A harmonic one-dimensional element for non-linear thermo-mechanical analysis of axisymmetric structures under asymmetric loads: The case of hot strip rolling

This work presents a one-dimensional harmonic finite element for the transient elasto-plastic analysis of axisymmetric structures loaded by non-axisymmetric thermal and mechanical loads. The one-dimensional element exploits a semi-analytical approach, based on Fourier series decomposition of the applied loads. The initial stress method is used for the non-linear solution of elasto-plastic analysis. As a case study, the proposed one-dimensional harmonic element is applied for modelling a two-dimensional circle under thermal and mechanical loadings rotating over its surface, which is used as an approximation of a work roll in hot strip rolling. With the one-dimensional harmonic element, the cyclic thermo-mechanical behaviour of the work roll can be simulated by considering localized plasticity caused by thermo-mechanical loads representative of strip and back-up roll. Compared to two-dimensional models already used in the literature, the one-dimensional element allows a significant reduction in the computational time to be achieved; it follows that the whole transient thermo-mechanical response can be simulated, thus permitting a more complete evaluation of the stress–strain response that is necessary for fatigue life assessment.