In reply to some remarks by N. Challamel on our paper “Instability of elastic bodies” (original) (raw)

On the foundation of the stability theory of elastic structures

Meccanica, 1975

S OMMARIO: Vengono esaminate alcune difflcolth e problemi ancora aperti nella teoria della stabilith dei sistemi continui. Dopo aver approfondito il significato e/'importanza della scdta della "distanza" ira due configura~oni di un sistema continuo, il problema della stabilitA dell'equitibrio delte strutture elastiche viene formulato in un opportuno spazio funzionale, nel quale ~ possibile dimostrare la validith del criterio dell'energia come condizione sufficiente di stabilith nel senso di Lyapunov.

Essay on the Contributors to the Elastic Stability Theory

Meccanica, 2005

This paper revisits the historical aspects of the contributions made into the elastic stability theory from the structural engineering point of view. Extensive quotations are brought in order to substantiate the claims made. It is hoped that the review constitutes a contribution to the identification of the main ideas pertinent to engineering mechanics.

On the stability of non-conservative elastic systems under mixed perturbations

Revue européenne de génie civil, 2009

Cet article étudie l'influence du mode de chargement sur la stabilité de systèmes élastiques discrets non conservatifs. La stabilité du système contraint est comparée à celle du système libre, par l'introduction de multiplicateurs de Lagrange. L'approche est illustrée avec le pendule généralisé de Ziegler. Elle est ensuite appliquée à un modèle à deux degrés de liberté représentant un sol contraint par un chargement isochore. On montre que le chargement isochore affecte sensiblement la frontière de stabilité pour le problème conservatif et pour le problème non conservatif. En dehors des instabilités par flottement, le critère de travail du second-ordre constitue une borne inférieure de la frontière de stabilité du système libre ainsi que la frontière du domaine de stabilité du système sous chargements mixtes proportionnels en déplacement.

Recent Developments in the Dynamic Stability of Elastic Structures

Frontiers in Applied Mathematics and Statistics

Dynamic instability in the mechanics of elastic structures is a fascinating topic, with many issues still unsettled. Accordingly, there is a wealth of literature examining the problems from different perspectives (analytical, numerical, experimental etc.), and coverings a wide variety of topics (bifurcations, chaos, strange attractors, imperfection sensitivity, tailor-ability, parametric resonance, conservative or non-conservative systems, linear or non-linear systems, fluid-solid interaction, follower forces, etc.). This paper provides a survey of selected topics of current research interest. It aims to collate the key recent developments and international trends, as well as describe any possible future challenges. A paradigmatic example of Ziegler paradox on the destabilizing effect of small damping is also included.

Non-Classical Problems in the Theory of Elastic Stability

Applied Mechanics Reviews, 2001

Items with a reviewer byline (coded R) are by AMR's corps of dedicated outside volunteer reviewers. AMR will attempt to get critical reviews of all relevant textbooks, reference works, and monographs. Items without a reviewer byline (coded N) are prepared by AMR in-house staff and are largely based on material such as a book's table of contents and editor's preface or foreword. In the interest of timeliness, most conference proceedings and multi-author contributed volumes will receive descriptive notes in this fashion. Books deemed to be somewhat peripheral to AMR's basic scope may simply be listed by title. Also listed by title when first received are books under review.

Remarks on robustness of stability with respect to thickness for elastic structures

ESAIM: Proceedings, 1998

Models of elastic systems are often inherently dependent upon small parameters such as thickness. Using the results on the original model to obtain information on the system as the thickness tends to zero can be far from straightforward. An illustration of stability results and discussion of the difficulties that arise in deriving stability for the limiting system are presented.

New Results in Dynamics Stability Problems of Elastic Rods

structural mechanics and building structures, Saint-Petersburg, Polytechnicheskaya st., 29, Russian a lalin@cef.spbstu.ru, b dasha_kushova@mail.ru Keywords: large displacements and rotations, conjugate pairs of strain and stress vectors, the functional of variational formulation, the stability equations, dynamic stability, dynamic approach to study the stability problem, dynamic stability criterion Abstract. This article is about the nonlinear dynamic stability problems of the exact (Cosserat) theory of elastic rods. There is examined the general geometrically nonlinear theory with no restrictions on displacements and rotations being imposed.