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

• Elastic buckling behavior of simply supported plates is studied.
• Effect of in-plane boundary conditions is considered.
• Eigenvalues and mode shapes are obtained using finite element software.
• Effect of size, shape, and eccentricity of cut-out is also studied.
• Results show the importance of considering different in-plane boundary conditions.

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.