Extremum theorem and convergence criterion for an iterative solution to the finite-step problem in elastoplasticity with mixed nonlinear hardening
Comi, Claudia ; Maier, Giulio
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti, Tome 83 (1989), p. 177-186 / Harvested from Biblioteca Digitale Italiana di Matematica
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For a class of elastic-plastic constitutive laws with nonlinear kinematic and isotropic hardening, the problem of determining the response to a finite load step is formulated according to an implicit backward difference scheme (stepwise holonomic formulation), with reference to discrete structural models. This problem is shown to be amenable to a nonlinear mathematical programming problem and a criterion is derived which guarantees monotonie convergence of an iterative algorithm for the solution of the finite-step analysis problem. This communication anticipates in an abbreviated form results to be presented elsewhere in an extended form: here proofs and various comments are omitted.

Per una classe di leggi costituitive elastoplastiche con incrudimento nonlineare cinematico ed isotropo, il problema relativo alla determinazione della risposta ad un passo di carico finito viene formulato in base ad uno schema implicito per "differenza all'indietro" (formulazione olonoma nel passo) con riferimento a modelli strutturali discreti. Il problema è ricondotto alla programmazione nonlineare e se ne deduce un criterio di convergenza monotona di un algoritmo iterativo per la risoluzione del problema di analisi nel passo finito. In questa nota alcuni risultati da presentare altrove in forma più estesa e dettagliata vengono comunicati in forma abbreviata omettendo dimostrazioni e vari commenti.

Publié le : 1989-12-01
@article{RLINA_1989_8_83_1_177_0,
     author = {Claudia Comi and Giulio Maier},
     title = {Extremum theorem and convergence criterion for an iterative solution to the finite-step problem in elastoplasticity with mixed nonlinear hardening},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti},
     volume = {83},
     year = {1989},
     pages = {177-186},
     zbl = {0732.73017},
     mrnumber = {1142456},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RLINA_1989_8_83_1_177_0}
}

Comi, Claudia; Maier, Giulio. Extremum theorem and convergence criterion for an iterative solution to the finite-step problem in elastoplasticity with mixed nonlinear hardening. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti, Tome 83 (1989) pp. 177-186. http://gdmltest.u-ga.fr/item/RLINA_1989_8_83_1_177_0/

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