Total Potential Optimization Using Hybrid Metaheuristics: A Tunnel Problem Solved via Plane Stress Members

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Springer Science and Business Media Deutschland GmbH

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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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Finite element method with energy minimization, Flower pollination algorithm, Harmony search, Hybrid algorithms, Plane stress analysis, Total potential optimization using metaheuristic algorithms


Studies in Systems, Decision and Control

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