Multi-harmonic balance method in structural element ratcheting problems

The ratcheting theory originated in the 1960s. In mechanics of deformable bodies, it is used to assess the strength of structural elements (gas turbines, high-temperature reactors, etc.) operating under intense cyclic thermal stresses. This study aims to investigate possible modes of elastic-plastic deformation in pressure vessels under cyclically varying temperature conditions, assuming an elastic-ideal plastic material behavior model. Due to material hardening, analytical methods are not sufficient to solve this problem, and numerical methods must be used. The number of calculation cycles significantly affects a process's result: a large number of these cycles can create modeling difficulties due to limited time and computational resources. Therefore, the Direct Cyclic Method (DCM) has become increasingly popular in engineering practice for solving this type of problems. This method is an application of the multi-harmonic balance technique to the problems of quasistatic cyclic loading of viscoelastic-plastic materials. The validity of the DCM method is evaluated by comparing it with the method of direct nonlinear analysis of loading history when assessing the adaptability of vessels under cyclic thermal stresses. The computational efficiency of the DCM was investigated for varying finite element mesh sizes and loading cycles. It is shown that the limitations of the DCM become apparent in cases where a stable periodic solution does not exist.