows for the stable passing of critical points on the primary path. This, in some cases, requires the special treatment of the residual forces with respect to bifurcation modes.…”

Section: Summary Of Procedures Documented So Farmentioning

confidence: 99%

“…The approach derived in [13] is a purely damped Newton scheme. In other words, the fictitious stabilization contributes only to the stiffness matrix while the residual forces remain unchanged.…”

Section: Summary Of Procedures Documented So Farmentioning

confidence: 99%

“…Compared to [13] the generation of the automatic imperfection force is further enhanced. The corrector iteration requires certain considerations before a smooth branch switching initiated by the imperfection forces is possible.…”

Section: Introduction To the Stabilization Scheme Proposed Herementioning

confidence: 99%

“…The stabilization procedure proposed here is based on the experience gained from the algorithms described in [13,14]. This investigation will refer frequently to both articles.…”

Section: Introduction To the Stabilization Scheme Proposed Herementioning

confidence: 99%

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Postbuckling analysis stabilized by penalty springs and intermediate corrections

Müller¹

2008

Comput Mech

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Whenever a critical point in a non-linear finite element analysis is reached, an implicit Newton procedure is prevented from proceeding until the stiffness matrix is stabilized. Most stabilization procedures result in a damped Newton scheme. This can cause a reduced convergence rate. Based on documented stabilization strategies, an iterative procedure to reduce negative impact on the convergence rate resulting from the damping is to be proposed here. This will be done by a corrector iteration carried out between two successive equilibrium iterative steps. The equilibrium iteration is a Newton-Raphson scheme. Since the stiffness matrix has already been factorized within the preceding standard equilibrium iterative step, the stiffness matrix will be held constant during the corrector iteration, which in turn allows for a computational efficient treatment of the additional iterations. The proposed procedure has been strongly driven by Wright and Gaylord's (ASCE J. Struct. Div., 94, 1143-1163 investigation.

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Section: Summary Of Procedures Documented So Farmentioning

confidence: 99%

Section: Summary Of Procedures Documented So Farmentioning

confidence: 99%

Section: Summary Of Procedures Documented So Farmentioning

confidence: 99%

Section: Introduction To the Stabilization Scheme Proposed Herementioning

confidence: 99%

“…The stabilization procedure proposed here is based on the experience gained from the algorithms described in [13,14]. This investigation will refer frequently to both articles.…”

Section: Introduction To the Stabilization Scheme Proposed Herementioning

confidence: 99%

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Postbuckling analysis stabilized by penalty springs and intermediate corrections

Müller¹

2008

Comput Mech

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The influence of geometric effects on the behavior of strain softening frames

Tangaramvong

Tin‐Loi

2010

Comput Mech

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This paper presents a mathematical programming based approach for the analysis of elastoplastic softening frames in the presence of geometric nonlinearity. Arbitrarily large deformations, albeit within a small strain regime, can be accommodated, if necessary. For the sake of efficiency, and without undue loss of accuracy, the algorithm processes the nonholonomic (path-dependent) problem in a stepwise holonomic (path-independent) fashion. This analysis capability has been used to investigate what level or order of geometric nonlinearity needs to be adopted to obtain sufficiently accurate results for practical frames. Two examples are provided for illustrative purposes.

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A robust continuation method to pass limit-point instability

Jorabchi

Suresh

2011

Finite Elements in Analysis and Design

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Passing of instability points by applying a stabilized Newton–Raphson scheme to a finite element formulation: Comparison to arc-length method

Cited by 6 publications

References 15 publications

Postbuckling analysis stabilized by penalty springs and intermediate corrections

Postbuckling analysis stabilized by penalty springs and intermediate corrections

The influence of geometric effects on the behavior of strain softening frames

A robust continuation method to pass limit-point instability

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