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On the general solution of stress equation for the membrane theory of shells of revolution

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Sommario

Si presenta un nuovo metodo per risolvere l'equazione di Neményi-Truesdell, nella teoria delle membrane dei gusci sottili di rivoluzione. Si tratta di un'equazione differenziale lineare ordinaria del secondo ordine, della quale sono noti metodi risolutivi dovuti a Truesdell ed a Mitrinovitch. Il metodo proposto è basato sulla trasformazione dell'equazione data in un'equazione integrale lineare di Volterra e consente di esprimere l'integrale generale dell'equazione degli sforzi esclusivamente in termini della equazione del meridiano generatore del guscio.

Summary

A new method is presented to solve the equation of Neményi-Truesdell, in the membrane theory of thin shells of revolution. It is an ordinary linear differential equation of the second order, for which resolution methods of Truesdell and Mitrinovitch are known. The proposed method is based on the transformation of the given equation into a linear integral equation of Volterra type. This allows to write the general solution of stress equation only in terms of equation of the meridian generating the shell.

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References

  1. Neményi P., Truesdell C.,A stress function for the membrane theory of shells of revolution, Proc. Nat. Acad. Sci. U.S.A., 29, 1943, 159–162.

    Google Scholar 

  2. Neményi P.,Beiträge zur Berechnung der Shalen unter-unsymmetrischer und unstetiger Belastung, Bygningsst. Meddel., 8, 1936, 53–72.

    Google Scholar 

  3. Truesdell C.,The membrane theory of shells of revolution, Trans. Amer. Math. Soc., 58, 1945, 96–166.

    Google Scholar 

  4. Flügge W.,Stresses in shells, Berlin, 1966.

  5. Reissner H.,Spannungen in Kugelschalen (Kuppeln), Müller-Breslau Festschrift, Leipzig, 1912, 181–193.

    Google Scholar 

  6. Mitrinovitch D.S.,Mise en correspondance d'un problème non résolu de la théorie de l'Elasticté avec un problème résolu par Darboux et Drach, Comp. Rend. Ac. Sc. Paris, 231, 1950, 327–328.

    Google Scholar 

  7. Mitrinovitch D.S.,On an equation of Neményi and Truesdell, Jour. Wash. Acad. Sc.,41, 1951, 129.

    Google Scholar 

  8. Mitrinovitch D.S.,Sur un procédé d'integration d'une équation de Monge, Comp. Rend. Ac. Sc. Paris, 232, 1951, 1334–1336.

    Google Scholar 

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Authors and Affiliations

  1. Istituto di Matematica, Università di Genova, via L.B. Alberti 4, 16132, Genova

    Guido Ravera

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  1. Guido Ravera
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Ravera, G. On the general solution of stress equation for the membrane theory of shells of revolution. Meccanica 19, 242–245 (1984). https://doi.org/10.1007/BF01743738

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  • DOI: https://doi.org/10.1007/BF01743738

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