Postbuckling of bilaterally constrained rectangular thin plates

The post-buckling response of bilaterally constrained thin plates submitted to a height reduction is investigated by a joint experimental-theoretical-numerical study. A detailed determination of the shape of plates is compared to predictions based on modelling the plate as an Elastica and a phase portrait of the system is worked out. An integral relationship for unloaded plates is derived and checked experimentally. The variation of the length of flat contacts with compression is first identified from measurements and then introduced in a virtual work analysis so as to determine the plate reaction. The existence of asymmetric solutions is clarified and the robustness of the Elastica to friction is demonstrated. These results improve the predictions of the Euler model in the fully non-linear regime and validate its relevance beyond the ideal limits of frictionless rod or of frictionless infinite plate on which it is established. They should therefore be useful for addressing buckling in different, albeit close, configurations.