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An exact derivation of the thin plate equation

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Abstract

It is shown that, when the traditional assumptions of thin plate theory are taken as exact methematical hypotheses, the desired field and boundary equations can be obtained by mere integration over the thickness of the corresponding equations for a three-dimensional cylindrical body made of a homogeneous, linearly elastictransversely isotropic, constrained material, yet avoiding some inconsistencies usually to be found in textbooks of structural mechanics.

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References

  1. F. Andreussi and P. Podio-Guidugli: Sull'immersione di corpi monodimensionali in un continuo vincolato.Atti Ist. Scienza d. Costruz. Univ. Pisa 12 (1971) 23.

    Google Scholar 

  2. A.-L. Cauchy: Sur l'équilibre et le mouvement d'une plaque solide.Exercises de mathématique 3 (1828).

  3. M.E. Gurtin: The linear theory of elasticity. In: C. Truesdell (ed.),Handbuch der Physik, Vol. VIa/2. Berlin: Springer (1972).

    Google Scholar 

  4. M.E. Gurtin.An Introduction to Continuum Mechanics. New York: Academic Press (1981).

    Google Scholar 

  5. M.E. Gurtin and P. Podio-Guidugli. The thermodynamics of internal constraints.Arch. Rational Mech. Anal. 51 (1973) 192.

    Google Scholar 

  6. G. Kirchhoff: Über das Gleichgewicht und die Bewegung einer elastichen Scheibe.J. reine angew. Math. 40 (1850) 51 (Ges. Abh., 237).

    Google Scholar 

  7. A.E.H. Love:A Treatise on the Mathematical Theory of Elasticity, 4th edn. Cambridge University Press (1927) (Dover Publications Edition, 1944).

    Google Scholar 

  8. V.V. Novozhilov:Foundations of the Nonlinear Theory of Elasticity. Rochester: Graylock (1953).

    Google Scholar 

  9. A.C. Pipkin: Constraints in linearly elastic materials.J. Elasticity 6 (1976) 179.

    Google Scholar 

  10. S. Marzano and P. Podio-Guidugli: Materiali elastici approssimativamente vincolati.Rend. Sem. Matem. Univ. Padova 73 (1985) 1.

    Google Scholar 

  11. P. Podio-Guidugli and M. Vianello: Constraint manifolds for isotropic solids.Arch. Rational Mech. Anal. 105 (1989) 105.

    Google Scholar 

  12. P. Podio-Guidugli and E.G. Virga: Transversely isotropic elasticity tensors.Proc. Royal Soc. London A 411 (1987) 85.

    Google Scholar 

  13. S.-D. Poisson: Mémoire sur l'équilibre et le mouvement des corps élastiques.Paris, Mém. de l'Acad. 8 (1829).

  14. S.P. Timoshenko and S. Woinowsky-Krieger:Theory of Plates and Shells. 23rd Printing, Int. Student Edn. McGraw-Hill Int. Book Co. (1982).

  15. K. Washizu:Variational Methods in Elasticity and Plasticity. Oxford: Pergamon Press (1968).

    Google Scholar 

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  1. Dipartimento di Ingegneria Civile Edile, Università di Roma 2, Via O.Raimondo, 00173, Roma, Italy

    P. Podio-Guidugli

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  1. P. Podio-Guidugli
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Podio-Guidugli, P. An exact derivation of the thin plate equation. J Elasticity 22, 121–133 (1989). https://doi.org/10.1007/BF00041107

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