Multi-objective design optimization of geometrically nonlinear truss structures

Abstract

The design optimization of geometrically nonlinear truss structures has been carried out generally by utilizing a single objective function (weight of truss structure and etc.) and an optimality criterion (uniform strain density distribution among truss members and etc.) as a design constraint. However, the interaction between optimality criteria and objective function prevents a correct and complete evaluation about optimal designations. In this study, three conflicted design criteria (weight of truss structure, critical load and uniform strain density distribution among truss members) and one design constrain (a pre-defined yielding limit) are simultaneously involved into the size and shape optimization of truss structures. For this purpose, an arc-length method as a nonlinear structural analysis is incorporated into search mechanism of a traditional pareto-ranking based multi-objective optimization method. Thus, a designer easily examines the entire solution space and makes a trade-off analysis between optimal designations (pareto solutions). Furthermore, this traditional multi-objective optimization method is improved by incorporating the multiple populations into its optimization procedure. Consequently, it is demonstrated that the computing efficiency of improved pareto-ranking based multi-objective optimization method is higher compared to both the traditional one and existing optimization approaches in Literature considering both the quality degrees of pareto solutions and the values of quality indicators named spread and inverted generational distance.