Higher-order asymptotics for edge-buckling of pre-stressed thin plates under in-plane bending

Singular perturbation techniques are used to investigate the linear eigenvalue problem that describes the partial wrinkling of a pre-stressed rectangular thin elastic plate under in-plane bending. The dependence of the critical load and the wavelength of the localised oscillatory pattern on the non-dimensional bending rigidity of the plate is captured with a higher-order boundary-layer analysis. Comparisons with direct numerical simulations of the original eigenproblem confirm the accuracy and versatility of the asymptotic technique explored in this work.