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A numerical analysis of infinitesimal mechanisms
Author(s) -
Garcea Giovanni,
Formica Giovanni,
Casciaro Raffaele
Publication year - 2005
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1158
Subject(s) - infinitesimal , indeterminacy (philosophy) , simplicity , mathematics , indeterminate , displacement (psychology) , stability (learning theory) , degree (music) , measure (data warehouse) , order (exchange) , statically indeterminate , mathematical optimization , calculus (dental) , mathematical analysis , computer science , structural engineering , pure mathematics , engineering , philosophy , dentistry , database , psychotherapist , acoustics , psychology , epistemology , quantum mechanics , machine learning , medicine , physics , finance , economics
Abstract The paper presents a numerical algorithm, based on Koiter's theory of the elastic stability, for detecting the order of infinitesimal mechanisms, i.e. kinematically indeterminate systems of pin‐jointed bars. In cases of one degree of indeterminacy the algorithm improves, in terms of computational simplicity and efficiency, an analogous algorithm proposed by Salerno in 1992. This is shown to be due to the vanishing of the terms higher than the third‐order of the asymptotic expressions of the energy, owing to the use of the Green strain measure and a mixed (displacement and stress) formulation of the problem. Moreover, the proposed algorithm is able to provide a correct definition of mechanism in cases of several degrees of indeterminacy, mainly for structures like those first studied by Connelly and Servatius in 1994, which the paper will treat in depth. Copyright © 2005 John Wiley & Sons, Ltd.