Layout and cross-sectional size optimization of truss structures with mixed design variables based on gradient method

Authors

DOI:

https://doi.org/10.15587/1729-4061.2023.292692

Keywords:

shape optimization, mixed variables, gradient method, finite element method, sensitivity analysis

Abstract

The object of the study was truss-type rod structures, which were investigated for the purpose of finding the optimal design solution in a mixed (continuous and discrete) space of variables. The parameters of the geometric scheme of the truss, as well as the dimensions of the cross-sections of its elements, were considered as design variables. The stated optimization problem is represented as a nonlinear programming task, in which the objective function and nonlinear constraints of the mathematical model are continuously differentiable functions of the design variables. The system of constraints includes strength and stability inequalities, formulated for the design cross-sections of the rod elements of the structure, which is subject to the effect of the design load combinations of the ultimate limit states. As a part of the system of constraints, the displacement constraints formulated for the specified structural nodes, which is subject to the action of design load combinations of the serviceability limit states, are considered. To solve the stated optimization problem, a method of the objective function gradient on the surface of active constraints was used, with the simultaneous elimination of residuals in the violated restrictions. For design variables, the variation of which must be performed according to a given set of possible discrete values, a discretization procedure for the optimal solution obtained in the continuous space of design variables is proposed. A comparison of the proposed optimization methodology with alternative metaheuristic methods and algorithms reported in the literature was performed. On the considered problem of parametric optimization of a 47-span tower structure, a design solution with a weight of 835,403 kg was obtained, which is 1.53...4.6 % better than the optimal solutions obtained by other authors

Author Biographies

Ivan Peleshko, Lviv Polytechnical National University

PhD, Associate Professor

Department of Building Production

Vitalina Yurchenko, Kyiv National University of Construction and Architecture

Doctor of Technical Sciences, Professor

Department of Steel and Wooden Structures

Pavlo Rusyn, National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute"

