Abstract
The article presents the dynamic analysis of plane trusses with the imperfection in the length of elements. The establishment of the finite element method is formulated on the basis of a mixed model. To study plane trusses with element imperfection in length under dynamic loading, taking into account the geometrical nonlinearity, the establishment procedure of the calculation algorithm can be performed by assuming that the imperfection length is a parameter. The article proposes an approach based on mixed FEM formulation to solve the trusses with imperfection in the length of elements subjected to dynamic loads. The article establishes the dynamic equilibrium equation for the proposed mixed finite element formulation of trusses based on the compatibility equation considering the geometrical nonlinearity. The Newmark and iterative Newton-Raphson methods are applied in solving the nonlinear system of dynamic equations of trusses. The established incremental-iterative algorithm based on these methods is used to write a program for dynamic analysis with imperfections in element length in trusses. The obtained results verify the efficiency and accurateness of the mixed FEM formulation that proposed by authors in the dynamic analysis of trusses with imperfection in length.
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References
Wilson, E.L., Farhoomand, I., Bathe, K.J.: Nonlinear dynamic of complex structures. Earthq. Eng. Struct. Dyn. 1, 241–252 (1973)
Leung, A.Y.T., Yang, H.X., Zhu, P.: Nonlinear vibrations of viscoelastic plane truss under harmonic excitation. Int. J. Struct. Stab. Dyn. 4(14) (2014)
Le Guennec, Y., Savin, E., Clouteau, D.: A time-reversal process for beam trusses subjected to impulse load. In: Journal of Physics: Conference Series, vol. 464, no. 012001 (2013)
Chang, S.-Y.: Numerical characteristics of constant average acceleration method in solution of nonlinear systems. J. Chin. Inst. Eng. 4, 519–529 (2009)
Bathe, K.J.: Finite Element Procedures. Prentice Hall (2016)
Wagg, D., Neild, S.: Nonlinear Vibration with Control for Flexible and Adaptive Structures. Springer, Cham (2015)
Quyen, V.T.B., Tien, D.N., Huong, N.T.L.: Mixed finite element method for geometrically nonlinear buckling analysis of truss with member imperfection in length. In: IOP Conference Series: Materials Science and Engineering, vol. 960, p. 022075 (2020)
Belytschko, T., Liu, W.K., Moran, B., Elkhodary, K.I.: Nonlinear Finite Elements for Continuant Structures. Wiley, Chichester (2014)
Newmark, N.M.: A method of computation for structural dynamic. J. Eng. Mech. Div. ASCE 85, 67–94 (1959)
Khatir, A., et al.: A new hybrid PSO-YUKI for double cracks identification in CFRP cantilever beam. Compos. Struct. 311, 116803 (2023). https://doi.org/10.1016/j.compstruct.2023.116803
Khatir, A., Tehami, M.: Finite element analysis of local buckling of steel-concrete continuous composite beams. In: Proceeding of the 2015 Congress on Advanced in Structural Engineering and Mechanics (ASEM 2015) (2015). https://doi.org/10.13140/RG.2.1.2107.5606
Achouri, F., Khatir, A., Smahi, Z., et al.: Structural health monitoring of beam model based on swarm intelligence-based algorithms and neural networks employing FRF. J. Braz. Soc. Mech. Sci. Eng. 45, 621 (2023). https://doi.org/10.1007/s40430-023-04525-y
Khatir, A., Tehami, M., Khatir, S., Abdel Wahab, M.: Multiple damage detection and localization in beam-like and complex structures using co-ordinate modal assurance criterion combined with firefly and genetic algorithms. J. Vibroengineering 20(1), 832–842 (2018). https://doi.org/10.21595/jve.2016.19719. Republished Paper
Capozucca, R., Khatir, A., Magagnini, E.: Experiences on Anchorage systems for FRP rods. In: Capozucca, R., Khatir, S., Milani, G. (eds.) ICSCES 2022. LNCE, vol. 317, pp. 48–58. Springer, Cham (2023). https://doi.org/10.1007/978-3-031-24041-6_4
Crisfield, M.A.: A fast incremental/iterative solution procedure that handles snap-through. Comput. Struct. 13(1–3), 55-62A (1981)
Nguyen, P.C.: Nonlinear inelastic earthquake analysis of 2D steel frames. Eng. Technol. Appl. Sci. Res. 10(6), 6393–6398 (2020)
Zhou, Z., Wu, J., Meng, S.: Influence of member geometric imperfection on geometrically nonlinear buckling and seismic performance of suspen-dome structures. Int. J. Struct. Stab. Dyn. 14(03), 1350070 (2014). https://doi.org/10.1142/S0219455413500703
Gordini, M., Habibi, M.R., Tavana, M.H., Amiri, M., Roudsari, M.T.: Influence of member length imperfection on the capacity of spatial structures. Open Civ. Eng. J. 12, 481–494 (2018). https://doi.org/10.2174/1874149501812010481
Brezzi, F., Fortin, M.: Mixed and Hybrid Finite Element Method. Springer Series in Computational Mathematics, p. 352. Springer, Cham (1991). https://doi.org/10.1007/978-1-4612-3172-1
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Tien, D.N., Van, T.T.T. (2024). Applying Mixed FEM in Non-linear Dynamic Analysis of Plane Truss with Imperfection in Length. In: Benaissa, B., Capozucca, R., Khatir, S., Milani, G. (eds) Proceedings of the International Conference of Steel and Composite for Engineering Structures. ICSCES 2023. Lecture Notes in Civil Engineering, vol 486. Springer, Cham. https://doi.org/10.1007/978-3-031-57224-1_24
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DOI: https://doi.org/10.1007/978-3-031-57224-1_24
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