Simultaneous Influence of Imperfect Length and Load on the Dynamic Buckling of Plane Trusses under Step Loading
Received: 24 April 2024 | Revised: 14 May 2024 | Accepted: 17 May 2024 | Online: 27 May 2024
Corresponding author: Ta Duy Hien
Abstract
The influence of imperfections in element length and loading on the dynamic buckling of plane trusses is investigated in the present study. Finite element formulation and the Euler formula are employed to tackle the problem of large displacements. Equivalently, the Newmark integration method and the Newton–Raphson iteration algorithm are deployed to solve the nonlinear dynamic equilibrium equations. The dynamic applied load considered in this study is a step-imperfect load with an imperfection in the element length. The relationship between the load and maximum displacement is determined, and the simultaneous influence of the imperfect parameters on the dynamic limit load is discussed. The imperfect element length and loading significantly affect the dynamic limit load, demonstrating the need to consider both imperfections when studying the dynamic buckling of truss systems.
Keywords:
dynamic buckling, dynamic stability, dynamic limit load, dynamic response, length imperfection, loading imperfection, nonlinear analysisDownloads
References
D. T. Thuy, L. N. Ngoc, D. N. Tien, and H. V. Thanh, “An Analytical Solution for the Dynamics of a Functionally Graded Plate resting on Viscoelastic Foundation,” Engineering, Technology & Applied Science Research, vol. 13, no. 1, pp. 9926–9931, Feb. 2023. DOI: https://doi.org/10.48084/etasr.5420
T. T. Nguyen, “Influence of Material and Geometry Defects on Local Buckling Resistance of FRP Columns,” Transport and Communications Science Journal, vol. 74, no. 5, pp. 611–626, 2023.
P. C. Nguyen, B. Le-Van, and S. D. T. V. Thanh, “Nonlinear Inelastic Analysis of 2D Steel Frames : An Improvement of the Plastic Hinge Method,” Engineering, Technology & Applied Science Research, vol. 10, no. 4, pp. 5974–5978, Aug. 2020. DOI: https://doi.org/10.48084/etasr.3600
P. C. Nguyen, “Nonlinear Inelastic Earthquake Analysis of 2D Steel Frames,” Engineering, Technology & Applied Science Research, vol. 10, no. 6, pp. 6393–6398, Dec. 2020. DOI: https://doi.org/10.48084/etasr.3855
N. C. T. Thanh, “Analytical truss model for concrete beams reinforced with FRP bars,” Transport and Communications Science Journal, vol. 74, pp. 456–468, May 2023. DOI: https://doi.org/10.47869/tcsj.74.4.6
H. T. Duy, N. D. Diem, G. V. Tan, V. V. Hiep, and N. V. Thuan, “Stochastic Higher-order Finite Element Model for the Free Vibration of a Continuous Beam resting on Elastic Support with Uncertain Elastic Modulus,” Engineering, Technology & Applied Science Research, vol. 13, no. 1, pp. 9985–9990, Feb. 2023. DOI: https://doi.org/10.48084/etasr.5456
D. H. Duc, D. V. Thom, and P. M. Phuc, “Buckling Analysis of Variable Thickness Cracked Nanoplates Considering the Flexoelectric Effect,” Transport and Communications Science Journal, vol. 73, no. 5, pp. 470–485, 2022.
N. T. Dao and T. V. T. Thi, “Hybrid Finite Element Method in Nonlinear Dynamic Analysis of Trusses,” International Journal of Structural Stability and Dynamics, vol. 23, no. 20, Dec. 2023, Art. no. 2450195. DOI: https://doi.org/10.1142/S0219455424501955
J. P. Pascon, “Nonlinear analysis of hyperelastoplastic truss-like structures,” Archive of Applied Mechanics, vol. 86, no. 5, pp. 831–851, May 2016. DOI: https://doi.org/10.1007/s00419-015-1065-9
E. Murtha‐Smith, “Nonlinear Analysis of Space Trusses,” Journal of Structural Engineering, vol. 120, no. 9, pp. 2717–2736, Sep. 1994. DOI: https://doi.org/10.1061/(ASCE)0733-9445(1994)120:9(2717)
A. K. Noor, “Nonlinear Analysis of Space Trusses,” Journal of the Structural Division, vol. 100, no. 3, pp. 533–546, Mar. 1974. DOI: https://doi.org/10.1061/JSDEAG.0003737
M. Greco and C. E. R. Vicente, “Analytical solutions for geometrically nonlinear trusses,” Rem: Revista Escola de Minas, vol. 62, no. 2, pp. 205–214, Jun. 2009. DOI: https://doi.org/10.1590/S0370-44672009000200012
