Analyses of plane stress and plane strain through energy minimization

The stable equilibrium state of a structural system corresponds to the relative minimum total potential energy state. In order to analyze the structures by energy principle, energy minimization is addressed as an optimization problem. In early studies, few structural problems are investigated with the aid of energy minimization; flat and curved plates, bending plates, sandwich plates, cylindrical shell elements, truss elements, hyper-elastic membranes. The aim of this paper is to investigate the analysis of plane stress/strain elements through energy minimization. For this purpose, three state-of-art parameter-less metaheuristic algorithms were used to find the relative minimum total potential energy; Teaching-Learning Based Optimization (TLBO), Elitist Teaching-Learning Based Optimization (ETLBO), and Jaya Algorithm (JA). Additionally, a modification of Jaya Algorithm that named The Modified Jaya Algorithm (MJA) is proposed to analyze the plane stress/strain elements. According to the analysis results of the benchmark problems, TLBO and MJA are robust for the plane stress/strain analysis. In addition, MJA is more suitable algorithm in respect of computational efficiency from the other compared metaheuristic algorithms.