An analytical algorithm is proposed for studying the stability of a cylindrical shell subjected to nonuniform external pressure. The algorithm is based on a perturbation procedure and Padé approximants. Unlike the commonly used perturbation method, this approach is not limited by the smallness of the perturbation parameter. The approximate formulas obtained are sufficiently accurate and can be used in engineering practice.
MushtariKM. On the stability of a cylindrical shell under the action of non-uniform loads. Trudi Fiziko-tekhnic Inst Kazanskogo Filiala AN1954; 1: 77–103.
2.
HoffNJ. Buckling of thin cylindrical shell under hoop stresses varying in axial direction. J Appl Mech1957; 24: 405–412.
3.
WeingartenVI. The buckling of cylindrical shells under longitudinally varying loads. J Appl Mech1962; 29: 81–85.
4.
AlmrothBO. Buckling of a cylindrical shell subjected to nonuniform external pressure. J Appl Mech1962; 29: 675–682.
5.
BrushDOAlmrothBO. Buckling of bars, plates, and shells. New York: McGraw-Hill, 1975.
6.
KundurpiPSSamavedamGJohnsDJ. Stability of cantilever shells under wind loads. J Eng Mech Div1975; 101: 517–530.
7.
MaderspachVGauntGTSwordJH. Buckling of cylindrical shells due to wind loading. Stahlbau1973; 42: 269–277.
8.
GrigolyukEIKabanovVV. Stability of shells. Moscow: Nauka, 1978.
9.
MyachenkovVI. The stability of cylindrical shells under axisymmetric transverse pressure. Soviet Appl Mech1970; 6: 19–23.
10.
PogorelovAVBabenkoVI. Geometric methods in the theory of stability of thin shells (review). Soviet Appl Mech1992; 28: 1–17.
11.
AndreevLVObodanNILebedevAG. Shell stability under non-axisymmetric loading. Moscow: Nauka, 1988.
12.
ObodanNILebedevOGGromovVA. Nonlinear behaviour and stability of thin-walled shells. Berlin: Springer, 2013.
13.
KarmishinAVLyaskovetsVAMyachenkovVIet al. Statics and dynamics of thin-walled shell structures. Moscow: Mashinostroyenie, 1975.
14.
KabanovVVMikhailovVD. Stability of a cylindrical shell under nonuniform asymmetric loading. Soviet Appl Mech1980; 16: 661–664.
15.
KabanovVVKurtsevichTI. Stability of a cylindrical shell under nonaxisymmetric pressure. Soviet Appl Mech1977; 13: 15–19.
16.
KabanovVVZheleznovLP. Finite-element investigation of the nonlinear deformation and stability of cylindrical shells under nonaxisymmetrical pressure. Soviet Appl Mech1981; 17: 460–465.
17.
GusicGCombescureAJullienJF. The influence of circumferential thickness variations on the buckling of cylindrical shells under lateral pressure. Comput Struct2000; 74: 461–477.
18.
VolmirAS. Stability of elastic systems. Wright-Patterson Air Force Base, OH: Foreign Technology Division, Air Force Systems Command, 1967.
19.
AndrianovIVAwrejcewiczJManevitchLI. Asymptotical mechanics of thin-walled structures: a handbook. Berlin: Springer, 2004.
20.
BakerGAGraves-MorrisP. Padé approximants. Cambridge: Cambridge University Press, 1996.
21.
AlfutovNA. Stability of elastic structures. Berlin: Springer, 2000.
22.
Gol’denveizerAL. Theory of elastic thin shells. New York: Pergamon Press, 1961.
23.
NayfehAH. Perturbation methods. New York: John Wiley and Sons, 2000.
