Application of Three Nodded Finite Element Beam Model to Beam on Elastic Foundation

Maurice Eyo Ephraim; ThankGod Ode; Nukah Dumale Promise

doi:doi:10.11648/j.ajce.20180602.13

| Peer-Reviewed

Application of Three Nodded Finite Element Beam Model to Beam on Elastic Foundation

Maurice Eyo Ephraim, ThankGod Ode, Nukah Dumale Promise

Published in American Journal of Civil Engineering (Volume 6, Issue 2)

Received: 12 March 2018 Accepted: 27 March 2018 Published: 3 May 2018

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

The convergence of numerical solution based on two nodded beam finite element require considerable number of iterations and time; and is also plagued with shear locking. To address these deficiencies a three nodded beam element is proposed in this study to simulate the behavior of beams on elastic foundation. The analytical formulation of the model and development of shape functions are achieved with assumption of Winkler hypothesis for beam on elastic foundation A Matlab programme was developed to determine the combined beam and foundation stiffness as well as the load vector. The proposed model reliably simulates the deformations and stress resultants of beam on elastic foundation under general loading conditions. The result showed faster convergence devoid of shear locking. The maximum deflection and bending moment differ from the classical solution by about 5 percent.

Published in	American Journal of Civil Engineering (Volume 6, Issue 2)
DOI	10.11648/j.ajce.20180602.13
Page(s)	68-77
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2018. Published by Science Publishing Group

Keywords

Elastic Foundation, Beam, Finite Element, Shear Locking, Winkler Model

References

[1]	Winkler, E. (1867). Die lehre von elasticitat und festigkeit. H. Dominic us, prague, 182-184.
[2]	Filonenko-Borodich, M. M. (1945). Avery simple model on elastic foundation capable of spreading the load. Sb. Tr. Mosk, Electro, Inst. Inzh Trans.
[3]	Paternak, P. L. (1954). A new method of analysis of elastic foundation by means of two foundation constant. Gos. Izd Lit. po Strait I Arkh,.
[4]	Hetenyi, M. (1946). Beam on elastic foundation: Theory with applications in the field of civil engineering. Michigan: University of Michigan press.
[5]	Bowles, J. E. (1974). Analysis and computer methods in foundation engineering. New York: McGraw Hill.
[6]	Kerr A. D., Elastic and Viscoelastic Foundation Models. J. of Appl. Mech., 31, 3, 491–498 (1964).
[7]	Vallabhan C. V. G., Das Y. C., Modified Vlasov Model for Beams on Elastic Foundations. J. of Geotechn. Engng., 117, 6, 956–966 (1991).
[8]	Suchart, L., Woraphot, P., Nattapong, D., Minho, K., & Wooyoung, J. (2013). Exact Stiffness for Beams on Kerr-type foundation: the virtual force approach. Journal of applied mathematics, Vol.
[9]	Zhan, Y. (2012). Modelling Beams on Elastic Foundation using Plate Element in Finite Element. Zhenjiang, Jiangsu: Jiangsu University of Science and Technology, China.
[10]	Roland, J. (2010). Solution Methods for Beam and Frames on elastic foundation using finite element method. International Scientific Conference, Ostrava Journal papers.
[11]	Harden, C. W., & Hutchinson, T. C. (2009). Beam on nonlinear Winkler foundation modelling of shallow rocking dominated footings. Earthquake Spectra Vol 25 No 2, 277-300.
[12]	Reddy, J. N. (1993). An Introduction to the Finite Element Method, 2nd Edition. New york: McGraw-Hill.
[13]	Falsone, G., & Settineri, D. (2011). An Euler-Bernuilli-like finite element method for Timoshenko beams. Mechanics Research Communication 30, 12-16.
[14]	Reddy, J. N. (1997). On locking free shear deformation beam elements. Computer Methods in Apllied Mechanics and Engineering 149, 113-132.
[15]	Prathap, G. (2005). Finite Element Analysis as Computation. india.
[16]	Eric Q, S. (2006). Shear locking and hourglassing in MSC Nastran, Abaqus and Ansys. MSC Software users meeting, 461-479.
[17]	Dobromir Dinev (2012). Analytical Solution of Beam on Elastic Foundation. Engineering Mechanics Vol 9 No 6, 381-392.
[18]	Daryl L, L. (2007). A First Course in the Finite Element Method Fourth Edition. Toronta, Ontario, Canada: Chris Carson.
[19]	Mukherjee, S., & Prathap, S. (2001). Analysis of Shear Locking in Timoshenko beam elements using the function space approach. Computation Numerical Methods in Engineering, 385-393.
[20]	Parvanova, S. (2011). Lectures notes: Structural analysis II,. Bulgaria: University of Architecture, Civil Engineering Geodesy, Sofia.

