Geodesic
A variationally consistent generalized variable formulation of the elastoplastic rate problem
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 2 (1991) no. 2, pp. 177-190.

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The elastoplastic rate problem is formulated as an unconstrained saddle point problem which, in turn, is obtained by the Lagrange multiplier method from a kinematic minimum principle. The finite element discretization and the enforcement of the min-max conditions for the Lagrangean function lead to a set of algebraic governing relations (equilibrium, compatibility and constitutive law). It is shown how important properties of the continuum problem (like, e.g., symmetry, convexity, normality) carry over to the discrete problem if «generalized variables» are used in the discretization. A couple of dual kinematic and static minimum properties in generalized variables are finally derived.
Il problema elastoplastico per il continuo, in termini di velocità di variazione, viene formulato come un problema di punto sella non vincolato partendo da un principio di minimo cinematico e utilizzando il metodo dei moltiplicatori di Lagrange. L'imposizione delle condizioni di min-max per la funzione lagrangiana, discretizzata ad elementi finiti, porta ad un sistema algebrico di equazioni governanti (equilibrio, congruenza e legge costitutiva). Si dimostra come importanti proprietà del problema continuo (quali ad es. simmetria, convessità, normalità) si trasferiscano al problema discreto qualora si utilizzino variabili generalizzate per la discretizzazione. Infine, si formula una coppia di proprietà duali di minimo cinematico e statico. 
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Comi, Claudia; Perego, Umberto. A variationally consistent generalized variable formulation of the elastoplastic rate problem. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 2 (1991) no. 2, pp. 177-190. http://geodesic.mathdoc.fr/item/RLIN_1991_9_2_2_a10/

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