Uncovering the finite difference model equivalent to Hencky bar-net model for axisymmetric bending of circular and annular plates

Abstract

• Energy preserving finite difference model (FDM) is discovered for axisymmetric bending of circular/annular plates. • Exact bending solutions for circular plate using Hencky bar-net model (HBM) or equivalent FDM are obtained for the first time. • Bending solutions for annular plates which may be tediously obtained from continuum theory are efficiently obtained via HBM. As there are a few finite difference models in the literature for axisymmetric bending of plates, only one of these models is equivalent to the Hencky bar-net model (HBM) that comprises a finite number of rigid circular arcs and straight radial segments joined by frictionless hinges with elastic rotational springs. This paper is concerned with uncovering the one finite difference model (FDM) that is equivalent to the HBM. Based on the energy formulation, the governing equation for HBM is derived and it will be used to identify the FDM that has the same discrete set of equations. By using this equivalency between the HBM and the identified FDM, the expressions of edge spring stiffnesses of HBM are derived for various boundary conditions. As illustrative examples, the HBM is used to solve the bending problems of circular plates under uniformly and linearly increasing distributed loads. The analytical solutions of HBM avoids the singularity problem faced in FDM at the plate center. This paper also presents some benchmark bending solutions for annular plates with and without an internal ring support for different boundary restraints by using the HBM.