Cite This Article

Plain Text BibTeX RIS

APA Style

Maurice Eyo Ephraim, ThankGod Ode, Nukah Dumale Promise. (2018). Application of Three Nodded Finite Element Beam Model to Beam on Elastic Foundation. American Journal of Civil Engineering, 6(2), 68-77. https://doi.org/10.11648/j.ajce.20180602.13

Copy | Download

ACS Style

Maurice Eyo Ephraim; ThankGod Ode; Nukah Dumale Promise. Application of Three Nodded Finite Element Beam Model to Beam on Elastic Foundation. Am. J. Civ. Eng. 2018, 6(2), 68-77. doi: 10.11648/j.ajce.20180602.13

Copy | Download

AMA Style

Maurice Eyo Ephraim, ThankGod Ode, Nukah Dumale Promise. Application of Three Nodded Finite Element Beam Model to Beam on Elastic Foundation. Am J Civ Eng. 2018;6(2):68-77. doi: 10.11648/j.ajce.20180602.13

Copy | Download

@article{10.11648/j.ajce.20180602.13,
  author = {Maurice Eyo Ephraim and ThankGod Ode and Nukah Dumale Promise},
  title = {Application of Three Nodded Finite Element Beam Model to Beam on Elastic Foundation},
  journal = {American Journal of Civil Engineering},
  volume = {6},
  number = {2},
  pages = {68-77},
  doi = {10.11648/j.ajce.20180602.13},
  url = {https://doi.org/10.11648/j.ajce.20180602.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajce.20180602.13},
  abstract = {The convergence of numerical solution based on two nodded beam finite element require considerable number of iterations and time; and is also plagued with shear locking. To address these deficiencies a three nodded beam element is proposed in this study to simulate the behavior of beams on elastic foundation. The analytical formulation of the model and development of shape functions are achieved with assumption of Winkler hypothesis for beam on elastic foundation A Matlab programme was developed to determine the combined beam and foundation stiffness as well as the load vector. The proposed model reliably simulates the deformations and stress resultants of beam on elastic foundation under general loading conditions. The result showed faster convergence devoid of shear locking. The maximum deflection and bending moment differ from the classical solution by about 5 percent.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - Application of Three Nodded Finite Element Beam Model to Beam on Elastic Foundation
AU  - Maurice Eyo Ephraim
AU  - ThankGod Ode
AU  - Nukah Dumale Promise
Y1  - 2018/05/03
PY  - 2018
N1  - https://doi.org/10.11648/j.ajce.20180602.13
DO  - 10.11648/j.ajce.20180602.13
T2  - American Journal of Civil Engineering
JF  - American Journal of Civil Engineering
JO  - American Journal of Civil Engineering
SP  - 68
EP  - 77
PB  - Science Publishing Group
SN  - 2330-8737
UR  - https://doi.org/10.11648/j.ajce.20180602.13
AB  - The convergence of numerical solution based on two nodded beam finite element require considerable number of iterations and time; and is also plagued with shear locking. To address these deficiencies a three nodded beam element is proposed in this study to simulate the behavior of beams on elastic foundation. The analytical formulation of the model and development of shape functions are achieved with assumption of Winkler hypothesis for beam on elastic foundation A Matlab programme was developed to determine the combined beam and foundation stiffness as well as the load vector. The proposed model reliably simulates the deformations and stress resultants of beam on elastic foundation under general loading conditions. The result showed faster convergence devoid of shear locking. The maximum deflection and bending moment differ from the classical solution by about 5 percent.
VL  - 6
IS  - 2
ER  -

