**4**, 2, pp. 307–324, 1956

### Wytrzymałość żebrowanej powłoki stożkowej obciążonej kołowo symetrycznie

**The strength of a conical shell with ribs subjected to an axially symmetrical load**

The case of an axially symmetrical loading of a conical shell reinforced with circumferential and longitudinal ribs (along the generators) is considered. The problem is solved assuming that the ribs are closely spaced so that the shell can be treated as orthotropic. General differential equations are derived and a method of determining asymptotic solutions of these equations is developed. In particular, when the ratio of the tensile rigidities in both principal directions is equal to that of the corresponding flexural rigidities, the solution is the same as in the case of a conical orthotropic shell of constant thickness. In the general case approximate relations are derived. These relations determine the internal forces in the shell and are analogous to those for isotropic conical shells of constant thickness.

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#### References

S. Timoshenko, Theory of Plates and Shells, New York 1940.

E. Steuermann, Zur Theorie der polarsymmetrischen Deformation der elastischen anisotropen Schalen, Zeitschr. Angew. Math. Mech., t. 5, 6 (1925).

A.E.H. Love, A Treatise on the Mathematical Theory of Elasticity, New York 1944.

G. Sansone, Equazioni differenziali nel campo reale, t. 2, Bolonia 1949.

J. Geekeler, Über die Festigkeit achsensymmetrischen Schalen, Beruin 1926.

W. F1ügge, Statik und Dynamik der Schalen, Berlin 1934.