Effect of in-plane boundary conditions on elastic buckling behavior of solid and perforated plates

In this work, finite element method is used to obtain elastic buckling loads and mode shapes of plates. The effect of four different in-plane boundary conditions on the elastic buckling load of simply supported plates subjected to in-plane uni-axial compressive loading is studied. Elastic buckling behavior of plates with cut-outs (circular and square with curved corners) is also studied to illustrate the effect of the size, shape and the eccentricity of the cut-out on buckling loads. Results of the study show that the in-plane boundary conditions affect the elastic buckling behavior of the plate to a significant extent. Aspect ratio influences both the mode shape and the elastic buckling load for perforated plates, whereas its influence is generally limited to mode shape only in case of a solid plate. Restraints on the in-plane movements of plate's unloaded edges have different influence on the elastic buckling behavior of the plate when the position of cut-out is changed along the x-axis (loading direction) and along the y-axis (normal to loading direction) of the plate. Also, results show that a large cut-out in the vicinity of edges makes the plate unstable at a much lower load compared to the plate with no cut-out. It is envisioned that the results of this study may provide insight to predict buckling loads in practical scenarios.