Geodesic
Unconditionally stable mid-point time integration in elastic-plastic dynamics
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 1 (1990) no. 4, pp. 367-376.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

The dynamic analysis of elastoplastic systems discretized by finite elements is dealt with. The material behaviour is described by a rather general internal variable model. The unknown fields are modelled in terms of suitable variables, generalized in Prager's sense. Time integrations are carried out by means of a generalized mid-point rule. The resulting nonlinear equations expressing dynamic equilibrium of the finite step problem are solved by means of a Newton-Raphson iterative scheme. The unconditional stability of the adopted integration method is proved according to two nonlinear stability
Si considera l'analisi dinamica di sistemi elastoplastici discretizzati ad elementi finiti. Il comportamento del materiale è descritto da un modello alquanto generale a variabili interne. I campi incogniti sono modellati in funzione di opportune variabili, generalizzate nel senso di Prager. Le integrazioni nel tempo sono effettuate per incrementi finiti adottando il metodo detto del punto medio generalizzato. Le equazioni non lineari di equilibrio dinamico che così si formulano vengono risolte per mezzo di uno schema iterativo tipo Newton-Raphson. Si dimostra che il metodo di integrazione adottato è incondizionatamente stabile secondo due criteri di stabilità validi in campo non lineare. 
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     title = {Unconditionally stable mid-point time integration in elastic-plastic dynamics},
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Corigliano, Alberto; Perego, Umberto. Unconditionally stable mid-point time integration in elastic-plastic dynamics. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 1 (1990) no. 4, pp. 367-376. http://geodesic.mathdoc.fr/item/RLIN_1990_9_1_4_a11/

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