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: 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.
- 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
C. B. Biezeno, Über die Bestimmung der “Durchschlagkraft” einer schwachgekrümmten, kreisförmigen Platte, Z.A.M.M. 15, 10-22 (1935)
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)
- 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
- 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 63245
- 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
- Eric Reissner, Stresses and small displacements of shallow spherical shells. II, J. Math. Phys. Mass. Inst. Tech. 25 (1947), 279–300. MR 19028, DOI https://doi.org/10.1002/sapm1946251279
- 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
R. M. Simons, On the non-linear theory of thin spherical shells, Ph.D. thesis, M.I.T. Math. Dept., 1955
- Stephen P. Timoshenko, Theory of elastic stability, Engineering Societies Monographs, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1961. 2nd ed; In collaboration with James M. Gere. MR 0134026
S. Timoshenko, Theory of plates and shells, McGraw-Hill Book Co., Inc., New York, 1940
H. S. Tsien, A theory for the buckling of thin shells, J. Aeronaut. Sci. 9, (1940)
H. S. Tsien, Lower buckling load in the non-linear buckling theory for thin shells, Quart. Appl. Math. 5, 236 (1947)
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)
- Th. von Kármán and Hsue-Shen Tsien, The buckling of spherical shells by external pressure, J. Aeronaut. Sci. 7 (1939), 43–50. MR 3177
- 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 38225
R. R. Archer, On the post buckling behavior of thin spherical shells, Ph.D. thesis, M.I.T. Math. Dept., 1956
C. B. Biezeno, Über die Bestimmung der “Durchschlagkraft” einer schwachgekrümmten, kreisförmigen Platte, Z.A.M.M. 15, 10-22 (1935)
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)
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
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)
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)
E. Reissner, Stresses and small displacements of shallow spherical shells II, J. Math. and Phys. 25, 279-300 (1947)
E. Reissner, On axisymmetrical deformation of thin shells of revolution, Proc. Symp. on Appl. Math., Am. Math. Soc. 3, 27-52 (1950)
R. M. Simons, On the non-linear theory of thin spherical shells, Ph.D. thesis, M.I.T. Math. Dept., 1955
S. Timoshenko, Theory of elastic stability, McGraw-Hill Book Co., Inc., New York, 1936
S. Timoshenko, Theory of plates and shells, McGraw-Hill Book Co., Inc., New York, 1940
H. S. Tsien, A theory for the buckling of thin shells, J. Aeronaut. Sci. 9, (1940)
H. S. Tsien, Lower buckling load in the non-linear buckling theory for thin shells, Quart. Appl. Math. 5, 236 (1947)
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)
Th. von Karman and H. S. Tsien, The buckling of spherical shells by external pressure, J. Aeronaut. Sci. (2) 7, 43-50 (1939)
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)
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Article copyright:
© Copyright 1958
American Mathematical Society
