A Kerr-type elastic foundation model for the buckling analysis of a beam bonded on an elastic layer

A Kerr-type elastic foundation model is proposed to study the buckling of a beam bonded on the top of a linear elastic layer. The layer's lower-surface is either bonded or sliding on a rigid substrate. The present Kerr-type model provides a linear differential relation between the pressure and the normal deflection of the layer's upper-surface, and reduces to the existing foundation models when high-order differential relations are neglected. The critical buckling force is then obtained for both an infinitely long beam and a simply-supported beam of finite length, based on a simple formula which is valid for both a compressible and an incompressible layer. Reasonable agreement with the existing numerical results and our finite element results shows that the present model has the capability to capture the support effect of the elastic layer, and can be used to study the buckling or the bending of a beam bonded on an elastic layer.