## 1 Introduction  
In the analysis of structural members, the general trend for linear systems is to find deflections after forming a matrix equation involving the stiffness matrix, loads, and deflections. By using very elaborate matrix methods, linear equations thus formed are solved with great success. This is not the case for nonlinear systems, where the use of additional iterative methods becomes a must [1; 2; 3; 4] since the stiffness matrix halts to be a constant one. Effectively, in those cases, the stiffness function is in turn a function of displacements. Detailed information about the optimization and design of various structure types can be found in [PERSON] et al. [5]. In recent years, total potential optimization using metaheuristic algorithms (TPO/MA) has been proposed as an iterative analysis method [6]. As is already known, all mechanical systems are in stable equilibrium in the case of minimum total potential energy. Thus, the minimization of the total potential energy of a system can be performed by considering the deflections as design variables. TPO/MA have been used successfully for the analysis of several structural systems. The first application area of TPO/MA is the truss structures. Different metaheuristic algorithms, such as local search [6], harmony search (HS) [7], and particle swarm optimization (PSO) [8], are employed with TPO/MA to analyze truss structures. In TPO/MA, since the displacements are the basic unknowns of the problem, the method becomes effective in finding second-order effects directly without the requirement of an additional process. Additionally, the finding of non-unique solutions [9] and material non-linearity [10] can be easily tackled. Different to truss structures, other truss-like systems, such as tensegric structures [11] and cable systems [12], are also solved via TPO/MA. In order to enhance the capacity of the method in solving large scale systems, hybrid metaheuristic algorithms combining the flower pollination algorithm (FPA), the teaching learning-based optimization (TLBO), and the Jaya algorithm (JA) are also proposed [13]. In this study, an innovation has been performed for enlarging the application area of the method TPO/MA to plates and plate-like structures. For this purpose, a simple approach has been adopted, which consists of dividing the system into triangles, of which the nodal displacements are the unknowns of the problem. Then, the strain energy of each triangle is expressed in terms of these variables. The summation of all these energies yields the total strain energy of the system. Adding to this value algebraically, the work done by the external forces again expressed in terms of the nodal deflections yield the total potential energy of the whole system considered. The rest of the technique is the determination of nodal displacements that will minimize the total potential energy through a metaheuristic optimization algorithm. Only plane stress problems are considered in this first trial. According to previous studies, HS is a suitable and effective algorithm for TPO/MA. For the numerical examples of the study, HS is effective to find close values to the finite element method (FEM) results and other new generated algorithms. Additionally, HS is also a well-proved algorithm for structural optimization problems [14; 15]. Several recent applications in the last decade are mentioned as follows. [PERSON] and [PERSON] developed a hybrid algorithm that is based on PSO with passive congregation, ant colony optimization, and HS to solve the optimum design of plane and space truss structures [16]. An adaptive HS algorithm was proposed by [PERSON] et al., and the proposed method for the optimum design of large-scale steel frame structures has the ability to automatically adjust the algorithm parameters [17]. [PERSON] proposed HS for structural frameworks for size, shape and topology optimization in order to conduct a multimodal optimization proposing a range of good alternative solutions instead of a single optimum one [18].