Rigid-Plastic Circular Plates on Elastic Foundation

A method for the solution of a rigid-ideally plastic circular plate resting on an elastic foundation has been developed. In case of axially symmetric loads, three distinctly different deformation modes are possible. For loads of low magnitude the plate penetrates the elastic half space as a rigid indenter. For higher load magnitudes, a plastic hinge develops at midspan and the plate deforms into a conical surface. For even higher values of external load, separation occurs at the plate half-space interface. Governing mixed boundary value problem is solved by reducing it to a system of dual integral equations. Simple closed-form formulas are derived for bending moments and deflections at each stage of deformation. It is rather remarkable that the results of this rigorous approach are just as simple as the results derived for various approximate models.