Shakedown analysis of a torispherical head with a piping nozzle under combined loads by the stress compensation method

Shakedown assessment is an important task in determining the load-bearing capacity of structures and evaluating their safety. The traditional shakedown analyses, which are based on the upper or lower bound shakedown theorem to establish the mathematical programming formulation and solve an optimisation problem, are difficult to apply in engineering practice owing to limitations of the computing scale and computational efficiency. In this study, a numerical shakedown analysis using the recently developed stress compensation method (SCM) is performed for a torispherical head with a piping nozzle, which is a typical structural component of pressure vessel equipment. The loads applied to the structural component include an internal pressure, axial force, twisting moment, out-of-plane and in-plane bending moments, and thermal loading, all of which vary independently of each other. Two- and three-dimensional strict shakedown boundaries for the torispherical head under different combinations of these loads are presented and analysed. In addition, the effect of a temperature-dependent yield strength on the shakedown domain is also investigated. These investigations demonstrate that the proposed SCM is capable of solving the practical shakedown problem for structures under complicated combined loads in industrial applications. The obtained results can provide guidance for the safe structural design of torispherical heads with piping nozzles.