Yu. L. Sachkov, S. V. Levyakov, “Stability of inflectional elasticae centered at vertices or inflection points”, Differential equations and topology. II, Collected papers. In commemoration of the centenary of the birth of Academician Lev Semenovich Pontryagin, Trudy Mat. Inst. Steklova, 271, MAIK Nauka/Interperiodica, Moscow, 2010, 187–203; Proc. Steklov Inst. Math., 271 (2010), 177

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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2010, Volume 271, Pages 187–203 (Mi tm3244)

This article is cited in 23 scientific papers (total in 23 papers)

Stability of inflectional elasticae centered at vertices or inflection points

Yu. L. Sachkov^a, S. V. Levyakov^b

^a Program Systems Institute, Russian Academy of Sciences, Pereslavl-Zalessky, Russia
^b Novosibirsk State Technical University, Novosibirsk, Russia

Full-text PDF (3552 kB) Citations (23)

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Abstract: Stability conditions for inflectional Euler's elasticae centered at vertices or inflection points are obtained. Theoretical results are compared with experimental data for elastic rods.

Received in February 2010

English version:
Proceedings of the Steklov Institute of Mathematics, 2010, Volume 271, Pages 177–192
DOI: https://doi.org/10.1134/S0081543810040140

Bibliographic databases:

Document Type: Article

UDC: 517.97

Language: Russian

Citation: Yu. L. Sachkov, S. V. Levyakov, “Stability of inflectional elasticae centered at vertices or inflection points”, Differential equations and topology. II, Collected papers. In commemoration of the centenary of the birth of Academician Lev Semenovich Pontryagin, Trudy Mat. Inst. Steklova, 271, MAIK Nauka/Interperiodica, Moscow, 2010, 187–203; Proc. Steklov Inst. Math., 271 (2010), 177–192

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tm3244

https://www.mathnet.ru/eng/tm/v271/p187

This publication is cited in the following 23 articles:

Tatsuya Miura, Kensuke Yoshizawa, “General rigidity principles for stable and minimal elastic curves”, Journal für die reine und angewandte Mathematik (Crelles Journal), 2024
Yu. L. Sachkov, “Left-invariant optimal control problems on Lie groups that are integrable by elliptic functions”, Russian Math. Surveys, 78:1 (2023), 65–163
Ryzhak I E., “Investigation of Buckling of Rectilinear Beams With Additional Constraint At An Arbitrary Internal Point”, Q. J. Mech. Appl. Math., 75:1 (2022), 29–62
Oshri O., “Volume-Constrained Deformation of a Thin Sheet as a Route to Harvest Elastic Energy”, Phys. Rev. E, 103:3 (2021), 033001
Hafner Ch., Bickel B., “The Design Space of Plane Elastic Curves”, ACM Trans. Graph., 40:4 (2021), 126
Christian Hafner, Bernd Bickel, “The design space of plane elastic curves”, ACM Trans. Graph., 40:4 (2021), 1
Miura T., “Elastic Curves and Phase Transitions”, Math. Ann., 376:3-4 (2020), 1629–1674
Jin M., “Stability to Discontinuous Perturbations For One Inflexion Euler Elasticas With One End Fixed and the Other Clamped in Rotation”, Eur. J. Mech. A-Solids, 81 (2020), 103954
James F. Doyle, Spectral Analysis of Nonlinear Elastic Shapes, 2020, 185
James F. Doyle, Spectral Analysis of Nonlinear Elastic Shapes, 2020, 1
Spagnuolo M., Andreaus U., “A Targeted Review on Large Deformations of Planar Elastic Beams: Extensibility, Distributed Loads, Buckling and Post-Buckling”, Math. Mech. Solids, 24:1 (2019), 258–280
Cazzolli A., Dal Corso F., “Snapping of Elastic Strips With Controlled Ends”, Int. J. Solids Struct., 162 (2019), 285–303
T.P. Kasharina, “Improving the Reliability of Shell Structures Made of Composite Nanomaterials”, SSP, 265 (2017), 365
Doicheva A., “T-Shaped Frame Critical and Post-Critical Analysis”, J. THEOR. APPL. MECH.-BULG., 46:1 (2016), 65–82
T.P. Kasharina, “Results of the Study on the Influence of Shell Structures on their Stability”, Procedia Engineering, 150 (2016), 1811
Jin M., Bao Z.B., “An Improved Proof of Instability of Some Euler Elasticas”, J. Elast., 121:2 (2015), 303–308
Batista M., “on Stability of Elastic Rod Planar Equilibrium Configurations”, Int. J. Solids Struct., 72 (2015), 144–152
Batista M., “a Simplified Method To Investigate the Stability of Cantilever Rod Equilibrium Forms”, Mech. Res. Commun., 67 (2015), 13–17
Jin M., Bao Z.B., “‘Stability in the Large’ of Columns Just At the First Bifurcation Point”, Mech. Res. Commun., 67 (2015), 31–33
Beharic J., Lucas T.M., Harnett C.K., “Analysis of a Compressed Bistable Buckled Beam on a Flexible Support”, J. Appl. Mech.-Trans. ASME, 81:8 (2014), 081011

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Труды Математического института имени В. А. Стеклова

Proceedings of the Steklov Institute of Mathematics

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