Communications - Scientific Letters of the University of Zilina 2023, 25(3):B228-B244 | DOI: 10.26552/com.C.2023.059

Shape Optimization of a Column Modelling the Bridge Span under a Specific Load - Numerical and Experimental Studies

Janusz Szmidla ORCID..., Anna Jurczyńska ORCID...*
Czestochowa University of Technology, Czestochowa, Poland

This work is dedicated to the problem of optimizing the shape of columns modelling bridge span subjected to the selected specific load case. Based on Hamilton's principle, motion equations and boundary conditions were defined. Taking into account the static criterion of loss of stability and the condition of constant volume of systems, the values of geometric parameters of the analyzed column were determined at which the maximum critical load value was obtained. The simulated annealing algorithm was used to find the maximum critical force being a function of many variables. Within the kinetic criterion of loss of stability, the range of changes in the natural frequency of optimized columns as a function of external load was determined. Based on the obtained results it was concluded that it is possible to control the dynamic properties while improving the stability of the system.

Keywords: bridge span, shape optimization, nonprismatic rod, free vibrations, stability
Grants and funding:

The authors received no financial support for the research, authorship and/or publication of this article.

Conflicts of interest:

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Received: March 1, 2023; Accepted: June 18, 2023; Prepublished online: July 10, 2023; Published: July 11, 2023  Show citation

ACS AIP APA ASA Harvard Chicago Chicago Notes IEEE ISO690 MLA NLM Turabian Vancouver
Szmidla, J., & Jurczyńska, A. (2023). Shape Optimization of a Column Modelling the Bridge Span under a Specific Load - Numerical and Experimental Studies. Communications - Scientific Letters of the University of Zilina, 25(3), B228-244. doi: 10.26552/com.C.2023.059
Share...
Download citation
  • BibTeX (.bib)
  • Bookends (.ris)
  • EasyBib (.ris)
  • EndNote (.enw)
  • EndNote 8 (.xml)
  • ISI WoS (.isi)
  • Medlars (.medlars)
  • Mendeley (.ris)
  • MODS (.xml)
  • Papers (.ris)
  • RefWorks (.txt)
  • RefManager (.ris)
  • RIS (.ris)
  • MS Word (.xml)
  • Zotero (.ris)
    • Open full article

