Sommario
Caratteristiche peculiari della teoria sviluppata sono: discretizzazione della struttura in elementi finiti, linearizzazione a tratti delle leggi costitutive, suddivisione del problema in una preliminare soluzione elastica lineare ed in una fase nonlineare “correttiva”, utilizzazione di concetti e tecniche della teoria delle programmazioni quadratiche e lineari.
Si ottengono, per l'analisi di continui a deformabilità limitata soggetti a dati carichi e distorsioni, due teoremi di estremo corrispondenti a programmi quadratici negli “sforzi di bloccaggio”; per l'analisi limite al “bloccaggio” del sistema, due teoremi già noti, che qui si deducono dalle condizioni di solubilità dei precedenti programmi quadratici e si presentano in veste di programmi lineari duali. I risultati ottenuti vengono generalizzati ai casi definibili a deformabilità imperfettamente limitata. Alcuni esempi illustrano le tecniche risolutive che sorgono dalla teoria svolta.
Summary
The theory developed exhibits the following peculiar features: structures are discretizised in finite elements, the constitutive laws piecewise linearized, the problem is split in a preliminary linear elastic solution and a “corrective” nonlinear subproblem; concepts and techniques of quadratic and linear programming theory are utilized. The main results are: for the analysis under given loads and dislocations, a pair of extremum theorems for locking stresses, corresponding to dual quadratic programs; for the limit analysis with respect to locking situations two already known theorems, which are here deduced from the solvability conditions of the above quadratic programs and formulated as dual linear programs. The extension of the results to imperfectly locking behavior is carried out. Some examples illustrate the solution techniques based on the theory expounded.
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The study presented here forms part of a research program supported by the C.N.R.
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Dell'Acqua, L.C., Maier, G. A matrix theory of elastic-locking structures. Meccanica 4, 298–313 (1969). https://doi.org/10.1007/BF02133096
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DOI: https://doi.org/10.1007/BF02133096