A Unified Dimensionless Parameter for Finite Element Mesh for Beams Resting on Elastic Foundation

Abstract

Discretising a structure into elements is a key step in finite element (FE) analysis. The discretised geometry used toformulate an FE model can greatly affect accuracy and validity. This paper presents a unified dimensionless parameterto generate a mesh of cubic FEs for the analysis of very long beams resting on an elastic foundation. A uniform beamresting on elastic foundation with various values of flexural stiffness and elastic supporting coefficients subject to staticload and moving load is used to illustrate the application of the proposed parameter. The numerical results show that(a) Even if the values of the flexural stiffness of the beam and elastic supporting coefficient of the elastic foundation aredifferent, the same proposed parameter “s” can ensure the same accuracy of the FE solution, but the accuracy maydiffer for use of the same element length; (b) The proposed dimensionless parameter “s” can indeed be used as aunified index to generate the mesh for a beam resting on elastic foundation, whereas the use of the same elementlength as a criterion may be misleading; (c) The errors between the FE and analytical solutions for the maximumvertical displacement, shear force and bending moment of the beam increase with the dimensionless parameter “s”;and (d) For the given allowable errors for the vertical displacement, shear force and bending moment of the beamunder static load and moving load, the corresponding values of the proposed parameter are provided to guide themesh generation.