An Extended Separation-of-Variable Method for the Eigenbuckling of Open Thin Circular Cylindrical Shells

Thin-walled circular cylindrical shells are important components in diverse engineering fields. There have been extensive researches on the buckling of open circular cylindrical shells, but still few researches on analytical solutions for non-Levy boundary conditions (BCs). This work develops an extended separation-of-variable (eSOV) method for eigenbuckling analysis of open circular cylindrical shells with arbitrary homogenous BCs. In this eSOV method, buckling mode functions are the product of eigenfunctions of two coordinate directions, and critical buckling loads corresponding to two-direction eigenfunctions are independent of each other. By employing Rayleigh principle, two eighth-order characteristic differential equations are derived, and the two-direction eigenfunctions are expressed in terms of the eigenvalues of the corresponding characteristic differential equations, then closed-form mode functions and explicit equations for critical load are achieved. The results in this work are validated by numerical methods, and several interesting phenomena are found.