Parametric optimization of bar structures with discrete and continuous design variables using improved gradient projection method
DOI:
https://doi.org/10.32347/2410-2547.2023.110.178-198Keywords:
shape optimization, bar structures, nonlinear programming, design code constraints, gradient projection method, optimization software, finite element methodAbstract
The paper considers a parametric optimization problem for the bar structures formulated as nonlinear programming task, where the purpose function and non-linear constraints of the mathematical model are continuously differentiable functions of the design variables. The method of the objective function gradient projection onto the active constraints surface with simultaneous correction of the constraints violations has been used to solve the parametric optimization problem. A discretization technique for the design variables that should vary discretely has been proposed. The discretization of the optimal design solution obtained in the continuous space of the design variables is performed by the purposefully selecting discrete points around the point of the continuous optimum. The comparison of the optimization results presented by the paper demonstrates that improved gradient method together with proposed discretization technique for the discrete design variables converges to better solutions of the problem comparing to the meta-heuristic algorithms.
References
Bilyk S.I., Yurchenko V. V. Size optimization of single edge folds for cold-formed structural members // Strength of Materials and Theory of Structures: Scientific-and-technical collected articles. – Kyiv: KNUBA, 2020. – Issue 105. – p. 73-86. doi: 10.32347/2410-2547.2020.105.73-86
Cheng W., Liu F., Li L. J. Size and geometry optimization of trusses using teaching learning-based optimization // International Journal of Optimization in Civil Engineering. – 2013. – Vol. 3(3). – p. 431–444.
Crowder N. P., Denbo R. S., Mulvey J. M. Reporting computational experiments in mathematical programming // Mathematical Programming. – Vol. 15, 1978. – p. 316–329.
Dede T., Ayvaz Y. Combined size and shape optimization of structures with a new meta-heuristic algorithm // Applied Soft Computing. – 2015. – Vol. 28. – p. 250–258. doi: 10.1016/j.asoc.2014.12.007.
Dede T. Jaya algorithm to solve single objective size optimization problem for steel grillage structures // Steel and Composite Structures. – 2018. – 26(2). p. 163–170. doi: 10.12989/scs.2018.26.2.163.
Degertekin S. O., Lamberti L., Ugur I. B. Sizing, layout and topology design optimization of truss structures using the Jaya algorithm // Applied Soft Computing. – 2018. – Vol. 70. – p. 903–928, 2018. doi: 10.1016/j.asoc.2017.10.001.
Farqad K. J. Jawad, Celal Ozturk, Wang Dansheng, Mohammed Mahmood, Osama Al-Azzawi, Anas Al-Jemely. Sizing and layout optimization of truss structures with artificial bee colony algorithm // Structures. – 2021. – Vol. 30. – p. 546-559. doi: 10.1016/j.istruc.2021.01.016
Gholizadeh S. Layout optimization of truss structures by hybridizing cellular automata and particle swarm optimization // Computers and Structures. – 2013. – Vol. 125. – p. 86-99. doi: 10.1016/j.compstruc.2013.04.024.
Grzywinski M., Dede T., Özdemir Y. I. Optimization of the braced dome structures iy using Jaya algorithm with frequency constraints // Steel and Composite Structures. – 2019. – Vol. 30(1). – p. 47–55. doi: 10.12989/scs.2019.30.1.047.
Grzywinski M, Selejdak J., Dede T. Shape and size optimization of trusses with dynamic constraints using a metaheuristic algorithm // Steel and Composite Structures. – 2019. – Vol. 33(5). – p. 747–753. doi: 10.12989/scs.2019.33.5.747.
Grzywiński M. Size and shape design optimization of truss structures using the jaya algorithm // Computer Assisted Method in Engineering and Science. – 2020. – Vol. 27(2–3). – p. 177–184. doi: 10.24423/cames.282
Hasanqehi O., Erbatur F. Layout optimization of trusses using improved GA methodologies // ACTA Mechanica. – 2001. – Vol. 146(1). – p. 87-107.
Haug E. J., Arora J. S. Applied optimal design: mechanical and structural systems. – John Wiley & Sons, 1979. – 520 p.
Kaveh A., Kalatjari V. Size/geometry optimization of trusses by the force method and genetic algorithm // Journal of Applied Mathematics and Mechanics. – 2004. – Vol. 84(5). – p. 347–357. doi: 10.1002/zamm.200310106.
Kaveh A., Bijari Sh. Simultaneous analysis and optimal design of truss structures via displacement method // Scientia Iranica. Transactions A: Civil Engineering. – 2020. – Vol. 27(3). – p. 1176 – 1186. doi: 10.24200/sci.2019.51563.2253
Li L. J., Liu F. Group search optimization for applications in structural design. – Springer Berlin Heidelberg, 1st ed., Heidelberg, German, 2011.
Peleshko I. D., Yurchenko V. V. Parametric Optimization of Metallic Rod Constructions with using the Modified Method of Gradient Projection // International Applied Mechanics. – 2021. – Vol. 57, No. 4. – P. 78–95. doi: 10.1007/S10778-021-01096-0
Peleshko I., Yurchenko V. Parametric optimization of steel structures based on gradient projection method // Strength of Materials and Theory of Structures: Scientific-and-technical collected articles. – Kyiv: KNUBA, 2020. – Issue 105. – P. 192-220. doi: 10.32347/2410-2547.2020.105.192-220
Peleshko I., Yurchenko V. An improved gradient-based method to solve parametric optimisation problems of the bar structures // Strength of Materials and Theory of Structures: Scientific-and-technical collected articles. – Kyiv: KNUBA, 2020. – Issue 104. – P. 265-288. doi: 10.32347/2410-2547.2020.104.265-288
Rajeev S., Krishnamoorhty C. S. Genetic algorithms based methodologies for design optimization of trusses // Structural Engineering. – 1997. – Vol. 123(3). – p. 350-358.
Rao R.V. Jaya: A simple and new optimization algorithm for solving constrained and unconstrained optimization problems // International Journal of Industrial Engineering Computations. – 2016. – Vol. 7(1). – p. 19–34. doi: 10.5267/j.ijiec.2015.8.004.
Yurchenko V., Peleshko I. Improved gradient projection method for parametric optimisation of bar structures // Magazine of Civil Engineering. 2020. 98(6). Article No. 9812. doi: 10.18720/MCE.98.12
Yurchenko V., Peleshko I. Parametric optimization of steel lattice portal frame with CHS structural members // Strength of Materials and Theory of Structures: Scientific-and-technical collected articles. – Kyiv: KNUBA, 2021. – Issue 107. – P. 45-74. DOI: 10.32347/2410-2547.2021.107.45-74
Wang D., Zhang W. H., Jiang J. S. Combined shape and sizing optimization of truss structures // Computational Mechanics. – 2002. – Vol. 29(4–5). – p. 307–312. doi: 10.1007/s00466-002-0343-x.
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