×

Buckling of a complete spherical shell under uniform external pressure. (English) Zbl 0378.73042

MSC:

74G60 Bifurcation and buckling
74K15 Membranes
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35G20 Nonlinear higher-order PDEs
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Bauer, Axisymmetric buckling of hollow spheres and hemispheres, Comm. Pure Appl. Math. 23 pp 529– (1970) · Zbl 0194.26804 · doi:10.1002/cpa.3160230402
[2] Berke, Experimental studies of the postbuckling behavior of complete spherical shells, Experimental Mechanics 8 pp 548– (1968) · doi:10.1007/BF02327517
[3] Budiansky, Buckling of clamped spherical shells, Proc. IUTAM Symp. Theory of Thin Elastic Shells (Delft, 1959) pp 64– (1960) · Zbl 0118.41506
[4] Gabril’iants, Axially-symmetric forms of equilibrium of an elastic spherical shell under uniformly distributed pressure, Prikl Mat. Meh. 25 pp 1629– (1961)
[5] Hutchinson, Imperfection sensitivity of externally pressurized shells, Trans. ASME Ser. E. J. Appl. Mech. 34 pp 49– (1967) · Zbl 0159.27006 · doi:10.1115/1.3607667
[6] H. B. Keller Buckling of complete spherical shells under slightly nonuniform loads Nonlinear Elasticity R. W. Dickey Academic New York 1973
[7] Koiter, The nonlinear buckling problem of a complete spherical shell under uniform external pressure, Nederl. Akad. Wetensch. Proc. Ser. B. 72 pp 41– (1969) · Zbl 0197.22302
[8] Mescall, Numerical solutions of nonlinear equations for shells of revolution, AIAA J. 4 pp 2041– (1966) · Zbl 0152.43601 · doi:10.2514/3.3839
[9] Orszag, Numerical simulation of incompressible flows within simple boundaries, I. Galerkin (spectral) representations, Studies in Appl. Math. L pp 293– (1971) · Zbl 0237.76012 · doi:10.1002/sapm1971504293
[10] Polak, A globally converging secant method with applications to boundary value problems, SIAM J. Numer. Anal. 11 pp 529– (1974) · Zbl 0286.65028 · doi:10.1137/0711044
[11] Rauch, Contributions to Analysis (1974)
[12] Reissner, On axisymmetrical deformations of thin shells of revolution, Proc. Symp. Appl. Math. 3 pp 27– (1950) · Zbl 0041.53201 · doi:10.1090/psapm/003/0039489
[13] Thompson, The rotationally symmetric branching behavior of a complete spherical shell, Nederl. Akad. Wetensch. Proc. Ser. B 67 pp 295– (1964) · Zbl 0121.41804
[14] Von Karman, The buckling of spherical shells by external pressure, J. Aeronaut. Sci. 7 pp 43– (1939) · doi:10.2514/8.1019
[15] WHittaker, A Course of Modern Analysis, 4. ed. (1946)
[16] Jacobs, Dissertation (1976)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.