Buckling of vertical cylindrical shells under combined end pressure and body force

This paper is concerned with the elastic buckling of vertical cylindrical shells under combined end pressure and body force. Such buckling problems are encountered when cylindrical shells are used in a high-g environment such as the launching of rockets and missiles under high-propulsive power. The vertical shells may have any combination of free, simply supported, and clamped ends. Based on the Goldenveizer-Novozhilov thin shell theory, the total potential energy functional is presented and the buckling problem is solved using the Ritz method. Highlight in the formulation is the importance of the correct potential energy functional which includes the shell shortening due to the circumferential displacement. The omission of this contributing term leads to erroneous buckling solutions when the cylindrical shell is not of moderate length (length-to-radius ratio smaller than 0.7 or larger than 3). New solutions for body-force buckling parameters are presented for stubby cylindrical shells to long tube-like shells that approach the behavior of columns. The effects of the shell thickness and length on buckling parameter are also investigated.