End condition effect on initial buckling performance of thin plates resting on tensionless elastic or rigid foundations

It is well accepted that the non-contact buckling response of long rectangular plates subjected to compressive or shearing loadings is solely dependent on material and section properties, as well as boundary conditions along the two unloaded side edges. In addition, the boundary conditions at the loaded ends do not influence the critical load. The above rule was also applied to the analysis and design of plates in unilateral contact with elastic or rigid mediums although without any reasonable verification. The results contained in this paper reveal that the boundary condition at the loaded edges (end conditions) significantly affects the contact buckling performance. To investigate the end condition effect, a transfer function method is employed herein to study the initial buckling behaviour of thin plates with different boundary conditions resting on tensionless elastic or rigid foundations. For very long plates with both ends clamped, the buckling mode can be considered as a series of periodically repeating buckling waves and an infinite plate model with only one buckle wave being effective to predict the buckling behaviour. However, for long plates with simply supported loaded ends, local effects dominate the buckling mode and the buckling loads can be reduced by up to 18% compared to long plates with clamped loaded ends. Experimental tests and ABAQUS modelling also verify that the critical stresses for plates with simply supported loaded ends are lower than those for plates with clamped loaded ended plates.