Engineering Transactions, 72, 2, pp. 159–202, 2024
10.24423/EngTrans.3223.2024

Advancing Computational Approaches for Geometry Optimization of Steel Structures

Artur LAX
Cracow University of Technology
Poland

Sławomir MILEWSKI
Cracow University of Technology
Poland

The primary objective of this study is to develop and assess computational methods for optimizing the geometry of specific building structures modeled through parametric description. The focus is on steel bar structures, including trusses and beams, subjected to varying load conditions with fixed and uncertain parameters. The decision variables in the single- or multicriteria non-linear optimization problem correspond to selected geometric features of these structures. The proposed methodology revolves around dividing the entire construction into distinct structural patterns. This allows for addressing separate local optimization problems with a reduced number of decision variables, followed by a global optimization considering
the interactions between these patterns. This approach is versatile, serving both the design of objects meeting required architectural and structural conditions and constraints, and the optimization of all or specific parameters, incorporating diverse economic (e.g., material usage) and engineering criteria (e.g., limit states).
Keywords: topological optimization; parametric description; deterministic methods; probabilistic methods; steel structures; finite element method
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References

Rozvany G.I.N., Aims, scope, methods, history and unified terminology of computer aided topology optimization in structural mechanics, Structural and Multidisciplinary Optimization, 21(2): 90–108, 2001, doi: 10.1007/s001580050174.

Rozvany G.I.N., A critical review of established methods of structural topology optimization, Structural and Multidisciplinary Optimization, 37(3): 217–237, 2009, doi: 10.1007/s00158-007-0217-0.

Sigmund O., Maute K., Topology optimization approaches, Structural and Multidisciplinary Optimization, 48(6): 1031–1055, 2013, doi: 10.1007/s00158-013-0978-6.

Dunning P.D., On the co-rotational method for geometrically nonlinear topology optimization, Structural and Multidisciplinary Optimization, 62(5): 2357–2374, 2020, doi: 10.1007/s00158-020-02605-4.

Wang W., Feng D., Yang L., Li S., Wang C. C., Topology optimization of self-supporting lattice structure, Additive Manufacturing, 67: 103507, 2023, doi: 10.1016/j.addma.2023.103507.

Wang B., Bai J., Lu S., Zuo W., Structural topology optimization considering geometrical and load nonlinearities, Computers and Structures, 289 107190, 2023, doi: 10.1016/j.compstruc.2023.107190.

Zhang L., Zhang Y., van Keulen F., Topology optimization of geometrically nonlinear structures using reduced-order modeling, Computer Methods in Applied Mechanics and Engineering, 416 116371, 2023, doi: 10.1016/j.cma.2023.116371.

Liu Y., Gao R., Li Y., Fang D., EMsFEM based concurrent topology optimization method for hierarchical structure with multiple substructures, Computer Methods in Applied Mechanics and Engineering, 418 116549, 2024, doi: 10.1016/j.cma.2023.116549.

Christensen C.F., Wang F., Sigmund O., Topology optimization of multiscale structures considering local and global buckling response, Computer Methods in Applied Mechanics and Engineering, 408: 115969, 2023, doi: 10.1016/j.cma.2023.115969.

Movahedi Rad M., Habashneh M., Lógó J., Reliability based bi-directional evolutionary topology optimization of geometric and material nonlinear analysis with imperfections, Computers and Structures, 287 107120, 2023, doi: 10.1016/j.compstruc.2023.107120.

Freitag S., Peters S., Edler P., Meschke G., Reliability-based optimization of structural topologies using artificial neural networks, Probabilistic Engineering Mechanics, 70: 103356, 2022, doi: 10.1016/j.probengmech.2022.103356.

Yu Y., Wei M., Yu J., Cui Y., Gao R., Dong Z., Wang X., Reliability-based design method for marine structures combining topology, shape, and size optimization, Ocean Engineering, 286: 115490, 2023, doi: 10.1016/j.oceaneng.2023.115490.

Tran Q. D., Shin D., Jang G.W., Bayesian optimization-based topology optimization using moving morphable bars for flexible structure design problems, Engineering Structures, 300: 117103, 2024, doi: 10.1016/j.engstruct.2023.117103.

Yan F., Lin Z., Wang X., Azarmi F., Sobolev K., Evaluation and prediction of bond strength of GFRP-bar reinforced concrete using artificial neural network optimized with genetic algorithm, Composite Structures, 161: 441–452, 2017, doi: 10.1016/j.compstruct.2016.11.068.

Sonmez M., Discrete optimum design of truss structures using artificial bee colony algorithm, Structural and Multidisciplinary Optimization, 43(1): 85–97, 2011, doi: 10.1007/s00158-010-0551-5.

Fredricson H., Topology optimization of frame structures – joint penalty and material selection, Structural and Multidisciplinary Optimization, 30(3): 193–200, 2005, doi: 10.1007/s00158-005-0515-3.

Cai J., Huang L., Wu H., Yin L., Topology optimization of truss structure under load uncertainty with gradient-free proportional topology optimization method, Structures, 58: 105377, 2023, doi: 10.1016/j.istruc.2023.105377.

Guo X., Cheng G. D., Olhoff N., Optimum design of truss topology under buckling constraints, Structural and Multidisciplinary Optimization, 30(3): 169–180, 2005, doi: 10.1007/s00158-004-0511-z.

Ben-Tal A., Bendsoe M.P., A new method for optimal truss topology design, SIAM Journal on Optimization, 3(2): 322–358, 1993, doi: 10.1137/0803015.

