Buckling analyses of cylindrical shells with axial variable elastic modulus under external pressure

This paper conducts the first analytical investigation on the effects of axial variable elastic modulus on the buckling of thin-walled cylinders under lateral pressure, which are caused by design considerations (shells with continuous or discrete design temperatures, different materials along the length), manufacturing process (non-uniform cooling speeds or forging ratios), material imperfections (continuous or discrete axial neutron radiation damage) and so on. Elastic modulus of the shell arbitrarily varies in the axial direction. The closed solutions for shell buckling analyses are derived by asymptotic analysis and Fourier series, which directly establish the relation between buckling pressure factor and elastic modulus function. Using the presented formulas, uniform, linear, stepwise and cosine elastic modulus variations are analyzed and discussed in detail. The comparative studies are also carried out and the results show that buckling pressure factors predicted by the analytical formulas are in good agreement with those by numerical methods. Especially, the maximum error between analytical formulas and FE method is 1.71%. The presented analytical formulas are also adequately validated and can be applied to evaluate buckling pressure of a laterally compressed cylinder with axial variable elastic modulus.