Limit and Shakedown Analysis of Circular Tube Containing External Pit

The circular tubes containing external pit defects are analyzed in a lower-bound finite element computational form based on the static shakedown theorem. The shakedown analysis has not been commonly used in the engineering due to the large amount of computations. To overcome the numerical difficulties, a temperature parameter method is used, in which a pseudo-temperature field is applied to the structure and the resulting self-equilibrium thermoelastic stress is treated as the residual stress field which is used in the analysis. The pseudo temperature is assumed as a harmonic function satisfying the uniqueness theorem, therefore the nodal temperature matrix of the whole structure can be expressed by the boundary nodal temperature matrix. The nonlinear yield condition is piece-wise linearized so that the shakedown analysis is transformed into a linear programming problem in which the strategic variable is boundary nodal temperature and objective variable is the loading multiplier. The relations of limit and shakedown pressures to geometric parameters of various defects are presented.