    References

    1. UZNY, S., SOKOL, K. Critical load of a differently mounted columns determined according to the Bernoulli-Euler and Timoshenko theories. Machine Dynamics Research. 2015, 39(2), p. 5-14. ISSN 2080-9948.
    2. TOMSKI, L., UZNY, S. A hydraulic cylinder subjected to Euler's load in aspect of the stability and free vibrations taking into account discrete elastic elements. Archives of Civil and Mechanical Engineering [online]. 2011, XI (3), p. 769-785. ISSN 1644-9665. Available from: https://doi.org/10.1016/S1644-9665(12)60115-0 Go to original source...
    3. PRZYBYLSKI, J., SOKOL, K. Shape control of an eccentrically loaded column by means of a piezoceramic rod. Thin - Walled Structures [online]. 2011, 49(5), p. 652-659. ISSN 0263-8231, eISSN 1879-3223. Available from: https://doi.org/10.1016/j.tws.2010.09.014 Go to original source...
    4. SZMIDLA, J., JURCZYNSKA, A. Stability of geometrically nonlinear pre-stressed column loaded by a force directed towards the positive pole partially lying on winkler elastic foundation. In: International Conference on Numerical Analysis and Applied Mathematics 2014 ICNAAM-2014: proceedings. AIP. 2014. ISBN 978-0-7354-1287-3, ISSN 0094-243X.
    5. COLMENARES, D., ANDERSSON, A., KAROUMI, R. Closed-from solution for mode superposition analysis of continuous beams on flexible supports under moving harmonic loads. Journal of Sound and Vibration [online]. 2021, 520, 116587. ISSN 0022-460X, eISSN 1095-8568. Available from: https://doi.org/10.1016/j.jsv.2021.116587 Go to original source...
    6. APSEMETOV, M., MADANBEKOV, N., MUKTAROV, T. Determination of the own forms of vibration of the span of beam bridges on elastic supporting parts. E3S Web of Conferences [online]. 2021, 263, 02018. eISSN 2267-1242. Available from: https://doi.org/10.1051/e3sconf/202126302018 Go to original source...
    7. RUILAN, T., XINWEI, Y., ZHANG, Q., XIUYING, G. Vibration reduction in beam bridge under moving loads using nonlinear smooth and discontinuous oscillator. Advances in Mechanical Engineering [online]. 2020, 8(6), p. 1-12. ISSN 1687-8132, eISSN 1687-8140. Available from: https://doi.org/10.1177/168781401665256 Go to original source...
    8. WAGG, D., NEILD, S. Nonlinear vibration with control for flexible and adaptive structures. Chapt. 1: Introduction to nonlinear vibration and control, serial solid mechanics and its applications [online]. Vol. 218. Switzerland: Springer International Publishing, 2015. ISBN 978-90-481-2836-5, p. 1-35. Available from: https://doi.org/10.1007/978-90-481-2837-2 Go to original source...
    9. AKOUR, S. N. Parametric study of nonlinear beam vibration resting on linear elastic foundation. Journal of Mechanical Engineering and Automation [online]. 2012, 2(6), p. 114-134. ISSN 2163-2405, eISSN 2163-2413. Available from: https://doi.org/10.5923/j.jmea.20120206.02 Go to original source...
    10. GIZEJOWSKI, M. A., SZCZERBA, J., GAJEWSKI, M. D., STACHURA, Z. Buckling resistance assessment of steel I-section beam-columns not susceptible to LT-buckling. Archives of Civil and Mechanical Engineering [online]. 2017, 17, p. 205-221. ISSN 1644-9665. Available from: https://doi.org/10.1016/j.acme.2016.09.003 Go to original source...
    11. SZMIDLA, J., JURCZYNSKA, A. Local loss of a rectilinear form of a static equilibrium of geometrically nonlinear system with non-prismatic element under force directed towards the pole. Acta Physica Polonica A [online]. 2020, 138(2), p. 140-143. ISSN 1898-794X. Available from: https://doi.org/10.12693/APhysPolA.138.140 Go to original source...
    12. YAGHOOBI, H., TORABI, M. An analytical approach to large amplitude vibration and post-buckling of functionally graded beams rest on non-linear elastic foundation. Journal of Theoretical and Applied Mechanics. 2013, 51 (1), p. 39-52. ISSN 1429-2955.
    13. ELMAGUIRI, M. N., HATERBOUCH, M., BOUAYAD, A., OUSSOUADDI, O. Geometrically nonlinear free vibration of functionally graded beams. Journal of Materials and Environmental Science. 2015, 6(12), p. 3620-3633. ISSN 2028-2508.
    14. KUMAR, S., MITRA, A., ROY, H. Geometrically nonlinear free vibration analysis of axially functionally graded taper beams. An International Journal of Engineering Science and Technology [online]. 2015, 18(4), p. 579-593. eISSN 2215-0986. Available from: https://doi.org/10.1016/j.jestch.2015.04.003 Go to original source...
    15. SZMIDLA, J., WAWSZCZAK, A. Optimization of the shape of columns implementing selected cases of Euler load using a modified algorithm of simulated annealing a (in Polish). In: 13th Structural Dynamics Symposium DYNKON 2008: proceedings. Vol. 258, Mechanics series74. p. 333-344.
    16. NIKOLIC, A., SALINIC, S. Buckling analysis of non-prismatic columns: a rigid multibody approach. Engineering Structures [online]. 2017, 143, p. 511-521. ISSN 0141-0296, eISSN 1873-7323. Available from: https://doi.org/10.1016/j.engstruct.2017.04.033 Go to original source...
    17. SZMIDLA, J., JURCZYNSKA, A. The tapered column shape optimisation in a plane perpendicular to the buckling plane subjected to a load by the follower force directed to the positive pole. Machine Dynamics Research. 2015, 39(2), p. 33-44. ISSN 2080-9948.
    18. ZHOU, G., QIAN, C., CHEN, C. Research on the approximate calculation method of the fundamental frequency and its characteristics a tensioned string bridge. Processes [online]. 2022, 10, 126. eISSN 2227-9717. Available from: https://doi.org/10.3390/pr10010126 Go to original source...
    19. GARINEI, A. Vibrations of simple beam-like modelled bridge under harmonic moving loads. International Journal of Engineering Science [online]. 2006, 44(11-12), p. 778-787. ISSN 0020-7225, eISSN 1879-2197. Available from: https://doi.org/10.1016/j.ijengsci.2006.04.013 Go to original source...
    20. RASPOPOV, A., ARTYOMOV, V., RUSU, S. The simulation of vibrations of railway beam bridges in the object-oriented environment Delphi. The Archives of Transport [online]. 2010, XXII(4), p. 463-476. ISSN 0866-9546. Available from: https://doi.org/10.2478/v10174-010-0028-8 Go to original source...
    21. ZANGENEH, A., MUSEROS, P., PACOSTE, C., KAROUMI, R. Free vibration of viscoelastically supported beam bridges under moving loads: closed-form equation for maximum resonant response. Engineering Structures [online]. 2021, 244, 112759. ISSN 0141-0296, eISSN 1873-7323. Available from: https://doi.org/10.1016/j.engstruct.2021.112759 Go to original source...
    22. KOPIIKA, N., VEGERA, P., VASHKEVYCH, R., BLIKHARSKYY, Z. Stress-strain state of damaged reinforced concrete bended elements at operational load level. Production Engineering Archives [online]. eISSN 2353-7779. 2021, 27(4), p. 242-247. Go to original source...
    23. DOUNGPORN, W., NATHNARONG, K., YONG, H. W. Effect of beam joinery on bridge structural stability. Advances in Difference Equations [online]. 2019, 2019, 225. eISSN 2731-4235. Available from: https://doi.org/10.1186/s13662-019-2158-5 Go to original source...
    24. LI, Q. S. Exact solutions for buckling of non-uniform columns under axial concentrated and distributed loading. European Journal of Mechanics - A/Solids [online]. 2001, 20(3), p. 485-500. ISSN 0997-7538, eISSN 1873-7285. Available from: https://doi.org/10.1016/S0997-7538(01)01143-3 Go to original source...
    25. LI, Q. S. Stability of non-uniform columns under the combined action of concentrated follower forces and variably distributed loads. Journal of Constructional Steel Research [online]. 2008, 64(3), p. 367-376. ISSN 0143-974X, eISSN 1873-5983. Available from: https://doi.org/10.1016/j.jcsr.2007.07.006 Go to original source...
    26. SERNA, M. A., IBANEZ, J. R., LOPEZ, A. Elastic flexural buckling of non-uniform members: closed-form expression and equivalent load approach. Journal of Constructional Steel Research [online]. 2011, 67(7), p. 1078-1085. ISSN 1873-5983, eISSN 0143-974X. Available from: https://doi.org/10.1016/j.jcsr.2011.01.003 Go to original source...

    This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International License (CC BY 4.0), which permits use, distribution, and reproduction in any medium, provided the original publication is properly cited. No use, distribution or reproduction is permitted which does not comply with these terms.


    Return to the content