Buckling of elastic beams on non-local foundation: A revisiting of Reissner model

The buckling of an axially loaded elastic beam resting on linearly elastic non-local medium is analytically studied in this paper. We show that Reissner foundation model can be expressed in an integral format therefore inducing the non-local character of this elastic foundation model. The variational format of Reissner model is given, leading to meaningful natural and higher-order boundary conditions. Physical arguments are detailed for the mathematical identification of the non-local constitutive law associated to the reaction soil medium. Buckling solutions are obtained in case of simply supported elastically founded column, and the sensitivity of the solution to the choice of higher-order boundary conditions is specifically studied. The scale effects are highlighted for this non-local model.