C. Cichon and L. Corradi, “Large displacement analysis of elastic-plastic trusses with unstable bars,” Engineering Structures, vol. 3, no. 4, pp. 210–218, Oct. 1981. DOI: https://doi.org/10.1016/0141-0296(81)90003-1
H.-T. Thai and S.-E. Kim, “Large deflection inelastic analysis of space trusses using generalized displacement control method,” Journal of Constructional Steel Research, vol. 65, no. 10, pp. 1987–1994, Oct. 2009. DOI: https://doi.org/10.1016/j.jcsr.2009.06.012
J. A. T. de Freitas and A. C. B. S. Ribeiro, “Large displacement elastoplastic analysis of space trusses,” Computers & Structures, vol. 44, no. 5, pp. 1007–1016, Aug. 1992. DOI: https://doi.org/10.1016/0045-7949(92)90323-R
S. S. Ligarò and P. S. Valvo, “Large displacement analysis of elastic pyramidal trusses,” International Journal of Solids and Structures, vol. 43, no. 16, pp. 4867–4887, Aug. 2006. DOI: https://doi.org/10.1016/j.ijsolstr.2005.06.100
A. El-Sheikh, “Approximate dynamic analysis of space trusses,” Engineering Structures, vol. 22, no. 1, pp. 26–38, Jan. 2000. DOI: https://doi.org/10.1016/S0141-0296(98)00075-3
D. R. Sherman, “Latticed Structures: State-of-the-Art Report,” Journal of the Structural Division, vol. 102, no. 11, pp. 2197–2230, Nov. 1976. DOI: https://doi.org/10.1061/JSDEAG.0004479
S. M. Holzer, W. S. White, A. E. Somers, and R. H. Plaut, “Stability of Lattice Structures Under Combined Loads,” Journal of the Engineering Mechanics Division, vol. 106, no. 2, pp. 289–305, Apr. 1980. DOI: https://doi.org/10.1061/JMCEA3.0002585
A. Y. T. Leung, H. X. Yang, and P. Zhu, “Nonlinear Vibrations of Viscoelastic Plane Truss Under Harmonic Excitation,” International Journal of Structural Stability and Dynamics, vol. 14, no. 04, May 2014, Art. no. 1450009. DOI: https://doi.org/10.1142/S0219455414500096
Y. L. Guennec, É. Savin, and D. Clouteau, “A time-reversal process for beam trusses subjected to impulse loads,” Journal of Physics: Conference Series, vol. 464, no. 1, Oct. 2013, Art. no. 012001. DOI: https://doi.org/10.1088/1742-6596/464/1/012001
A. Kassimali and E. Bidhendi, “Stability of trusses under dynamic loads,” Computers & Structures, vol. 29, no. 3, pp. 381–392, Jan. 1988. DOI: https://doi.org/10.1016/0045-7949(88)90391-4
K. Zhu, F. G. A. Al-Bermani, and S. Kitipornchai, “Nonlinear dynamic analysis of lattice structures,” Computers & Structures, vol. 52, no. 1, pp. 9–15, Jul. 1994. DOI: https://doi.org/10.1016/0045-7949(94)90250-X
C.-Y. Wang, R. Wang, C.-C. Chuang, and T.-R. Wu, “Nonlinear Dynamic Analysis of Reticulated Space Truss Structures,” Journal of Mechanics, vol. 22, pp. 199–212, Sep. 2006. DOI: https://doi.org/10.1017/S1727719100000848
G. Liu, G. Chen, and F. Cui, “Nonlinear dynamic analysis of ring truss antenna equivalent to the cylindrical shell with thermal excitation,” European Journal of Mechanics - A/Solids, vol. 85, Jan. 2021, Art. no. 104109. DOI: https://doi.org/10.1016/j.euromechsol.2020.104109
B. Budiansky and J. W. Hutchinson, “Dynamic buckling of imperfection-sensitive structures,” in Applied Mechanics, Berlin, Heidelberg, Germany: Springer, 1966, pp. 636–651. DOI: https://doi.org/10.1007/978-3-662-29364-5_85
K. Kondoh and S. N. Atluri, “Influence of local buckling on global instability: Simplified, large deformation, post-buckling analyses of plane trusses,” Computers & Structures, vol. 21, no. 4, pp. 613–627, Jan. 1985. DOI: https://doi.org/10.1016/0045-7949(85)90140-3
M. A. M. Torkamani and J.-H. Shieh, “Higher-order stiffness matrices in nonlinear finite element analysis of plane truss structures,” Engineering Structures, vol. 33, no. 12, pp. 3516–3526, Dec. 2011. DOI: https://doi.org/10.1016/j.engstruct.2011.07.015
A. K. Chopra, Dynamics of Structures: Theory and Applications to Earthquake Engineering, 2nd ed. Upper Saddle River, NJ, USA: Prentice Hall, 2000.
K.-J. Bathe, Finite Element Procedures, 2nd ed. Watertown, MA, USA: Klaus-Jürgen Bathe, 2014.
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