M.Sc Thesis

M.Sc StudentAlexander Schneiderman
SubjectElastoplastic Buckling of a Circular Cylindrical Shell under
Combined Loading of Axial Force and Hydrostatic
DepartmentDepartment of Aerospace Engineering
Supervisor Professor Emeritus Durban David
Full Thesis textFull thesis text - English Version


An investigation of plastic buckling of circular cylindrical shells subjected to combined axial compression/tension and internal/external pressure has been performed. A set of Donnell type differential equations, governing the onset of buckling, is solved by the separation of variables method. The coefficients of the buckling (eigenvalue) equations were determined by use of Ludwik’s model of plastic hardening, for both flow and deformation theories. Eigenmodes and eigenvalues (buckling loads) were determined over a range of loading combinations, shell geometry (thickness to radius ratio) and material properties. It was found that buckling loads predicted by deformation  theory are lower than those predicted by flow theory, for cylindrical shells of any practical geometry and loading program. An analytical expression for buckling loads combination with given geometry and material properties, for axisymmetrical buckling, was established. When the shell is subjected to axial compression and internal pressure buckling is axisymmetric. In contrast to the elastic buckling theory, where axial buckling load increases with increase of the internal pressure, in plastic range the internal pressure weakens the structure. For small values of external pressure, the buckling load increases, then for higher values of the external pressure drops drastically and the buckling becomes non axisymmetric. Those results facilitate the derivation of a semi analytical method for determination of buckling load combination at any geometry and material properties. Comparison of the calculated buckling loads with experimental results shows good correlation, given the assumptions taken in this investigation.