Elastic shakedown boundary determination of a cylindrical vessel–nozzle intersection subjected to steady internal pressures and cyclic out-of-plane bending moments

In the current research, a non-cyclic simplified technique is utilized to determine the elastic shakedown limit moments of a cylindrical vessel–nozzle intersection. The determined shakedown limit moments are utilized to generate the elastic shakedown boundary and the Bree diagram of the structure. The structure is subjected to a spectrum of steady internal pressure magnitudes and cyclic out-of-plane bending moments on the nozzle. The generated Bree diagram is compared with previously generated Bree diagram of the same structure, but subjected to in-plane bending. Noticeable differences regarding the magnitudes of the generated shakedown boundaries are observed. Moreover, only failure due to reversed plasticity response occurs upon exceeding the generated shakedown boundary unlike cyclic in-plane bending where the structure experienced both reversed plasticity and ratchetting failure responses. The simplified technique outcomes showed excellent correlation with the results of full elastic–plastic cyclic loading finite element simulations.