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On the stability of quasi‐static paths for finite dimensional elastic‐plastic systems with hardening
Author(s) -
Martins J.A.C,
Monteiro Marques M.D.P,
Petrov A.
Publication year - 2007
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200510315
Subject(s) - uniqueness , perturbation (astronomy) , stability (learning theory) , hardening (computing) , longitudinal static stability , quasistatic process , mathematics , lyapunov stability , lyapunov function , property (philosophy) , singular perturbation , mathematical analysis , mechanics , computer science , materials science , physics , composite material , nonlinear system , thermodynamics , philosophy , control (management) , epistemology , layer (electronics) , quantum mechanics , machine learning , artificial intelligence , aerodynamics
In this paper we prove the stability of quasi‐static paths of finite dimensional mechanical systems that have an elastic‐plastic behavior with linear hardening. The concept of stability of quasi‐static paths used here is essentially a continuity property relatively to the size of the initial perturbations (as in Lyapunov stability) and to the smallness of the rate of application of the external forces (which plays here the role of the small parameter in singular perturbation problems). The discussion of stability is preceded by the presentation of mathematical formulations (plus existence and uniqueness results) for those dynamic and quasi‐static problems, in a form that is convenient for the subsequent discussion of stability.