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Reference25 articles.
1. Sections 2.1, 2.2. Additional examples may be found in many books on tanks and shell roofs. A nonlinear problem of large deformations has been treated by E. Bromberg, J. J. Stoker: Non-linear theory of curved elastic sheets, Qu. Appl. Math. 3 (1945), 246–265. The authors show that in the realm of large deflections a membrane shell can satisfy a boundary condition prescribing the radial deflection. The nonlinear effect is restricted to a boundary zone, while elsewhere the linear theory applies. The subject has been studied in more detail by P.M. Riplog: Large deformations of symmetrically loaded shell membranes of revolution, Diss. Stanford 1956.
2. Section 2.3. The shape of an axisymmetric water drop has been studied by C. Runge, H. König: Vorlesungen über numerisches Rechnen, Berlin 1924, p. 320.
3. The use of Bessel functions for starting the solution was suggested by E. E. Zajac when he studied at Stanford.Figs. 20 and 21 have been prepared from numerical material offered by C. Codegone: Serbatoi a involucro uniformamente teso, Ann. Lavori Pubbl. 79 (1941), 179–183.
4. Test results were reported by C. A. Bouman: Strength tests on a spheroid tank (in Dutch), Be Ingenieur 53, P (1938), 39–46.
5. Tanks subjected to uniform gas pressure have been studied by F. Tölke: Über Rotationsschalen gleicher Festigkeit für konstanten Innen- oder Außendruck, Z. angew. Math. Mech. 19 (1939), 338–343. Except for the sphere, these shells need additional bulkheads, which must be acted upon by an axial force different from the resultant of the gas pressure.
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