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Energy Inequalities in an Elastic Cylinder

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Numerical Analysis of Partial Differential Equations

Part of the book series: C.I.M.E. Summer Schools ((CIME,volume 44))

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Abstract

More than a centrary ago, in 1855 and 1856, B.de Saint-Venant [l] stated a principle that has been applied steadily in the calculus of beams, but has not yet been proved. From the point of view of Numerical Analysis the importance of the Principle of Saint-Venant is obvious and great.

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References

  1. de Saint-Venant, B., Mémoires de l'Académie des Sciences des savants strangers, 14(1855) , 233–560 and Mémoire sur la flexion des prismes, Journal de Liouville, Ser. 2, (1856) , 89–189.

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  2. Toupin, R.A., Saint-Venant's principle, Arch. Rational Mech. Anal. 18(1965), 83–96

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  4. Dou, A., On the Principle of Saint-Venant, MRC Thecnical Summary Report # 472, May 1964.

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  5. Dou, A., Upper Estimate of the Potential Elastic Energy of a Cylinder, Comm. Pure Appl. Math. 19(1966), 83–93.

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  6. Bramble, J. H., and Payne, L. E., Pointwise bounds in the first biharmonic boundary value problem, J. Math. and Phys. 42 (1963), 278–286.

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  7. Dou, A., Bounded solutions of the Elasticity equations in the in the unbounded cylinder, Proceedings of the Inter. Congress of Math., Moscow, 1966. Abstracts of short communications.

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Authors and Affiliations

  1. University of Madrid, Madrid, Spain

    A. Dou

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  1. A. Dou
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Jacques Louis Lions (Coordinatore)

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Dou, A. (2010). Energy Inequalities in an Elastic Cylinder. In: Lions, J.L. (eds) Numerical Analysis of Partial Differential Equations. C.I.M.E. Summer Schools, vol 44. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11057-3_5

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