Finite element analysis of linear plates buckling under in-plane patch loading

The elastic buckling load is physically important in design because it is actually the critical step in the changing plate configuration that will eventually lead to complete failure. The present work investigates the problem of linear buckling of simply supported thin plates subjected to patch compression. In order to satisfy the boundary conditions in a rigorous way, the authors chose the finite element method using the exact stress distribution throughout the plate.In the present paper, the stability problem treated using the total energy is briefly outlined. The plate modelling is made by means of an eight noded rectangular element and a reduction of variable strategy is applied to estimate the number of degrees of freedom leading to little or no loss in seeking solution accuracy.The buckling coefficient is determined for different load cases applied to a range of plate with various edge ratios. The achieved results are summarised through different graphs representing variation of the buckling coefficient against the plate ratio for each load case treated. A comparison with previous works is made. Finally, it is shown that the resolution of the plate buckling problem using true stress distribution with the finite element method leads to a good agreement with results previously obtained by means of analytical methods using an exact stress distribution.