Abstract
The paper focuses on the formulation and solving technique of trusses with multi-freedom constraints loaded mechanically and thermally considering geometrically nonlinearity utilizing FEM with mixed primary unknown variable choice. For analysis of truss with dependent boundary conditions under thermal load using displacement-based FEM considering large displacement, it is needed to incorporate the expansion due to temperature change varying with the element’s length and the boundary relations of constraints to the FE stiffness equation for constructing the modified system of equations. To skip the incorporation process of temperature variation, in this research, a novel mixed form of finite truss element with temperature variation considering geometric non-linearity is established according to the mixed-based formulation. Utilizing the novel established element, the global equilibrium equation is built for the truss system according to the minimum total potential energy principle. The incorporation of multi-freedom constraints is done by using the Lagrange multipliers method to convert the boundary constraints. The mathematical technique based on the arc-length method has been implemented to establish an algorithm for solving a system of FEM nonlinear equations. Utilizing the incremental-iterative solution procedure established by the arc-length technique, the Matlab calculation program has been written to examine the buckling response of truss systems having boundary constraints under the action of simultaneous mechanical and thermal load.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Ibrahimbegovic, A., Hajdo, E., Dolarevic, S.: Linear instability or buckling problems for mechanical and coupled thermomechanical extreme conditions. Coupled Syst. Mech. 2(4), 349–374 (2013)
Gebrail, B., Rasim, T., Yusuf, C.T.: Analyses of truss structures under thermal effects. Recent Adv. Civ. Eng. Mech. (2014)
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 (ASEM15) (2015). https://doi.org/10.13140/RG.2.1.2107.5606
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. Vibroeng. 20(1), 832–842 (2018). https://doi.org/10.21595/jve.2016.19719
Strodiot, J.J.: Numerical Methods in Optimization. Namur – Belgium (2002)
Sun, W., Yuan, Y.-X.: Optimization Theory and Methods - Nonlinear Programming. Springer, Cham (2006). https://doi.org/10.1007/b106451
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
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., Capozucca, R., Magagnini, E., Khatir, S., Bettucci, E.: Structural health monitoring for RC beam based on RBF neural network using experimental modal analysis. In: Capozucca, R., Khatir, S., Milani, G. (eds.) ICSCES 2022. LNCE, vol. 317, pp. 82–92. Springer, Cham (2023). https://doi.org/10.1007/978-3-031-24041-6_7
Quyen, V.T.B., Tien, D.N., Huong, N.T.L.: Mixed finite element method for geometrically nonlinear buckling analysis of truss with member length imperfection. In: IOP Conference Series: Materials Science and Engineering, vol. 960 (2020)
Quyen, V.T.B., Tien, D.N., Huong, N.T.L.: Geometrically nonlinear buckling analysis of truss under mechanical and thermal load based on mixed finite element formulation. In: IOP Conference Series: Materials Science and Engineering, vol. 962 (2020)
Quyen, V.T.B., Tien, D.N.: Nonlinear dynamic analysis of truss with initial member length imperfection subjected to impulsive load using mixed finite element method. In: Akimov, P., Vatin, N. (eds.) Proceedings of FORM 2021. LNCE, vol. 170, pp. 249–258. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-79983-0_23
Quyen, V.T.B., Tien, D.N., Huong, N.T.L.: Treatment of nonlinear multi freedom boundary constraints in finite element analysis of frame system using Lagrange multiplier method. In: IOP Conference Series: Materials Science and Engineering, vol. 960 (2020)
Bertsekas D. P.: Constrained Optimization and Lagrange Multiplier Method. Academic Press, Inc. (1982)
Riks, E.: An incremental approach to the solution of snapping and buckling problems. Int. J. Solids Struct. 15(7), 529–551 (1979)
Batoz, J.-L., Dhatt, G.: Incremental displacement algorithms for nonlinear problems. Int. J. Numer. Methods Eng. 14(8), 1262–1267 (1979)
Ritto-Correa, M., Camotim, D.: On the arc-length and other quadratic control methods: established, less known and new implementation procedures. Comput. Struct. 86(11–12), 1353–1368 (2008)
Crisfield, M.A.: A fast incremental/iterative solution procedure that handles snap-through. Comput. Struct. 13(1–3), 55–62 (1981)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Dao, N.T., Quyen Vu, T.B., Van Tran, T.T. (2024). Mixed FEM for Geometrically Nonlinear Analysis of Truss System with Multi-freedom Constraints Subjected to Mechanical and Thermal Load. 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_12
Download citation
DOI: https://doi.org/10.1007/978-3-031-57224-1_12
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-57223-4
Online ISBN: 978-3-031-57224-1
eBook Packages: EngineeringEngineering (R0)