Sommario
Si applica la teoria degli operatori potenziali negli spazi di Hilbert per formulare una definizione rigorosa di carico conservativo.
Ciò consente di dimostrare in modo corretto una ben nota condizione di conservatività usualmente introdotta con una argomentazione inesatta.
I risultati generali ottenuti sono applicati al caso particolare di carico-pressione.
L'analisi è condotta nel campo delle grandi deformazioni ottenendo una condizione generale, necessaria e sufficiente, affinchè il carico-pressione sia conservativo.
Summary
The theory of potential operators in Hilbert spaces is applied to a rigorous definition of conservative loading.
This approach allows correct proof of a well-known condition of conservativeness, usually introduced with a misleading argument. The special case of pressure loading is then examined as an application of the previous results. The analysis is performed in the large (finite deformations) getting a general condition for the conservativeness of pressure loading, not previously found to the author's knowledge.
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References
M. M. Vainberg,Variational methods for the study of nonlinear operators, Holden-Day, 1964.
V. V. Bolotin,Nonconservative problems of the theory of elastic stability, Pergamon Press, 1963.
C. E. Pearson,General theory of elastic stability, Quart. Appl. Math.14, 133, 1956.
I. S. Sokolnikoff,Tensor analysis, II Ed., Wiley, 1967.
D. C. Leigh,Nonlinear continuum mechanics, McGraw-Hill, 1968.
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Paper orally presented to the 14th Polish Solid Mechanics Conference Kroscienko, September 2.11.1971.
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Romano, G. Potential operators and conservative systems. Meccanica 7, 141–146 (1972). https://doi.org/10.1007/BF02128759
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DOI: https://doi.org/10.1007/BF02128759