Academic Journal
Investigating the Numerical Stability of Dynamic Relaxation Methods with Automatic Load-Increment Schemes to Improve Snap-Back Prediction.
| Title: | Investigating the Numerical Stability of Dynamic Relaxation Methods with Automatic Load-Increment Schemes to Improve Snap-Back Prediction. |
|---|---|
| Authors: | Yang, Chao, Zhang, Pengfei, Luo, Yaozhi |
| Source: | International Journal of Structural Stability & Dynamics; 5/30/2026, Vol. 26 Issue 11, p1-25, 25p |
| Subject Terms: | Structural stability, Numerical analysis, Iterative methods (Mathematics), Structural analysis (Science), Bifurcation theory, Finite difference method |
| Abstract: | Automatic load incrementation schemes tailor-made for the dynamic relaxation (DR) method, including the minimum residual force (MRF) scheme, the minimum residual energy (MRE) scheme, the minimum displacement increment (MDI) scheme, and the minimum kinetic energy (MKE) scheme, are commonly used to capture snapping phenomena in post-buckling structural analysis. Analogous to DR incorporating arc-length constraints, these combined numerical schemes effectively handle snap-through problems, but their capability to address snap-back behavior remains largely unverified. This study aims to investigate the numerical stability of the DR-MRF, DR-MRE, DR-MDI, and DR-MKE methods. Unexpectedly, all these methods are found to be unconditionally unstable and inadequate for snap-back problems. Key findings include (1) the establishment of a general finite-difference equation in canonical form for these four methods, with numerical stability governed by the spectral radius of the recursive amplification matrix; and (2) the discovery of a special property of the tangent stiffness matrix, where a specific minor becomes negative during snap-back, causing the spectral radius to exceed one and leading to instability. These conclusions are supported by numerical verifications on nonlinear springs, trusses, and frames. Simulations consistently demonstrate the reliability of these findings across different structural configurations. [ABSTRACT FROM AUTHOR] |
| Copyright of International Journal of Structural Stability & Dynamics is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Complementary Index |
| FullText | Text: Availability: 0 |
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| Header | DbId: edb DbLabel: Complementary Index An: 192347531 RelevancyScore: 1061 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 1060.76330566406 |
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| Items | – Name: Title Label: Title Group: Ti Data: Investigating the Numerical Stability of Dynamic Relaxation Methods with Automatic Load-Increment Schemes to Improve Snap-Back Prediction. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Yang%2C+Chao%22">Yang, Chao</searchLink><br /><searchLink fieldCode="AR" term="%22Zhang%2C+Pengfei%22">Zhang, Pengfei</searchLink><br /><searchLink fieldCode="AR" term="%22Luo%2C+Yaozhi%22">Luo, Yaozhi</searchLink> – Name: TitleSource Label: Source Group: Src Data: International Journal of Structural Stability & Dynamics; 5/30/2026, Vol. 26 Issue 11, p1-25, 25p – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Structural+stability%22">Structural stability</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Iterative+methods+%28Mathematics%29%22">Iterative methods (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Structural+analysis+%28Science%29%22">Structural analysis (Science)</searchLink><br /><searchLink fieldCode="DE" term="%22Bifurcation+theory%22">Bifurcation theory</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+difference+method%22">Finite difference method</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Automatic load incrementation schemes tailor-made for the dynamic relaxation (DR) method, including the minimum residual force (MRF) scheme, the minimum residual energy (MRE) scheme, the minimum displacement increment (MDI) scheme, and the minimum kinetic energy (MKE) scheme, are commonly used to capture snapping phenomena in post-buckling structural analysis. Analogous to DR incorporating arc-length constraints, these combined numerical schemes effectively handle snap-through problems, but their capability to address snap-back behavior remains largely unverified. This study aims to investigate the numerical stability of the DR-MRF, DR-MRE, DR-MDI, and DR-MKE methods. Unexpectedly, all these methods are found to be unconditionally unstable and inadequate for snap-back problems. Key findings include (1) the establishment of a general finite-difference equation in canonical form for these four methods, with numerical stability governed by the spectral radius of the recursive amplification matrix; and (2) the discovery of a special property of the tangent stiffness matrix, where a specific minor becomes negative during snap-back, causing the spectral radius to exceed one and leading to instability. These conclusions are supported by numerical verifications on nonlinear springs, trusses, and frames. Simulations consistently demonstrate the reliability of these findings across different structural configurations. [ABSTRACT FROM AUTHOR] – Name: Abstract Label: Group: Ab Data: <i>Copyright of International Journal of Structural Stability & Dynamics is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1142/S0219455426500756 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 25 StartPage: 1 Subjects: – SubjectFull: Structural stability Type: general – SubjectFull: Numerical analysis Type: general – SubjectFull: Iterative methods (Mathematics) Type: general – SubjectFull: Structural analysis (Science) Type: general – SubjectFull: Bifurcation theory Type: general – SubjectFull: Finite difference method Type: general Titles: – TitleFull: Investigating the Numerical Stability of Dynamic Relaxation Methods with Automatic Load-Increment Schemes to Improve Snap-Back Prediction. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Yang, Chao – PersonEntity: Name: NameFull: Zhang, Pengfei – PersonEntity: Name: NameFull: Luo, Yaozhi IsPartOfRelationships: – BibEntity: Dates: – D: 30 M: 05 Text: 5/30/2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 02194554 Numbering: – Type: volume Value: 26 – Type: issue Value: 11 Titles: – TitleFull: International Journal of Structural Stability & Dynamics Type: main |
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