Buckling of a Circular Plate Resting Over an Elastic Foundation in Simple Shear Flow

The elastic instability of a circular plate adhering to an elastic foundation modeling the exposed surface of a biological cell resting on the cell interior is considered. Plate buckling occurs under the action of a uniform body force due to an overpassing simple shear flow distributed over the plate cross section. The problem is formulated in terms of the linear von Kármán plate bending equation incorporating the body force and the elastic foundation spring constant, subject to clamped boundary conditions around the rim. The coupling of the plate to the substrate delays the onset of the buckling instability and may have a strong effect on the shape of the bending eigenmodes. Contrary to the case of uniform compression, as the shear stress of the overpassing shear flow increases, the plate always first buckles in the left-to-right symmetric mode.