Buckling of unilaterally constrained plates: Applications to the study of delaminations in layered structures

The results from a combined experimental and analytical investigation of the problem of buckling of unilaterally constrained, finite, rectangular, elastic plates is reported. The plates are modeled along the lines of classical plate theory employing the Kirchhoff-Love hypothesis. The presence of a unilateral constraint is accounted for through the use of a nonlinear elastic foundation model that exhibits a deformation sign dependent force-displacement relation. Using Galerkinʹs method, the resulting system of governing nonlinear equations are solved iteratively. Different boundary conditions are considered and the results for some boundary conditions are compared and shown to be in good agreement with ‘exact’ results reported earlier for infinite plates. The results from an experimental investigation has further revealed that the buckling mode of the plate may involve regions or points of contact with the substrate beneath the buckling plate. The shadow Moiré technique is used to show clearly that the mode shape is periodic and contains points and/or regions of contact. The results obtained from the theoretical investigation are found to bound the experimental values. It is clear that the stiffness of a post-buckled plate with unilateral constraints is highly influenced by whether the buckled portion involves points (or regions) of contact or not. Thus, in analytical model development, associated with addressing the problem of delamination buckling in layered plates, the possibility of the delaminated portion contacting the substrate beneath cannot be excluded. The present study has demonstrated the validity of using nonlinear foundation models in the buckling analysis of unilaterally constrained rectangular plates.