###### Abstract  
Total Potential Optimization using Metaheuristic Algorithms (TPO/MA) is an alternative tool for the analysis of structures. It is shown that this emerging method is advantageous in solving nonlinear problems like trusses, tensegity structures, cable networks, and plane stress systems. In the present study, TPO/MA, which does not need any specific implementation for nonlinearity, is demonstrated to be successfully applied to the analysis of plane strain structures. A numerical investigation is performed using nine different metaheuristic algorithms and an adaptive harmony search in linear analysis of a structural mechanics problem having 8 free nodes defined as design variables in the minimization problem of total potential energy. For nonlinear stress-strain relation cases, two structural mechanics problems, one being a thick-walled pipe and the other being a cantilever retaining wall, are analyzed by employing adaptive harmony search, which was found to be the best one in linear analyses. The nonlinear stress-strain relations considered in these analyses are hypothetical ones due to the lack of any such relationship in the literature. The results have shown that TPO/MA can solve nonlinear plane strain problems that can be encountered as engineering problems in structural mechanics.  
T 2021  
all these energies by only summing all of them, it is possible to obtain a function of the whole system as a function of \(\mathbf{x}\) and \(\mathbf{p}\). By following the minimization of that function concerning \(\mathbf{x}\), the well-known minimum potential energy theorem in mechanics is provided. This approach, called Total Potential Optimization using Metaheuristic Algorithms (TPO/MA) is first applied successfully to analyses of trusses where the optimization part is conducted using different kinds of metaheuristic algorithms. This approach is followed by further applications, with metaheuristic algorithms and hybrid ones, on planar or space trusses [6; 7; 8], tensegrity structures [9], and cable systems [10; 11]. Latest applications concern plane stress problems, with well-known linear constitutive equations [12], or with hypothetical linear constitutive equations [13]. TPO/MA has advantages on special and nonlinear systems. TPO/MA uses iterative search like an optimization problem for both linear and nonlinear systems, while FEM is a direct solution method for linear systems, and also an iterative system for nonlinear ones.  
In this study, the main purpose is to add a new type of structure to the existing application area of TPO/MA, namely, plane strain type plates. It is also aimed to show that systems with nonlinear stress-strain relations can be analyzed with this method with the same ease as with systems with linear stress-strain relations. For this purpose, besides linear systems, nonlinear systems are analyzed too. In these applications nonlinear stress-strain relations are hypothetical ones created by the authors, being not aware of any such real relations in the literature. The literature survey conducted has shown that no such nonlinear relations exist in two-dimensional structures, while they are numerous in the one-dimensional case. The nonlinear two-dimensional relations used in this study are of three different types. To find the best suitable metaheuristic method, 10 metaheuristic methods, one of them being the adaptive harmony search (AHS), are applied on a linear case of the first example. The results on these applications have shown that AHS is the one giving the best solution, in the shortest time. Then, the nonlinear cases of the first example and the other problems that have a higher number of design variables than the first example are solved via employing AHS.