Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2013, Article ID 626287, 13 pages
http://dx.doi.org/10.1155/2013/626287
Research Article

Exact Stiffness for Beams on Kerr-Type Foundation: The Virtual Force Approach

1Department of Civil Engineering, Faculty of Engineering, Prince of Songkla University, Songkhla 90112, Thailand
2Civil Engineering Program, School of Engineering, University of Phayao, Phayao 5600, Thailand
3Department of Civil Engineering, ERI, Gyeongsang National University, Jinju 660-701, Republic of Korea
4Department of Civil Engineering, Gangneung-Wonju National University, Gangneung 210-720, Republic of Korea

Received 12 May 2013; Revised 17 July 2013; Accepted 6 August 2013

Academic Editor: Fayun Liang

Copyright © 2013 Suchart Limkatanyu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. D. Elata and S. Abu-Salih, “Analysis of electromechanical buckling of a prestressed microbeam that is bonded to an elastic foundation,” Journal of Mechanics of Materials and Structures, vol. 1, no. 5, pp. 911–923, 2006. View at Google Scholar
  2. E. Ghavanloo, F. Daneshmand, and M. Rafiei, “Vibration and instability analysis of carbon nanotubes conveying fluid and resting on a linear viscoelastic Winkler foundation,” Physica E, vol. 42, no. 9, pp. 2218–2224, 2010. View at Publisher · View at Google Scholar · View at Scopus
  3. M. M. Shokrieh and M. Heidari-Rarani, “A comparative study for beams on elastic foundation models to analysis of mode-l delamination in DCB specimens,” Structural Engineering and Mechanics, vol. 37, no. 2, pp. 149–162, 2011. View at Google Scholar · View at Scopus
  4. E. Winkler, Die Lehre Von Der Und Festigkeit, Dominicus, Prague, Czech Republic, 1867.
  5. K. Wieghardt, “Ü den balken auf nachgiebiger unterlage,” Zeitschrift für Angewandte Mathematik und Mechanik, vol. 2, pp. 165–184, 1922. View at Google Scholar
  6. A. D. Kerr, “Elastic and viscoelastic foundation models,” Journal Applied Mechanics Transaction, vol. 31, no. 4, pp. 491–498, 1964. View at Google Scholar
  7. M. M. Filonenko-Borodich, “Some approximate theories of elastic foundation,” Uchenyie Zapiski Moskovskogo Gosudarstvennogo Universiteta Mekhanica, vol. 46, pp. 3–18, 1940. View at Google Scholar
  8. S. N. Sokolov, Circular Plate on a Generalized Foundation, Inzhinierny Sbornik, Academy of Sciences, Moscow, Russia, 1952.
  9. P. L. Pasternak, On a New Method of Analysis of an Elastic Foundation by Means of Two Constants, Gosudarstvennoe Izdatelstvo Literaturi po Stroitelstvu I Arkhitekture, Moscow, Russia, 1954.
  10. M. Hetényi, “A general solution for the bending of beams on an elastic foundation of arbitrary continuity,” Journal of Applied Physics, vol. 21, no. 1, pp. 55–58, 1950. View at Publisher · View at Google Scholar · View at Scopus
  11. A. D. Kerr, “A study of a new foundation model,” Acta Mechanica, vol. 1, no. 2, pp. 135–147, 1965. View at Publisher · View at Google Scholar · View at Scopus
  12. A. Foppl, Vorlesungen Uber Technische Mechanik, B. B. Teubner, Leipzig, Germany, 1909.
  13. E. Reissner, “A note on deflection of plates on a viscoelastic foundation,” Journal Applied Mechanics, vol. 25, pp. 144–155, 1958. View at Google Scholar
  14. J. S. Horvath, A study of analytical methods for determining the response of mat foundations to static loads [Ph.D. thesis], Polytechnic Institute of New York, Brooklyn, NY, USA, 1979.
  15. J. J. Horvath, “New subgrade model applied to mat foundations,” Journal of Geotechnical Engineering, vol. 109, no. 12, pp. 1567–1587, 1983. View at Google Scholar · View at Scopus
  16. A. Worku, “Calibrated analytical formulas for foundation model parameters,” International Journal of Geomechanics, vol. 13, no. 4, pp. 340–347, 2013. View at Publisher · View at Google Scholar
  17. J. S. Horvath, “Discussion of modified Vlasov model for beams on elastic foundations,” Journal of Geotechnical Engineering, vol. 118, no. 9, pp. 1482–1484, 1992. View at Google Scholar
  18. J. S. Horvath and R. J. Colasanti, “Practical subgrade model for improved soil-structure interaction analysis: model development,” International Journal of Geomechanics, vol. 11, no. 1, pp. 59–64, 2010. View at Publisher · View at Google Scholar · View at Scopus
