Abstract
Total Potential Optimization using Metaheuristic Algorithms (TPO/MA) is an alternative structural analysis method starting with the same principles of the Finite Element Method (FEM). In TPO/MA as in FEM, the structure at hand is divided into finite parts. In these parts, if FEM is to be used, the equilibrium equations are written in a matrix form in local coordinates, then they are combined to give a matrix equation valid for the totality of the structure. The final step is solving this matrix equation to find the displacements in the structure. On the other hand, in TPO/MA, potential energies of the elements are written, then they are summed for the totality of the structure, yielding a functional to be minimized to find the equilibrium position according to the minimum potential energy principle. This minimization gives the displacements of the structure. That is why this method can also be called Finite Element Method with Energy Minimization (FEMEM). FEM is very efficient for linear systems, but for nonlinear systems the matrix obtained depends on material properties, displacements, and loads, i.e. it is not constant and may be ill-conditioned. This makes solutions difficult and sometimes impossible. It has been shown in the literature that TPO/MA can overcome these difficulties much more easily, and can solve problems that cannot be solved by FEM. In this study, TPO/MA is applied to tunnel problems with plane stress properties. Minimization process is applied to several metaheuristic algorithms and hybrid ones, which are then compared with each other as to accuracy and precision.
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References
Levy, R., Spillers, W.R.: Analysis of Geometrically Nonlinear Structures, 2nd edn. Kluwer Academic Publishers, Dordtrecht (2003)
Saffari, H., Fadaee, M.J., Tabatabaei, R.: Nonlinear analysis of space trusses using modified normal flow algorithm. J. Struct. Eng. 134(6), 998–1005 (2008)
Krenk, S.: Non-linear Modeling and Analysis of Solids and Structures. Cambridge University Press, Cambridge (2009)
Greco, M., Menin, R.C.G., Ferreira, I.P., Barros, F.B.: Comparison between two geometrical nonlinear methods for truss analyses. Struct. Eng. Mech. 41(6), 735–750 (2012)
Toklu, Y.C.: Nonlinear analysis of trusses through energy minimization. Comput. Struct. 82(20–21), 1581–1589 (2004)
Toklu, Y.C., Bekdas, G., Temur, R.: Analysis of trusses by total potential optimization method coupled with harmony search. Struct. Eng. Mech. 45(2), 183–199 (2013)
Toklu, Y.C., Temur, R., Bekdaş, G.: Computation of Non-unique Solutions for Trusses Undergoing Large Deflections. Int. J. Comput. Methods 12(3), 1550022 (2015)
Temür, R., Bekdaş, G., Toklu, Y.C.: Total potential energy minimization method in structural analysis considering material nonlinearity. Challenge J. Struct. Mech. 3(3), 129–133 (2017)
Toklu, Y.C., Uzun, F.: Analysis of tensegric structures by total potential optimization using metaheuristic algorithms. J. Aerosp. Eng. 29(5), Sept 04016023 (2016)
Toklu, Y.C., Bekdaş, G., Temur, R.: Analysis of cable structures through energy minimization. Struct. Eng. Mech. 62(6), 749–758 (2017)
Bekdas, G., Kayabekir, A.E., Nigdeli, S.M., Toklu, Y.C.: Advanced energy based analyses of trusses employing hybrid metaheuristics. Struc. Des. Tall Spec. Build. 28(9), e1609 (2019)
Kayabekir, A.E., Toklu, Y.C., Bekdaş, G., Nigdeli, S.M., Yücel, M., Geem, Z.W.: A novel hybrid harmony search approach for the analysis of plane stress systems via total potential optimization. Appl. Sci. 10(7), 2301 (2020)
Toklu, Y.C., Bekdaş, G., Kayabekir, A.E., Nigdeli, S.M., Yucel, M.: Total potential optimization using metaheuristics: analysis of cantilever beam via plane-stress members. In: 6th International Conference on Harmony Search, Soft Computing and Applications (ICHSA 2020), 16–17 July. Istanbul, Turkey (2020)
Toklu, Y.C., Kayabekir, A.E., Bekdaş, G., Nigdeli, S.M., Yücel, M.: Analysis of plane stress systems via total potential optimization method considering non-linear behavior. J. Struc. Eng. 146(11). https://doi.org/10.1061/(asce)st.1943-541x.0002808
Sörensen, K., Sevaux, M., Glover, F.: A history of metaheuristics. Handbook of Heuristics, 1–18 (2018)
Rao, R.: Jaya: A simple and new optimization algorithm for solving constrained and unconstrained optimization problems. Int. J. Ind. Eng. Comput. 7(1), 19–34 (2016)
Geem, Z.W., Kim, J.H., Loganathan, G.V.: A new heuristic optimization algorithm: harmony search. Simulation 76, 60–68 (2001)
Rao, R.V., Savsani, V.J., Vakharia, D.P.: Teaching–learning-based optimization: a novel method for constrained mechanical design optimization problems. Comput. Aided Des. 43(3), 303–315 (2011)
Yang, X.S.: Flower pollination algorithm for global optimization. In: Unconventional Computation and Natural Computation, pp. 240–249 (2012)
Cook, R.D.: Finite Element Modelling for Stress Analysis. John Wiley & Sons, Inc., USA, 0-471-10774-31995
Gazi H.: Sonlu Elemanlar Yönemi ile Çalışan Bir Bilgisayar Programının Geliştirilmesi ve Düzlem Gerilme—Düzlem Deformasyon Problemlerinin Analizi, MSc Thesis, Istanbul University, Turkey
Weawer, W., Johnston, P.R.: Finite Element for Structural Analysis. Prentice—Hall, Inc., New Jersey (1984)
Wolpert, D., Macready, W.G.: No free lunch theorems for optimization. IEEE Trans. Evol. Comput. 1(1), 67–82 (1997)
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Toklu, Y.C., Bekdaş, G., Kayabekir, A.E., Nigdeli, S.M., Yücel, M. (2021). Total Potential Optimization Using Hybrid Metaheuristics: A Tunnel Problem Solved via Plane Stress Members. In: Nigdeli, S.M., Bekdaş, G., Kayabekir, A.E., Yucel, M. (eds) Advances in Structural Engineering—Optimization. Studies in Systems, Decision and Control, vol 326. Springer, Cham. https://doi.org/10.1007/978-3-030-61848-3_8
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