Shakedown Analysis of Cylindrical Shells Containing Part-Through External Pit

Abstract

A lower-bound shakedown analysis for cylindrical shells containing defects is performed based on the static shakedown theorem in a finite element computational form. To overcome the numerical difficulties, the pseudo-temperature field is applied to a structure and the resulting thermo-elastic stress is considered as the self-equilibrium residual-stress field. 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.