Elastic buckling of unilaterally constrained rectangular plates in pure shear

For a certain class of systems, the buckling response may be unilateral rather than bilateral. Unilateral buckling is a contact problem whereby buckling is confined to take place in only one direction. For plate structures, this can occur when a thin steel plate is juxtaposed with a rigid concrete medium, and the steel may only buckle locally away from the concrete core. Examples of this include composite profiled beams, walls and concrete-filled steel tubes, as well as reinforced concrete beams that are strengthened and stiffened by gluing and/or bolting steel plates to their sides. This paper presents a Rayleigh–Ritz method of the local buckling analysis of rectangular unilaterally restrained plates in pure shear. The displacement functions are modelled as polynomials, and the restraining medium as a tensionless foundation. The method presented is shown to be very efficient computationally, and elastic local buckling coefficients are presented for a variety of restraint cases for various plate aspect ratios. The use of these coefficients in determining limiting width to thickness ratios is demonstrated.