The buckling problem of dished head under external pressure was analyzed by using finite elementmethod. It could be preliminarily inferred where the buckling appeared by observing distribution of stress in dished head. Also using Newton-Raphson and Arc-length method on the nonlinear buckling analysis so as to trace the typical structural characteristics when the buckling instability happening. Finally, introduces the stability safety factor which be used in the data processing of the finite element analysis result in order to obtain the permissive external pressure which can be applied in the project correctly. The analysis method and results have an important meaning for the design of dished head.

　　ANSYS provides two techniques for analyzing structural buckling loads and buckling modes: eigenvalue buckling analysis and nonlinear buckling analysis. The eigenvalue buckling analysis is a linear analysis. Because it does not consider any nonlinearity and initial disturbance, the prediction of the critical load of the structure by the eigenvalue buckling analysis is often higher than the actual critical load of the structure. In engineering, it is often expected to obtain the lower limit of critical load from safety considerations, so eigenvalue buckling analysis is generally not used in actual engineering structure analysis.

　　Non-linear buckling analysis is a non-linear static analysis technique that gradually increases the load. It can obtain the critical load that makes the structure unstable. Non-linear analysis can consider factors such as the initial defects of the structure, the nonlinearity of materials and the nonlinearity of the boundary, and its model and initial conditions are closer to the actual situation of the structure. In other words, the results of nonlinear buckling analysis are closer to the actual engineering results than eigenvalue buckling analysis.

　　Because eigenvalue buckling analysis is more time-saving than nonlinear buckling analysis, when buckling analysis, eigenvalue buckling analysis is usually performed first, and then the buckling load and mode are referred to, and the finite element model is applied during nonlinear buckling analysis Corresponding initial defects and loads, and finally determine the critical load of the structure.