Revisiting the flattened Brazilian disc configuration - Part I: The actual boundary conditions

Abstract

In a recently presented analytic solution for the Flattened Brazilian Disc (FBD), it was shown that under the usually adopted assumption of uniform pressure on the flat edges of the FBD these edges turn to appear bent after deformation. Taking into account the high rigidity and flatness of the loading platens this bent sounds somehow unnatural. In the present study an attempt is undertaken to confront this unnatural bent by considering alternative non-uniform stress distributions on the flat edges of the FBD. In this context, the present paper, which is the first part of an ongoing research project, deals with the 1st fundamental problem for a FBD when it is compressed between two rigid flat stamps of the same length with the flat edge of the FBD. The distribution of the normal compressive stresses, and that of the respective frictional ones, imposed to the flat edge of the FBD are adopted from the approach of Muskhelishvili for the contact problem of a rigid flat stamp compressed against an elastic half plane, here the FBD in question. After obtaining the complex potentials for this 1st fundamental problem for the FBD, the stresses and the displacements are calculated in closed form everywhere on the FBD’s cross section. For the assessment of the analytic solution, a numerical model is also developed, with the aid of the Finite Element Method. The agreement between the theoretical and numerical analyses is satisfactory.