Remarks on elastic buckling for sectorial plates

This work investigates the edge-buckling experienced by a sectorial plate in a uniform bi-axial state of stress and subject to in-plane bending. Since the governing differential equations have variable coefficients, it turns out that the neutrally stable eigenfunctions can be qualitatively quite different as the mode number varies. Our interactive boundary-layer analysis succeeds in capturing the most dangerous mode associated with the global minimum of the marginal stability curve, while a complementary WKB route supplies an explanation for the morphological transitions experienced by the eigenmodes. The validity of our analysis is confirmed by direct numerical simulations of the full fourth-order buckling equation, which are in excellent agreement with the theoretical considerations.