Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 

 

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
Full-text PDF Free Access

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.


References [Enhancements On Off] (What's this?)

  • [1] Robert Raymond Archer, ON THE POST BUCKLING BEHAVIOR OF THIN SPHERICAL SHELLS, ProQuest LLC, Ann Arbor, MI, 1956. Thesis (Ph.D.)–Massachusetts Institute of Technology. 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, Theodore von Kármán Anniversary Volume, California Institute of Technology, Pasadena, Calif., 1941, pp. 258–272. MR 0004599
  • [5] A. Kaplan and Y. C. Fung, A nonlinear theory of bending and buckling of thin elastic shallow spherical shells, NACA Tech. Note 1954 (1954), no. 3212, 58. MR 0063245
  • [6] H. M. Muštari and R. G. Surkin, On the nonlinear theory of the stability of elastic equilibrium of a thin spherical shell under the action of a uniformly distributed normal external pressure, Akad. Nauk SSSR. Prikl. Mat. Meh. 14 (1950), 573–586 (Russian). MR 0048285
  • [7] Eric Reissner, Stresses and small displacements of shallow spherical shells. II, J. Math. Phys. Mass. Inst. Tech. 25 (1947), 279–300. MR 0019028, https://doi.org/10.1002/sapm1946251279
  • [8] Eric Reissner, On axisymmetrical deformations of thin shells of revolution, Proc. Symposia Appl. Math. v. 3, McGraw-Hill Book Co., New York, N. Y., 1950, pp. 27–52. 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] Stephen P. Timoshenko, Theory of elastic stability, 2nd ed. In collaboration with James M. Gere. Engineering Societies Monographs, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1961. 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 Kármán and Hsue-Shen Tsien, The buckling of spherical shells by external pressure, J. Aeronaut. Sci. 7 (1939), 43–50. MR 0003177
  • [16] Yoshimura Yoshimura and Masuji Uemura, The buckling of spherical shells due to external pressure, Rep. Inst. Sci. Tech. Univ. Tokyo 3 (1949), 316–322 (Japanese, with English summary). MR 0038225

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 73.00

Retrieve articles in all journals with MSC: 73.00


Additional Information

DOI: https://doi.org/10.1090/qam/98515
Article copyright: © Copyright 1958 American Mathematical Society


Brown University The Quarterly of Applied Mathematics
is distributed by the American Mathematical Society
for Brown University
Online ISSN 1552-4485; Print ISSN 0033-569X
© 2017 Brown University
Comments: qam-query@ams.org
AMS Website