Open Access

ARTICLE

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

Ping Lou^{1, 2, ∗}, Xinlei Zhang¹, F. T. K. Au³, Zixian Zhang¹, Yi Huang¹

1 School of Civil Engineering, Central South University, Changsha, China.
2 Key Laboratory of Heavy Railway Engineering Structure of Education Ministry, Central South University, Changsha, China.
3 Department of Civil Engineering, University of Hong Kong, Hong Kong, China.

* Corresponding Author: Ping Lou. Email: .

Computer Modeling in Engineering & Sciences 2020, 122(3), 955-969. https://doi.org/10.32604/cmes.2020.08302

Received 13 August 2019; Accepted 13 December 2019; Issue published 01 March 2020

Abstract

Discretising a structure into elements is a key step in finite element (FE) analysis. The discretised geometry used to formulate an FE model can greatly affect accuracy and validity. This paper presents a unified dimensionless parameter to generate a mesh of cubic FEs for the analysis of very long beams resting on an elastic foundation. A uniform beam resting on elastic foundation with various values of flexural stiffness and elastic supporting coefficients subject to static load 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 are different, the same proposed parameter “s” can ensure the same accuracy of the FE solution, but the accuracy may differ for use of the same element length; (b) The proposed dimensionless parameter “s” can indeed be used as a unified index to generate the mesh for a beam resting on elastic foundation, whereas the use of the same element length as a criterion may be misleading; (c) The errors between the FE and analytical solutions for the maximum vertical 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 beam under static load and moving load, the corresponding values of the proposed parameter are provided to guide the mesh generation.

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Keywords

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