  19. I. E. Avramidis and K. Morfidis, “Bending of beams on three-parameter elastic foundation,” International Journal of Solids and Structures, vol. 43, no. 2, pp. 357–375, 2006. View at Publisher · View at Google Scholar · View at Scopus
  20. K. Morfidis, “Exact matrices for beams on three-parameter elastic foundation,” Computers and Structures, vol. 85, no. 15-16, pp. 1243–1256, 2007. View at Publisher · View at Google Scholar · View at Scopus
  21. K. Morfidis, “Vibration of Timoshenko beams on three-parameter elastic foundation,” Computers and Structures, vol. 88, no. 5-6, pp. 294–308, 2010. View at Publisher · View at Google Scholar · View at Scopus
  22. Y. Zhang, “Tensionless contact of a finite beam resting on Reissner foundation,” International Journal of Mechanical Sciences, vol. 50, no. 6, pp. 1035–1041, 2008. View at Publisher · View at Google Scholar · View at Scopus
  23. E. J. Sapountzakis and A. E. Kampitsis, “Nonlinear analysis of shear deformable beam-columns partially supported on tensionless three-parameter foundation,” Archive of Applied Mechanics, vol. 81, no. 12, pp. 1833–1851, 2011. View at Publisher · View at Google Scholar · View at Scopus
  24. J. Wang and S. Zeng, “Dynamics of piezoelectric smart beams using a three-parameter elastic foundation model,” Journal of Intelligent Material Systems and Structures, vol. 22, no. 1, pp. 3–16, 2011. View at Publisher · View at Google Scholar · View at Scopus
  25. R. J. Colasanti and J. S. Horvath, “Practical subgrade model for improved soil-structure interaction analysis: software implementation,” Practice Periodical on Structural Design and Construction, vol. 15, no. 4, pp. 278–286, 2010. View at Publisher · View at Google Scholar · View at Scopus
  26. J. S. Horvath and R. J. Colasanti, “New hybrid subgrade model for soil-structure interaction analysis: foundation and geosynthetics applications,” in Proceedings of the Geo-Frontiers: Advances in Geotechnical Engineering, pp. 4359–4368, Dallas, Tex, USA, March 2011. View at Publisher · View at Google Scholar · View at Scopus
  27. S. Limkatanyu and E. Spacone, “Frame element with lateral deformable supports: formulations and numerical validation,” Computers and Structures, vol. 84, no. 13-14, pp. 942–954, 2006. View at Publisher · View at Google Scholar · View at Scopus
  28. J. H. Argyris, Energy Theorems and Structural Analysis, Butterworths & Co., London, UK, 1960. View at MathSciNet
  29. S. Limkatanyu, K. Kuntiyawichai, E. Spacone, and M. Kwon, “Natural stiffness matrix for beams on Winkler foundation: exact force-based derivation,” Structural Engineering and Mechanics, vol. 42, no. 1, pp. 39–53, 2012. View at Google Scholar · View at Scopus
  30. S. Limkatanyu, N. Damrongwiriyanupap, M. Kwon, and P. Ponbunyanon, “Force-based derivation of exact stiffness matrix for beams on Winkler-Pasternak Foundation,” Zeitschrift Für Angewandte Mathematik Und Mechanik, 2013. View at Publisher · View at Google Scholar
  31. S. Wolfram, Mathematica Reference Guide, Addison-Wesley, Redwood City, Calif, USA, 1992.
  32. R. L. Taylor, “FEAP: a finite element analysis program. User manual: version 7.3,” Department of Civil and Environmental Engineering, University of California-Berkeley, 2000.
  33. R. D. Cook, VisualFEA and General User Manual, John Wiley and Son, New York, NY, USA, 2001.
  34. K. Morfidis, Research and development of methods for the modeling of foundation structural elements and soil [Ph.D. thesis], Department of Civil Engineering, Aristotle University of Thessaloniki, Greece, 2003.
  35. B. N. Alemdar and P. Gülkan, “Beams on generalized foundations: supplementary element matrices,” Engineering Structures, vol. 19, no. 11, pp. 910–920, 1997. View at Google Scholar · View at Scopus
  36. M. Eisenberger and J. Bielak, “Remarks on two papers dealing with the response of beams on two-parameter elastic foundations,” Earthquake Engineering and Structural Dynamics, vol. 18, no. 7, pp. 1077–1078, 1989. View at Google Scholar
  37. C. V. G. Vallabhan and Y. C. Das, “Modified vlasov model for beams on elastic foundations,” Journal of geotechnical engineering, vol. 117, no. 6, pp. 956–966, 1991. View at Google Scholar · View at Scopus