Kinematical structural stability

Jean Lerbet 1 Noël Challamel 2 François Nicot 3 Félix Darve 4, 5
1 IBISC - Informatique, Biologie Intégrative et Systèmes Complexes
2 LIMATB_UBS
LIMATB - Laboratoire d'Ingénierie des Matériaux de Bretagne
3 UR ETGR (ETNA) - Erosion torrentielle neige et avalanches
4 3SR - Laboratoire sols, solides, structures - risques [Grenoble]
5 GéoMécanique
3SR - Laboratoire sols, solides, structures - risques [Grenoble]
Abstract : This paper gives an overview of our results obtained from 2009 until 2014 about paradoxical stability properties of non conservative systems which lead to the concept of Kinematical Structural Stability (Ki.s.s.). Due to Fischer-Courant results, this ki.s.s. is universal for conservative systems whereas new interesting situations may arise for non conservative ones. A remarkable algebraic property of the symmetric part of linear operators may generalize this result for divergence stability but leading only to a conditional ki.s.s. By duality, the concept of geometric degree of nonconservativity is highlighting. Paradigmatic examples of Ziegler systems illustrate the general results and their effectiveness.
Keywords : Compression of linear operators Geomet-ric degree of nonconservativity Kinematical structural stability Second-order work criterion
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Journal articles
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https://hal.archives-ouvertes.fr/hal-01321988
Contributor : Frédéric Davesne <>
Submitted on : Thursday, May 26, 2016 - 3:19:17 PM
Last modification on : Thursday, February 20, 2020 - 4:36:02 PM

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Jean Lerbet, Noël Challamel, François Nicot, Félix Darve. Kinematical structural stability. Discrete and Continuous Dynamical Systems - Series S, American Institute of Mathematical Sciences, 2016, 9 (2), pp.529--536. ⟨10.3934/dcdss.2016010⟩. ⟨hal-01321988⟩

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