Elastic stability of near-perfect shallow spherical shells

Discussion: “Unsymmetric Buckling of Thin Shallow Spherical Shells” (Huang, Nai-Chien, 1964, ASME J. Appl. Mech., 31, pp. 447–457)

“…The membrane stress at buckling must be kept well below the yield stress of the material or the combined bending and membrane stress may invalidate the assumption of elastic behavior up to the initiation of buckling. The four shells tested in [2] for X > 8 ( Fig. 1) all violate the shallowness assumption, with segment angles up to 60 deg.…”

“…Briefly, the authors wish to conclude that the inclusion or exclusion of the second set of eigenvalues X" (2) = n (n = 0, 1, 2, . .…”

04.21: Buckling of externally pressurised spherical shells: Experimental results compared with recent design recommendations

“…The largest set of tests appears to have been those of Krenzke & Kiernan [12,13], published in 1963. A total of 73 clamped spherical aluminium dome models were tested with included angles ranging from 5 to 120 degrees.…”

On Asymmetric Buckling of Shallow Spherical Shells

“…The boundary conditions for G(p), H(p) are obtallled by subStltutlllg (18) into (11) or (14), collectmg terms of first order, and utilizing (21). In thiS way, one finds the followmg conditIOns for a clamped edge (23) and for a s~mply supported edge (24).…”

“…A comparIson of some recent expenmental results (Case C) ,vIth the present theoretical values is given III Fig 5 (see also Table 6). While the earher work [9,10] showed rather low expenmental buckhng loads Ph (approxImately .3 ~ Ph ~ .65), It IS mterestmg to note that in recent very carefully conducted expenments reported m [22,23,24] substantially higher values of Ph were obtained, most of WhICh fall between the two stabIlity curves Pc(J.L) for Cases C [22], [23], [24] and S. The results of [22] are III the range .60 ~ P b ~ .85 (omIttlllg a few peak values), those of [23] On the basis of the results of FIg 3, It IS hkely that the asymmetnc stabIhty curve (A) can be obtamed III a much simpler way. The malll dIfficulty IS the numencal solution of the aXIsymmetnc problem, 1 e., calculatIOn of the func-tIOns p and q entering Eqs.…”