Total Potential Optimization Using Metaheuristic Algorithms for Solving Nonlinear Plane Strain Systems

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, tensegrity 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.