Copy | Download

Author Information

Maurice Eyo Ephraim

Department of Civil Engineering, Rivers State University, Nkpolu, Port Harcourt, Nigeria
ThankGod Ode

Department of Civil Engineering, Rivers State University, Nkpolu, Port Harcourt, Nigeria
Nukah Dumale Promise

Department of Civil Engineering, Rivers State University, Nkpolu, Port Harcourt, Nigeria

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Maurice Eyo Ephraim, ThankGod Ode, Nukah Dumale Promise. (2018). Application of Three Nodded Finite Element Beam Model to Beam on Elastic Foundation. American Journal of Civil Engineering, 6(2), 68-77. https://doi.org/10.11648/j.ajce.20180602.13

Copy | Download

ACS Style

Maurice Eyo Ephraim; ThankGod Ode; Nukah Dumale Promise. Application of Three Nodded Finite Element Beam Model to Beam on Elastic Foundation. Am. J. Civ. Eng. 2018, 6(2), 68-77. doi: 10.11648/j.ajce.20180602.13

Copy | Download

AMA Style

Maurice Eyo Ephraim, ThankGod Ode, Nukah Dumale Promise. Application of Three Nodded Finite Element Beam Model to Beam on Elastic Foundation. Am J Civ Eng. 2018;6(2):68-77. doi: 10.11648/j.ajce.20180602.13

Copy | Download

@article{10.11648/j.ajce.20180602.13,
  author = {Maurice Eyo Ephraim and ThankGod Ode and Nukah Dumale Promise},
  title = {Application of Three Nodded Finite Element Beam Model to Beam on Elastic Foundation},
  journal = {American Journal of Civil Engineering},
  volume = {6},
  number = {2},
  pages = {68-77},
  doi = {10.11648/j.ajce.20180602.13},
  url = {https://doi.org/10.11648/j.ajce.20180602.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajce.20180602.13},
  abstract = {The convergence of numerical solution based on two nodded beam finite element require considerable number of iterations and time; and is also plagued with shear locking. To address these deficiencies a three nodded beam element is proposed in this study to simulate the behavior of beams on elastic foundation. The analytical formulation of the model and development of shape functions are achieved with assumption of Winkler hypothesis for beam on elastic foundation A Matlab programme was developed to determine the combined beam and foundation stiffness as well as the load vector. The proposed model reliably simulates the deformations and stress resultants of beam on elastic foundation under general loading conditions. The result showed faster convergence devoid of shear locking. The maximum deflection and bending moment differ from the classical solution by about 5 percent.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - Application of Three Nodded Finite Element Beam Model to Beam on Elastic Foundation
AU  - Maurice Eyo Ephraim
AU  - ThankGod Ode
AU  - Nukah Dumale Promise
Y1  - 2018/05/03
PY  - 2018
N1  - https://doi.org/10.11648/j.ajce.20180602.13
DO  - 10.11648/j.ajce.20180602.13
T2  - American Journal of Civil Engineering
JF  - American Journal of Civil Engineering
JO  - American Journal of Civil Engineering
SP  - 68
EP  - 77
PB  - Science Publishing Group
SN  - 2330-8737
UR  - https://doi.org/10.11648/j.ajce.20180602.13
AB  - The convergence of numerical solution based on two nodded beam finite element require considerable number of iterations and time; and is also plagued with shear locking. To address these deficiencies a three nodded beam element is proposed in this study to simulate the behavior of beams on elastic foundation. The analytical formulation of the model and development of shape functions are achieved with assumption of Winkler hypothesis for beam on elastic foundation A Matlab programme was developed to determine the combined beam and foundation stiffness as well as the load vector. The proposed model reliably simulates the deformations and stress resultants of beam on elastic foundation under general loading conditions. The result showed faster convergence devoid of shear locking. The maximum deflection and bending moment differ from the classical solution by about 5 percent.
VL  - 6
IS  - 2
ER  -

Copy | Download