Vol. 2, No. 2, 2014

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ISSN: 2325-3444 (e-only)
ISSN: 2326-7186 (print)
Geometric degree of nonconservativity

Jean Lerbet, Marwa Aldowaji, Noël Challamel, Oleg N. Kirillov, François Nicot and Félix Darve

Vol. 2 (2014), No. 2, 123–139
Abstract

This paper deals with nonconservative mechanical systems subjected to nonconservative positional forces leading to nonsymmetric tangential stiffness matrices. The geometric degree of nonconservativity of such systems is then defined as the minimal number of kinematic constraints necessary to convert the initial system into a conservative one. Finding this number and describing the set of corresponding kinematic constraints is reduced to a linear algebra problem. This index of nonconservativity is the half of the rank of the skew-symmetric part Ka of the stiffness matrix K that is always an even number. The set of constraints is extracted from the eigenspaces of the symmetric matrix Ka2. Several examples including the well-known Ziegler column illustrate the results.

Keywords
linear algebra, nonconservative system
Mathematical Subject Classification 2010
Primary: 15A18, 70G99
Milestones
Received: 9 November 2012
Revised: 15 April 2013
Accepted: 25 May 2013
Published: 9 June 2014

Communicated by Francesco dell'Isola
Authors
Jean Lerbet
Informatique Biologie Intégrative Systèmes Complexes
Université d’Evry-Val-d’Essonne
UFR Sciences & Technologies
40, Rue du Pelvoux
CE 1455 Courcouronnes
91020 Evry cedex
France
Marwa Aldowaji
Informatique Biologie Intégrative Systèmes Complexes
Université d’Evry-Val-d’Essonne
UFR Sciences & Technologies
40, Rue du Pelvoux
CE 1455 Courcouronnes
91020 Evry cedex
France
Noël Challamel
Laboratoire d’Ingénierie des Matériaux de Bretagne
Université de Bretagne Sud
Rue de saint Maudé
BP 92116
56321 Lorient cedex
France
Oleg N. Kirillov
Department of Magnetohydrodynamics
Institute of Fluid Dynamics
Helmholtz-Zentrum Dresden-Rossendorf
Bautzner Landstraße 400
P.O. Box 510119
01314 Dresden
Germany
François Nicot
Geomechanics Group
Irstea
Domaine Universitaire BP 76
38402 Saint Martin d’Hères cedex
France
Félix Darve
Laboratoire Sols Solides Structures
UJF-INPG-CNRS
BP 53
38041 Grenoble cedex 9
France