Stability limits for a clamped spherical shell segment under uniform pressure

Author:
Robert R. Archer

Journal:
Quart. Appl. Math. **15** (1958), 355-366

MSC:
Primary 73.00

DOI:
https://doi.org/10.1090/qam/98515

MathSciNet review:
98515

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Abstract | References | Similar Articles | Additional Information

Abstract: An integration procedure for the differential equations for the finite deflections of clamped shallow spherical shells under uniform pressure is developed. Stability limits for the clamped shell are obtained for a range of the central height to thickness ratio from about 1 to 35. This serves to correct and extend previously known stability limits for this problem.

**[1]**R. R. Archer,*On the post buckling behavior of thin spherical shells*, Ph.D. thesis, M.I.T. Math. Dept., 1956 MR**2938819****[2]**C. B. Biezeno,*Über die Bestimmung der ``Durchschlagkraft'' einer schwachgekrümmten, kreisförmigen Platte*, Z.A.M.M.**15**, 10-22 (1935)**[3]**V. I. Feodosev,*On the stability of a spherical shell under the action of an external uniform pressure*, (in Russian), Prikl. Mat. Mek. (1)**18**, 35-42 (1954)**[4]**K. O. Friedrichs,*On the minimum buckling load for spherical shells*, Theo. von Karman anniversary volume, California Institute of Technology, Pasadena, 1941, pp. 258-272 MR**0004599****[5]**A. Kaplan and Y. C. Fung,*A non-linear theory of bending and buckling of thin shallow spherical shells*, Natl. Advisory Comm. Aeronaut., Tech. Notes 3212, (1954) MR**0063245****[6]**H. M. Mushtari and R. G. Surkin,*On the non-linear stability theory of elastic equilibrium of a thin spherical shell under the influence of uniformly distributed normal external pressure*, (in Russian), Prikl. Mat. Mek. (6)**14**, 573-586 (1950) MR**0048285****[7]**E. Reissner,*Stresses and small displacements of shallow spherical shells II*, J. Math. and Phys.**25**, 279-300 (1947) MR**0019028****[8]**E. Reissner,*On axisymmetrical deformation of thin shells of revolution*, Proc. Symp. on Appl. Math., Am. Math. Soc.**3**, 27-52 (1950) MR**0039489****[9]**R. M. Simons,*On the non-linear theory of thin spherical shells*, Ph.D. thesis, M.I.T. Math. Dept., 1955**[10]**S. Timoshenko,*Theory of elastic stability*, McGraw-Hill Book Co., Inc., New York, 1936 MR**0134026****[11]**S. Timoshenko,*Theory of plates and shells*, McGraw-Hill Book Co., Inc., New York, 1940**[12]**H. S. Tsien,*A theory for the buckling of thin shells*, J. Aeronaut. Sci.**9**, (1940)**[13]**H. S. Tsien,*Lower buckling load in the non-linear buckling theory for thin shells*, Quart. Appl. Math.**5**, 236 (1947)**[14]**M. Uemura and Y. Yoshimura,*The buckling of spherical shells by external pressure II*, (in Japanese), Repts. Inst. Sci. and Technol., Tokyo (6)**6**, 367-371 (1950)**[15]**Th. von Karman and H. S. Tsien,*The buckling of spherical shells by external pressure*, J. Aeronaut. Sci. (2)**7**, 43-50 (1939) MR**0003177****[16]**Y. Yoshimura and M. Uemura,*The buckling of spherical shells due to external pressure I*, (in Japanese), Repts, Inst. Sci. and Technol., Tokyo**3**, 316-322 (1949) MR**0038225**

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Additional Information

DOI:
https://doi.org/10.1090/qam/98515

Article copyright:
© Copyright 1958
American Mathematical Society