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Practical integration of semidiscretized nonlinear equations of motion / Aram Soroushian in Journal of engineering mechanics, Vol. 139 N° 2 (Février 2013) 

Public ISBD [article]  in Journal of engineering mechanics > Vol. 139 N° 2 (Février 2013) . - pp.114–145. Titre : Practical integration of semidiscretized nonlinear equations of motion : proper convergence for systems with piecewise linear behavior Type de document : texte imprimé Auteurs : Aram Soroushian, Auteur ; Peter Wriggers, Auteur ; Jamshid Farjoodi, Auteur Année de publication : 2013 Article en page(s) : pp.114–145. Note générale : Applied mechanics Langues : Anglais (eng) Mots-clés : Time  integration  Piecewise  linear  Proper  convergence  Time  step  Nonlinearity  residual  Pseudoerror  Nonlinearity  tolerance  Order  of  accuracy  Space  of  nonlinearity  Accuracy-controlling  methods Résumé : Time integration is the most versatile tool for analyzing semidiscretized equations of motion. The responses are approximations, with deviations from the exact responses mainly depending on the integration method and the integration step sizes. When repeating the analyses with smaller steps, the responses generally converge to the exact responses. However, the convergence trends are different in linear and nonlinear analyses. Whereas in linear analyses, by decreasing the sizes of integration steps, the errors decrease with a rate, depending on the orders of accuracy, in nonlinear analyses, the change in errors might be unpredictable. The main reason is the inconsistency between the integration steps sizes and the residuals of nonlinearity iterations. In this paper, based on careful selection of nonlinearity tolerances, a methodology and a method to overcome this inconsistency for semidiscretized systems with piecewise linear behavior are introduced. When the responses converge, except for systems with very complex behaviors, the proposed method leads to proper convergence, with tolerable computational costs. In addition, by implementing the proposed method, more reliable error estimations can be expected from convergence-based accuracy controlling methods. ISSN : 0733-9399 En ligne : http://ascelibrary.org/doi/abs/10.1061/%28ASCE%29EM.1943-7889.0000434 [article] Practical integration of semidiscretized nonlinear equations of motion : proper convergence for systems with piecewise linear behavior [texte imprimé] / Aram Soroushian, Auteur ; Peter Wriggers, Auteur ; Jamshid Farjoodi, Auteur . - 2013 . - pp.114–145. Applied mechanics Langues : Anglais (eng) in Journal of engineering mechanics > Vol. 139 N° 2 (Février 2013) . - pp.114–145. Mots-clés : Time  integration  Piecewise  linear  Proper  convergence  Time  step  Nonlinearity  residual  Pseudoerror  Nonlinearity  tolerance  Order  of  accuracy  Space  of  nonlinearity  Accuracy-controlling  methods Résumé : Time integration is the most versatile tool for analyzing semidiscretized equations of motion. The responses are approximations, with deviations from the exact responses mainly depending on the integration method and the integration step sizes. When repeating the analyses with smaller steps, the responses generally converge to the exact responses. However, the convergence trends are different in linear and nonlinear analyses. Whereas in linear analyses, by decreasing the sizes of integration steps, the errors decrease with a rate, depending on the orders of accuracy, in nonlinear analyses, the change in errors might be unpredictable. The main reason is the inconsistency between the integration steps sizes and the residuals of nonlinearity iterations. In this paper, based on careful selection of nonlinearity tolerances, a methodology and a method to overcome this inconsistency for semidiscretized systems with piecewise linear behavior are introduced. When the responses converge, except for systems with very complex behaviors, the proposed method leads to proper convergence, with tolerable computational costs. In addition, by implementing the proposed method, more reliable error estimations can be expected from convergence-based accuracy controlling methods. ISSN : 0733-9399 En ligne : http://ascelibrary.org/doi/abs/10.1061/%28ASCE%29EM.1943-7889.0000434