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    Analysis of Non-linear Structural Systems via Hybrid Algorithms
    (Springer Science and Business Media Deutschland GmbH, 2022) Nigdeli S.M.; Bekdaş G.; Yücel M.; Kayabekir A.E.; Toklu Y.C.
    Metaheuristic methods are commonly used in the problems which are treating optimization of structural systems as to the topology, shape and size. It is currently shown that metaheuristic methods can also be used in the analysis of structural system by an application of the well-known mechanical principle of minimum energy. This method is called total potential optimization using metaheuristic methods (TPO/MA), and it is shown that this method has certain advantages in dealing with nonlinear problems and with the problems where classical methods including the Finite Element Method has some difficulties. In this paper, a retaining wall example that is generated via plane-strain members is presented and hybrid algorithms using the Jaya algorithm are investigated. The hybrid algorithms may have advantages on the needed iteration number to reach the final value. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.
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    A Modified Jaya Algorithm and Application to Structural Analysis of Trusses
    (American Institute of Physics Inc., 2023) Bekdaş G.; Nigdeli S.M.; Toklu Y.C.
    In the present study, a metaheuristic algorithm called Jaya Algorithm (JA) was investigated for a modified version. JA is a parameter-free algorithm. In the investigation, a parameter is added to the algorithm to adjust the weight of the additional part that is summed with the existing solution. Generally, these algorithms are used in the optimum design; but these can be used for solution and analysis of engineering systems. The investigation is done by using total potential optimization to analyze truss structures. Different weight parameters are checked for analysis of a truss system. © 2023 American Institute of Physics Inc.. All rights reserved.
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    Total Potential Optimization Using Hybrid Metaheuristics: A Tunnel Problem Solved via Plane Stress Members
    (Springer Science and Business Media Deutschland GmbH, 2021) Toklu Y.C.; Bekdaş G.; Kayabekir A.E.; Nigdeli S.M.; Yücel M.
    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. © 2021, Springer Nature Switzerland AG.
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    Total Potential Optimization Using Metaheuristics: Analysis of Cantilever Beam via Plane-Stress Members
    (Springer Science and Business Media Deutschland GmbH, 2021) Toklu Y.C.; Bekdaş G.; Kayabekir A.E.; Nigdeli S.M.; Yücel M.
    In addition to classical methods in structural analysis, the exact solution of the deformed shape of the structure is by using a metaheuristic method. According to the theory of total potential energy minimization, the static condition of the deformed shape of structures can be found directly by assigning the coordinates of the deformed shape of the structure and finding the case with the minimum potential energy. In that case, the analysis process is an optimization process, and metaheuristics are effective in this process. The total potential optimization using metaheuristic algorithms (TPO/MA) is an effective approach for several including plane-stress members. A cantilever beam is presented in the study, and it is solved via plane-stress members using TPO/MA. The problem is presented via two meshing options. For the frequent meshing, a hybrid algorithm of Jaya Algorithm (JA) using student phase of Teaching–Learning-Based Optimization (TLBO) is presented. TPO/MA is effective to find similar results with the finite element method. © 2021, The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.