Sommario
Si considera il problema dell’equilibrio delle reti di funi elastiche sottoposte a carichi conservativi, distribuiti o concentrati, e a distorsioni impresse. Alla singola fune è attribuito comportamento unilaterale (reagenza a sola trazione). La trattazione è condotta in forma lagrangiana, sotto la naturale ipotesi di grandi spostamenti. Si perviene ad una formulazione variazionale di stazionarietà di un funzionale sella nelle variabili di spostamento e di sforzo, queste ultime vincolate in segno, e sulla base di questa formulazione vengono discusse le proprietà di unicità della soluzione. Si deducono inoltre due formulazioni complementari di estremo vincolato, corrispondenti agli usuali principi di minimo dell’energia complementare e dell’energia potenziale totale. Il problema delle reti caricate solo nei nodi è esposto come caso particolare.
Summary
The static analysis of elastic cable networks submitted to generic, conservative loads and prescribed dislocations is considered in this paper. The cables are assumed as stress-unilateral (only tensile stresses are admitted), and represented according to a Lagrangian standpoint, under the customary large displacements hypothesis. A variational formulation of the problem is given, as the stationary of a saddle functional with respect to displacements and (signconstrained) tractions. Uniqueness properties for the solution are derived from this statement, together with two complementary (constrained) minimum formulations, which correspond to the well-known extremum principles of the total potential energy and the complementary energy. The case of a network loaded only at the nodes is exposed as a specialization.
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Cannarozzi, M. Stationary and extremum variational formulations for the elastostatics of cable networks. Meccanica 20, 136–143 (1985). https://doi.org/10.1007/BF02337632
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DOI: https://doi.org/10.1007/BF02337632