Shakedown analysis of thick-walled cylinders subjected to internal pressure with the unified strength criterion

Most previous studies on shakedown of thick-walled cylinders were based on the assumption that the compressive and tensile strengths of the materials were identical. In this paper the shakedown of an internally pressurized cylinder made of a material with a strength-difference and intermediate principal stress effects is dealt with by using a unified strength criterion which consists of a family of convex piecewise linear strength criteria. Through an elasto-plastic analysis the solutions for the loading stresses, residual stresses, elastic limit, plastic limit and shakedown limit of the cylinder are derived. It is shown that the present solutions include the classical plasticity solutions as special cases and have the ability to account for the strength-difference and intermediate principal stress effects. Finally, the influence of the two effects on the shakedown limit of the cylinder is investigated. The results show that the shakedown limit depends on the two effects and is underestimated if these effects are neglected as in the classical plasticity solution based on the Tresca criterion.