Department of Dynamics and Strength of Machines and Strength of Materials

Education and Research Institute of Mechanical Engineering

References

  1. Jawad, F. K. J., Mahmood, M., Wang, D., AL-Azzawi, O., AL-JAMELY, A. (2021). Heuristic dragonfly algorithm for optimal design of truss structures with discrete variables. Structures, 29, 843–862. doi: https://doi.org/10.1016/j.istruc.2020.11.071
  2. Dede, T., Ayvaz, Y. (2015). Combined size and shape optimization of structures with a new meta-heuristic algorithm. Applied Soft Computing, 28, 250–258. doi: https://doi.org/10.1016/j.asoc.2014.12.007
  3. Yang, X. (2010). Engineering Optimization: An Introduction with Metaheuristic Applications. John Wiley & Sons, Inc. doi: https://doi.org/10.1002/9780470640425
  4. Ahrari, A., Atai, A. A., Deb, K. (2014). Simultaneous topology, shape and size optimization of truss structures by fully stressed design based on evolution strategy. Engineering Optimization, 47 (8), 1063–1084. doi: https://doi.org/10.1080/0305215x.2014.947972
  5. Kaveh, A., Kalatjari, V. (2004). Size/geometry optimization of trusses by the force method and genetic algorithm. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift Für Angewandte Mathematik Und Mechanik, 84 (5), 347–357. doi: https://doi.org/10.1002/zamm.200310106
  6. Degertekin, S. O., Lamberti, L., Ugur, I. B. (2018). Sizing, layout and topology design optimization of truss structures using the Jaya algorithm. Applied Soft Computing, 70, 903–928. doi: https://doi.org/10.1016/j.asoc.2017.10.001
  7. Gonçalves, M. S., Lopez, R. H., Miguel, L. F. F. (2015). Search group algorithm: A new metaheuristic method for the optimization of truss structures. Computers & Structures, 153, 165–184. doi: https://doi.org/10.1016/j.compstruc.2015.03.003
  8. Lamberti, L., Pappalettere, C. (2010). Metaheuristic Design Optimization of Skeletal Structures: A Review. Computational Technology Reviews, 4, 1–32. doi: https://doi.org/10.4203/ctr.4.1
  9. Gholizadeh, S. (2013). Layout optimization of truss structures by hybridizing cellular automata and particle swarm optimization. Computers & Structures, 125, 86–99. doi: https://doi.org/10.1016/j.compstruc.2013.04.024
  10. Xiao, A., Wang, B., Sun, C., Zhang, S., Yang, Z. (2014). Fitness Estimation Based Particle Swarm Optimization Algorithm for Layout Design of Truss Structures. Mathematical Problems in Engineering, 2014, 1–11. doi: https://doi.org/10.1155/2014/671872
  11. Sonmez, M. (2011). Artificial Bee Colony algorithm for optimization of truss structures. Applied Soft Computing, 11 (2), 2406–2418. doi: https://doi.org/10.1016/j.asoc.2010.09.003
  12. Rao, R. V., Patel, V. (2012). An improved teaching-learning-based optimization algorithm for solving unconstrained optimization problems. Scientia Iranica. doi: https://doi.org/10.1016/j.scient.2012.12.005
  13. Yurchenko, V., Peleshko, I. (2022). Optimization of cross-section dimensions of structural members made of cold-formed profiles using compromise search. Eastern-European Journal of Enterprise Technologies, 5 (7 (119)), 84–95. doi: https://doi.org/10.15587/1729-4061.2022.261037
  14. Yurchenko, V., Peleshko, I. (2021). Methodology for solving parametric optimization problems of steel structures. Magazine of Civil Engineering, 107 (7), 10705. doi: https://doi.org/10.34910/MCE.107.5
  15. Yurchenko, V. V., Peleshko, I. D., Biliaiev, N. (2021). Application of improved gradient projection method to parametric optimization of steel lattice portal frame. IOP Conference Series: Materials Science and Engineering, 1164 (1), 012090. doi: https://doi.org/10.1088/1757-899x/1164/1/012090
  16. Perelmuter, A., Kriksunov, E., Gavrilenko, I., Yurchenko, V. (2010). Designing bolted end-plate connections in compliance with Eurocode and Ukrainian codes: consistency and contradictions. 10th International Conference “Modern Building Materials, Structures and Techniques”. Available at: https://www.yumpu.com/en/document/view/5533140/designing-bolted-end-plate-connections-in-compliance-with
  17. Yurchenko, V., Peleshko, I. (2020). Improved gradient projection method for parametric optimisation of bar structures. Magazine of Civil Engineering, 98 (6), 9812. doi: https://doi.org/10.18720/MCE.98.12
  18. Peleshko, I. D., Yurchenko, V. V. (2021). Parametric Optimization of Metal Rod Structures Using the Modified Gradient Projection Method. International Applied Mechanics, 57 (4), 440–454. doi: https://doi.org/10.1007/s10778-021-01096-0
  19. Salajegheh, E., Vanderplaats, G. N. (1993). Optimum design of trusses with discrete sizing and shape variables. Structural Optimization, 6 (2), 79–85. doi: https://doi.org/10.1007/bf01743339
  20. Hasancebi, O., Erbatur, F. (2001). Layout optimization of trusses using improved GA methodologies. Acta Mechanica, 146 (1-2), 87–107. doi: https://doi.org/10.1007/bf01178797
  21. Hasancebi, O., Erbatur, F. (2002). On efficient use of simulated annealing in complex structural optimization problems. Acta Mechanica, 157 (1-4), 27–50. doi: https://doi.org/10.1007/bf01182153
  22. Kaveh, A., Zaerreza, A. (2020). Size/Layout Optimization of Truss Structures Using Shuffled Shepherd Optimization Method. Periodica Polytechnica Civil Engineering. doi: https://doi.org/10.3311/ppci.15726
  23. Tang, W., Tong, L., Gu, Y. (2005). Improved genetic algorithm for design optimization of truss structures with sizing, shape and topology variables. International Journal for Numerical Methods in Engineering, 62 (13), 1737–1762. doi: https://doi.org/10.1002/nme.1244
  24. Panagant, N., Bureerat, S. (2018). Truss topology, shape and sizing optimization by fully stressed design based on hybrid grey wolf optimization and adaptive differential evolution. Engineering Optimization, 50 (10), 1645–1661. doi: https://doi.org/10.1080/0305215x.2017.1417400
  25. Jawad, F. K. J., Ozturk, C., Dansheng, W., Mahmood, M., Al-Azzawi, O., Al-Jemely, A. (2021). Sizing and layout optimization of truss structures with artificial bee colony algorithm. Structures, 30, 546–559. doi: https://doi.org/10.1016/j.istruc.2021.01.016
Layout and cross-sectional size optimization of truss structures with mixed design variables based on gradient method

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Published

2023-12-21

How to Cite

Peleshko, I., Yurchenko, V., & Rusyn, P. (2023). Layout and cross-sectional size optimization of truss structures with mixed design variables based on gradient method. Eastern-European Journal of Enterprise Technologies, 6(7 (126), 6–18. https://doi.org/10.15587/1729-4061.2023.292692

Issue

Vol. 6 No. 7 (126) (2023): Applied mechanics

Section

Applied mechanics

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Copyright (c) 2023 Ivan Peleshko, Vitalina Yurchenko, Pavlo Rusyn

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