Numeričke metode i njihova primena u dinamici konstrukcija

DOI: https://doi.org/10.5937/vojtehg71-42781
Ključne reči: numeričke metode, metoda centralnih diferencija, metoda linearnog ubrzanja, Njumarkova metoda, Vilsonova θ-metoda

Sažetak


Uvod/cilj: U radu su analizirane numeričke metode rešavanja diferencijalnih jednačina dinamičke ravnoteže u tehničkim problemima.

Metode: Predstavljene su numeričke metode: metoda centralnih diferencija, metoda linearnog ubrzanja, Njumarkova metoda i Vilsonova θ-metoda.  

Rezultati: Rešeni su različiti problemi koji se javljaju pri primeni numeričkih metoda u dinamici konstrukcija. 

Zaključak: Pokazano je da primena numeričkih metoda ima fundamentalan značaj u dinamici konstrukcija. 

Reference

Anahory Simoes, A., Ferraro, S.J., Marrero, J.C. & Martín de Diego, D. 2023. A nonholonomic Newmark method. Journal of Computational and Applied Mathematics, 421, art.number:114873. Available at: https://doi.org/10.1016/j.cam.2022.114873.  

Bamer, F., Shirafkan, N., Cao, X., Oueslati, A., Stoffel, G., Saxcé, M. & Markert, B. 2021. A Newmark space-time formulation in structural dynamics. Computational Mechanics, 67, pp.1331-1348. Available at: https://doi.org/10.1007/s00466-021-01989-4.

Bathe, K.-J. 2014. Finite Element Procedures, 2nd edition. New Jersey: Prentice-Hall. ISBN: 978-0-9790049-0-2. 

Clough, R.W. & Penzien, J. 2015. Dynamics of Structures, 2nd edition. Berkeley, CA, USA: Computers & Structures, Inc. ISBN: 978-0923907518.

Dhatt, G. & Touzot, G.1984. The Finite Element Method Displayed, 1st edition. Norwich: John Wiley & Sons. ISBN: 978-0471901105.  

Esen, I. 2017. A Modified FEM for Transverse and Lateral Vibration Analysis of Thin Beams Under a Mass Moving with a Variable Acceleration. Latin American Journal of Solids and Structures, 14(3), pp.485-511. Available at: https://doi.org/10.1590/1679-78253180.

Hassan, W.M. 2019. Numerical error assessment in nonlinear dynamic analysis of structures. HBRC Journal, 15(1), pp.1-31. Available at: https://doi.org/10.1080/16874048.2019.1619257. 

Hoffman, J.D. 2001. Numerical methods for Engineers and Scientists, 2nd edition. New York, NY, USA: Marcel Dekker. ISBN: 0-8247-0443-6.

Jin, X, Ma, Q. & Li, S. 2004. Comparison of four numerical methods for calculating seismic dynamic response of sdof system. In: 13th World Conference on Earthquake Engineering, Vancouver, B.C., Canada, Paper No. 2889, August 1-6 [online]. Available at: http://www.iitk.ac.in/nicee/wcee/article/13_2889.pdf [Accessed: 10 February 2023].

Karimi, Y., Rashahmadi, S. & Hasanzadeh, R. 2018. The Effects of Newmark Method Parameters on Errors in Dynamic Extended Finite Element Method Using Response Surface Method. International Journal of Engineering, 31(1), pp.50-57 [online]. Available at: https://www.ije.ir/article_73091.html [Accessed: 10 February 2023].

Liu, G., Lv, Z.R. & Chen, Y.M. 2018. Improving Wilson-θ and Newmark-β Methods for Quasi-Periodic Solutions of Nonlinear Dynamical Systems. Journal of Applied Mathematics and Physics, 6(8), pp.1625-1635. Available at: https://doi.org/10.4236/jamp.2018.68138.

Mohammadzadeh, S., Ghassemieh, M. & Park, Y. 2017. Structure-dependent improved Wilson-θ method with higher order of accuracy and controllable amplitude decay. Applied Mathematical Modelling, 52, pp.417-436. Available at:  https://doi.org/10.1016/j.apm.2017.07.058.    

Newmark, N.M. 1959. A Method of Computation for Structural Dynamics. Journal of the Engineering Mechanics Division, 85(3), pp.67-94. Available at: https://doi.org/10.1061/JMCEA3.0000098.   

Noh, G. & Bathe, K.J. 2019. For direct time integrations: A comparison of the Newmark and ρ∞-Bathe schemes. Computers & Structures, 225, art.number:106079, pp.1-12. Available at: https://doi.org/10.1016/j.compstruc.2019.05.015.     

Rao, S.S. 2001. Applied Numerical Methods for Engineers and Scientists, 1st edition. Hoboken, NJ, USA: Prentice Hall. ISBN: 978-0130894809.   

Subbaraj, K. & Dokainish, M.A. 1989. A survey of direct time integration methods in computational structural dynamics − Part II. Implicit methods. Computers & Structures, 32(6), pp.1387-1401. Available at: https://doi.org/10.1016/0045-7949(89)90315-5.  

Tapia Andrade, A. & Torres Berni, W. 2021. Evaluation of the dynamic properties of a 2D-frame (MDOF) in a shake table. Ingenius, 26, pp.49-62. Available at: https://doi.org/10.17163/ings.n26.2021.05.     

Vasiljevic, R. 2020. Transverse and longitudinal vibrations of a frame structure due to a moving trolley and the hoisted object using moving finite element. Journal of Theoretical and Applied Mechanics, 58(4), pp.825-839. Available at: https://doi.org/10.15632/jtam-pl/126755.        

Vasiljević, R., Gašić, M. & Savković, M. 2016. Parameters Influencing the Dynamic Behaviour of the Carrying Structure of a Type H Portal Crane. Strojniški Vestnik/Journal of Mechanical Engineering, 62(10), pp.591-602. Available at: https://doi.org/10.5545/sv-jme.2016.3553.          

Wilson, E.I. 2001. Three-Dimensional Static and Dynamic Analysis of Structures, 3rd edition. Berkeley, CA, USA: Computers and Structures Inc. ISBN: 978-0-923907-00-9. 

Wolfram, S. 2003. The Mathematica Book, 5th edition. Champaign, IL, USA: Wolfram Media. ISBN: 978-1–57955–022–3.  

Wu, J.-J. 2008. Transverse and longitudinal vibrations of a frame structure due to a moving trolley and the hoisted object using moving finite element. International Journal of Mechanical Sciences, 50(4), pp.613-625. Available at: https://doi.org/10.1016/j.ijmecsci.2008.02.001. 

 

Objavljeno
2023/03/27
Broj časopisa
Vol. 71 Br. 2 (2023): april-jun
Rubrika
Pregledni radovi

Sva prava zadržana (c) 2023 Rade R. Vasiljević

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