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Bifurcation analysis of a circular arch under hydrostatic pressure

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Sommario

Nel presente lavoro si studia la biforcazione di un arco circolare soggetto a pressione idrostatica nel campo elastico facendo uso di un modello di trave cinematicamente esatto. Le corrispondenti equazioni di campo nonlineari vengono risolte utilizzando una tecnica perturbativa. Vengono riportati in diagramma una serie di risultati numerici riguardanti la dipendenza del carico critico e del parametro di carico del secondo ordine dai parametri geometrici e meccanici.

Summary

In this paper the bifurcation analysis of a circular arch under hydrostatic pressure in the elastic postbuckling range is performed by means of a geometrically exact beam model. The relevant nonlinear field equations are solved by utilizing a perturbation technique. A number of numerical results regarding the dependence of the critical load and the second order load parameter on the geometric and mechanical parameters are plotted in diagrams.

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References

  1. Eisley J.G., Nonlinear deformation of elastic beams, rings and strings, Appl. Mech. Rev., 16 (1963).

  2. Antman S.S., The theory of rods,Handbuch der Physik, VI a/2, C. Truesdell ed., Springer, Berlin (1972).

    Google Scholar 

  3. Budiansky B., Theory of buckling and postbuckling behaviour of elastic structures, inAdvances in Applied Mechanics, 14, Chia-Shun Yih Editor, Academic Press, New York (1974).

    Google Scholar 

  4. Sills L.B.,Budiansky B., Postbuckling ring analysis, J. Appl. Mech., vol. 45 (1978).

  5. El Naschie M.S.,El Nashai A., Influence of loading behaviour on the postbuckling of circular rings, AIAA J., vol. 14, No. 2 (1976).

  6. Rehfield L.W., Initial postbuckling of circular rings under pressure loads, AIAA J., vol. 10, No. 10 (1972).

  7. Pignataro M.,Di Carlo A.,Rizzi N., A discussion on ≪Accurate determination of asymptotic post-buckling stresses by the finite element method≫, by J.F. Olesen and E. Byskov, Computers & Structures, vol. 21, No. 5 (1985).

  8. Rizzi N.,Tatone A., Symbolic manipulation in buckling and postbuckling analysis, Computers & Structures, vol. 21, No. 4 (1985).

  9. Antman S.S.,Dunn J.E., Qualitative behaviour of buckled nonlinearly elastic arches, J. Elasticity, vol. 10, No. 3 (1980).

  10. Reissner E., On one-dimensional finite-strain: the plane problem, Z.A.M.P., vol. 23 (1972).

  11. Pignataro M.,Rizzi N.,Tatone A., Analisi critica e postcritica di travi ad asse curvilineo (in Italian), Atti del VI Congresso Nazionale AIMETA, Sezione V, 84–95, Genova (1982).

  12. Love A.E.H.,A Treatise on the Mathematical Theory of Elasticity, Dover Publications, New York (1944).

    Google Scholar 

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Tatone, A., Rizzi, N. & Pignataro, M. Bifurcation analysis of a circular arch under hydrostatic pressure. Meccanica 23, 113–118 (1988). https://doi.org/10.1007/BF01556710

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  • DOI: https://doi.org/10.1007/BF01556710

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