Buckling of Unilaterally Constrained Infinite Plates

The problem of finding the buckling load of unilaterally constrained infinite plates is considered. The plates are modeled along the lines of classical plate theory employing Kirchhoff-Love hypotheses. The condition of contact at buckling, which renders the problem to be of the nonlinear eigenvalue type, is resolved by modeling the plate as having two distinct regions, a contacted and an uncontacted region. This results in a problem of the linear eigenvalue type. Simply supported and clamped-free boundary conditions on the unloaded edges are considered. An exact solution for the case of a simply supported plate resting on a rigid foundation is derived. Plates made up of isotropic as well as different orthotropic materials are examined. Due to the constraint on the deformation being one-sided, an increase in the buckling load of approximately 30% over the unconstrained situation is obtained. This study clearly shows that the neglect of unilateral constraints in a plate buckling problem can lead to inaccurate results, which in turn will lead to poor estimates, for example, in assessing the residual compressive stiffness of delaminated plates.