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A note on the linear theory of shallow shear-deformable shells

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Abstract

The solution of the tenth order problem of two-dimensionally homogeneous isotropic shallow shear-deformable elastic shells is expressed in terms of three functions, one of them solution of a second order equation and two of them solutions of two simultaneous fourth order equations, in such a way that known results for shear-deformable plates and for non-sheardeformable shells appear directly as special cases.

Zusammenfassung

Die Lösung des Problems der zwei-dimensional isotropischen flachen elastischen Schale wird ausgedrückt durch drei Funktionen. Zwei von diesen sind Lösungen von zwei simultanen Gleichungen der vierten Ordnung und die dritte ist Lösung einer Gleichung der zweiten Ordnung. Das neue in diesem Resultat, welches schon einmal in 1969 in einer etwas anderen Art und in einem allgemeineren Zusammenhang gegeben wurde, besteht darin, daß in der neuen Fassung bekannte Ergebnisse für schubverformbare Platten und für nichtschubverformbare Schalen unmittelbar als spezielle Fälle erhalten werden.

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References

  1. P. M. Naghdi,Note on the equations of shallow elastic shells. Quart. Appl. Math.14, 331–333 (1956).

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  3. E. Reissner,On the theory of transverse bending of elastic plates. Intern. J. Solids Structures12, 545–554 (1976).

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  4. S. Lukasiewiecz,Local loads in plates and shells. PWN-Polish Scientific Publishers (1979).

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Authors and Affiliations

  1. University of California San Diego, La Jolla, California

    E. Reissner

  2. University of British Columbia, Vancouver, Canada

    F. Y. M. Wan

Authors
  1. E. Reissner
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  2. F. Y. M. Wan
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Reissner, E., Wan, F.Y.M. A note on the linear theory of shallow shear-deformable shells. Z. angew. Math. Phys. 33, 425–427 (1982). https://doi.org/10.1007/BF00944452

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  • DOI: https://doi.org/10.1007/BF00944452

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