A design-focused, cost-ranked, structural-frame sizing optimization

Abstract

Virtual-work methods on simplified models can rapidly provide the optimal distribution of material within a frame structure with computational efficiency that is only weakly dependent on the problem size. The drawbacks to these methods are that they require simplified objective and constraint functions, and the results do not always translate to a near-optimal solution from the simplified model to the exact model. The main contribution of this paper is a new method that expands the applicability of traditional virtual-work methods by using the Pareto set of sizing variables related to any objective and constraint functions, to include their exact stiffness contribution and a detailed monetary-cost function. Using the Pareto set enables frame-sizing solutions with optimal or near-optimal cost, complying with any number of global compliance constraints, and all typical local constraints. This method is compared to several metaheuristic methods. Metaheuristic optimization methods are the typical choice for problems with complex objective and constraint functions, as they have no restrictions on the types of variables or the functions they are suited to. The proposed method consistently achieves improved solution quality, and orders-of-magnitude improved computational efficiency over the sampled metaheuristic methods. These improvements facilitate optimization of an expanded set of sizing problems that are currently impractical, and with better results.