Buckling of Long Thin Plates under Residual Stresses with Application to Strip Rolling

We present a simplified numerical method which can be used to predict efficiently the response of long thin plates under effects of residual stresses induced by production process such as rolling or continuous annealing. The principle consists in assuming harmonic buckling mode along the sheet length, and we consider Koiter-Budiansky post-buckling theory to compute the stress-deflection curve. In this way, only the width of the sheet has to be discretized by 1D finite elements. The size and shape of the flatness defects can be predicted efficiently and for a large number of cases. Various types of residual stresses and loadings can be accounted for. In particular, we will see the influence of the global traction on the buckling and post-buckling behavior. The numerical results are compared with experimental data and full numerical computations