Awad R., Sizing optimization of truss structures using the political optimizer (PO) algorithm, Structures, 33: 4871–4894, 2021, doi: 10.1016/j.istruc.2021.07.027.

Stolpe M., Truss optimization with discrete design variables: a critical review, Structural and Multidisciplinary Optimization, 53(2): 349–374, 2016, doi: 10.1007/s00158-015-1333-x.

Achtziger W., Stolpe M., Truss topology optimization with discrete design variables— Guaranteed global optimality and benchmark examples, Structural and Multidisciplinary Optimization, 34(1): 1–20, 2007, doi: 10.1007/s00158-006-0074-2.

Dillen W., Lombaert G., Schevenels M., A hybrid gradient-based/metaheuristic method for Eurocode-compliant size, shape and topology optimization of steel structures, Engineering Structures, 239 112137, 2021, doi: 10.1016/j.engstruct.2021.112137.

Bojczuk D., Rębosz A., Topology optimisation of trusses using bars exchange method, Bulletin of the Polish Academy of Sciences, Technical Sciences, 2012, doi: 10.2478/v10175-012-0025-6.

Kalita K., Chohan J.S., Jangir P., Chakraborty S., A new decomposition-based multi-objective symbiotic organism search algorithm for solving truss optimization problems, Decision Analytics Journal, 10 100371, 2024, doi: 10.1016/j.dajour.2023.100371.

Kim I.Y., de Weck O.L., Adaptive weighted-sum method for bi-objective optimization: Pareto front generation, Structural and Multidisciplinary Optimization, 29(2): 149–158, 2005, doi: 10.1007/s00158-004-0465-1.

Xu B., Jin Y.J., Multiobjective dynamic topology optimization of truss with interval parameters based on interval possibility degree, Journal of Vibration and Control, 20(1): 66–81, 2014, doi: 10.1177/1077546312456725.

Cai J., Huang L., Wu H., Yin L., Topology optimization of truss structure under load uncertainty with gradient-free proportional topology optimization method, Structures, 58: 105377, 2023, doi: 10.1016/j.istruc.2023.105377.

Bazaraa S.M., Sherali D.H., Shetty C.M. Nonlinear Programming: Theory and Algorithms, John Wiley and Sons, 2005.

Hillermeier C., Nonlinear Multiobjective Optimization, Birkhäuser, Basel, 2001.

Marler R., Arora J., The weighted sum method for multi-objective optimization: New insights, Structural and Multidisciplinary Optimization, 41: 853–862, 2010, doi: 10.1007/s00158-009-0460-7.

Kleiber M., Parameter Sensitivity in Nonlinear Mechanics: Theory and Finite Element Computations, Wiley, 1997.

Bojczuk D., Rębosz-Kurdek A., Optimal design of bar structures with their supports in problems of stability and free vibrations, Journal of Theoretical and Applied Mechanics, 52(2): 533–546, 2014.

Bojczuk D., Mróz Z., On optimal design of supports in beam and frame structures, Structural optimization, 16(1): 47–57, 1998, doi: 10.1007/BF01213999.

Lin M. H., Tsai J.F., Yu C.S., A Review of deterministic optimization methods in engineering and management, Mathematical Problems in Engineering, 2012: 2012, doi: 10.1155/2012/756023.

Liszka T., Orkisz J., The finite difference method at arbitrary irregular grids and its application in applied mechanics, Computers and Structures, 11(1): 83–95, 1980, doi: 10.1016/0045-7949(80)90149-2.

Shi Z.-J., Shen J., Step-size estimation for unconstrained optimization methods, Clinics, 24: 2005, doi: 10.1590/S1807-03022005000300005.

Holland J.H., Adaptation in Natural and Artificial Systems. Cambridge, MA, USA: MIT Press, 1992.

Burczyński T., Orantek P., Evolutionary and hybrid algorithms, [in:] Gajewski R.R. (Ed.), Neural Networks, Genetic Algorithms, Fuzzy Sets [in Polish], pp. 99–117, Rzeszów: BEL, 1999.

Kok S., Sandrock C., Locating and characterizing the stationary points of the extended rosenbrock function, Evolutionary computation, 17: 437–53, 2009, doi: 10.1162/evco.2009.17.3.437.

Okasha N., Frangopol D., Lifetime-oriented multi-objective optimization of structural maintenance considering system reliability, redundancy and life-cycle cost using GA, Structural Safety – STRUCT SAF, 31: 460–474, 2009, doi: 10.1016/j.strusafe.2009.06.005.

Hui-Jun L., Zeng-Li P., Chun-Liang Y., Yue-Ming T., Application of Advanced Reliability Algorithms in Truss Structures, International Journal of Space Structures, 29: 61–70, 2014, doi: 10.1260/0266-3511.29.2.61.

Milewski S., Recovery of thermal load parameters by means of the Monte Carlo method with fixed and meshless random walks, Inverse Problems in Science and Engineering, 1–40, 2021, doi: 10.1080/17415977.2021.2016738.

Huang C., El Hami A., Radi B., Overview of Structural Reliability Analysis Methods – Part I: Local Reliability Methods, Incertitudes et fiabilit´e des syst`emes multiphysiques, 17-1(Optimisation et Fiabilité), 2017, doi: 10.21494/ISTE.OP.2017.0115.




DOI: 10.24423/EngTrans.3223.2024