Buckling of Plates with Stiffening Elastically Restrained Edges

Buckling of rectangular plates under uniaxial loading is considered. The plates are uniform and elastic, and the load is uniform. The unloaded edges are simply supported, whereas the loaded edges have no out‐of‐plane deflection and are elastically restrained against rotation. Based on observations reported in the literature, this rotational resistance may increase as the plate is compressed. To take this stiffening behavior into account, the rotational stiffness at the loaded edges is assumed to be a linear function of the load. The equilibrium equation is solved analytically, leading to two characteristic equations. One corresponds to buckling modes that are symmetric in the direction of loading, and the other to antisymmetric modes. Critical loads are computed and plotted as a function of the aspect ratio for various cases. Results for load‐dependent conditions are compared to those for loaded edges that are simply supported, clamped, or elastically restrained with load‐independent stiffness. It is found that the critical load of a rectangular plate may be increased significantly if the loaded edges stiffen as they are compressed.