@Article{cmes.2020.08302,
AUTHOR = {Ping Lou, Xinlei Zhang, F. T. K. Au, Zixian Zhang, Yi Huang},
TITLE = {A Unified Dimensionless Parameter for Finite Element Mesh for Beams Resting on Elastic Foundation},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {122},
YEAR = {2020},
NUMBER = {3},
PAGES = {955--969},
URL = {http://www.techscience.com/CMES/v122n3/38382},
ISSN = {1526-1506},
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 “<i>s</i>” 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 “<i>s</i>” 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 “<i>s</i>”; 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.},
DOI = {10.32604/cmes.2020.08302}
}