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La plaque rectangulaire fléchie d'épaisseur linéairement variable

  • Henry Favre
  • Bernhard Gilg
Articles Originaux

Summary

This paper deals with bending of simply supported rectangular plates of linearly varying thickness. The solution of the partial differential equation of the middle surface may be reduced to the integration of a system of simpler equations by development in a series. Any of these equations has a form similar to the equation of a rectangular plate of constant thickness. The solution may be found either by the method of multiple trigonometrical series (Navier) or, for symmetrically distributed load, by simple series (Maurice Lévy).

The case of hydrostatic pressure is discussed in detail. A numerical example, with graphical results, clearly shows the influence of variability of thickness on bending, on twisting and bending moments, and on normal and shearing forces.

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Bibliography

  1. 2).
    Citons entre autres:R. Gran Olsson,Die Biegung der rechteckigen Platte veränderlicher Dicke, Thèse de l'Ecole polytechnique de Berlin (1933);Biegung der Rechteckplatte bei linear veränderlicher Biegungssteifigkeit, Ing.-Arch.5, 363 (1934);Biegung der Rechteckplatte von exponentiell veränderlicher Dicke, Bauingenieur21, 230 (1940);Biegung der Rechteckplatte bei linear veränderlicher Steifigkeit und beliebiger Belastung, Bauingenieur22, 10 (1941).-E. Reissner,Remark on the Theory of Bending of Plates of Variable Thickness, J. Math. Phys.14, 43 (1937).Google Scholar

Copyright information

© Birkhäuser Verlag 1952

Authors and Affiliations

  • Henry Favre
    • 1
  • Bernhard Gilg
    • 1
  1. 1.Zurich

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