A method of stability analysis of cylindrical shells under biaxial compression

Abstract

The paper applies the method of generalized power series to the analysis of stability of circular cylindrical shells under combined radial pressure and axial force. The numbers of halfwavelengths appearing in original formulas are eliminated using the condition of minimum loading, and effective formulas are derived, expressing the critical loadings in terms of material constants and the geometry of the shell only. Hydrostatic pressure is analyzed as a particular case. Inversion of series makes it possible to obtain direct formulas for the necessary wall thickness if the loadings are given. Separation lines between moderate-length and long shells and between the ranges of elastic and inelastic buckling are discussed in detail. The proposed procedure may be applied to other types of loading as well. Nomenclature E = Young's modulus P = axial force (compressive), referred to unit length of the perimeter R = mean radius of the shell S = intensity of loading U = ra2, number of circumferenti al half-waveleng ths squared V = n2, number of axial half-wavelengths squared V = value of V corresponding to one axial half-wavelength h = thickness of the shell I = length of the shell m = number of circumferenti al half-waveleng ths at the length of half-perimete r n = number of axial half-wavelengths at the length of halfperimeter p = radial external pressure q = dimensionless intensity of loading a = parameter determining the contribution of individual loadings X = transversal slenderness of the shell, proportional to R/h v = Poisson's ratio ap = proportional limit of the material at uniaxial compression