Keywords: structural design, truss and frame design, steel structures, structural optimization, multi-level optimization, discrete sizing optimization, shape optimization.

This paper describes a new optimization method for truss and frame structures that offers significant performance improvements compared to existing approaches. The scope of the problem involves the combined shape and member sizing optimization of frame structures to minimize weight while satisfying design performance requirements for safety and serviceability.

The proposed method partitions the problem into two hierarchical levels with different optimization strategies: subsystem and system. At the subsystem level, a specialized deterministic algorithm developed by the authors operates on discrete member sizing variables in order to find the best (e.g. minimum weight) solution for a given structural shape. The subsystem solution is then used to inform a gradient-based optimizer at the system level that operates on continuous shape variables to find the 'best' overall solution.

The proposed method is compared to other optimization approaches using two standard test case problems: an 18-bar truss and a 77-bar truss. In all three benchmarking studies conducted, the proposed method found minimum-weight designs that were superior to the best designs reported in the literature (2.8% on average). In addition, the proposed method was approximately an order of magnitude (10.3x on average) more computationally efficient than these other approaches in terms of number of analyses required to find the best design reported.

The improved performance of the method compared to other approaches can be attributed to the bi-level hierarchical structure. By separating the variables by type (e.g. continuous and discrete), specialized algorithms can be employed for each variable type. Previous researchers including Vanderplaats and Moses [1], Pedersen [2] and Kripakaran et al. [3] have also partitioned the problem in this way and have demonstrated that these multilevel methods consistently perform better than single-level methods where a single optimization algorithm must deal with both variable types simultaneously. The improved performance of the proposed approach compared to the other multilevel methods described above can be attributed to the novel combination of algorithms used at the system and subsystem levels.

It is worth noting that the convergence behaviour of the method does not appear to change significantly depending on the number of sizing design variables. Further research is planned to apply the proposed method to a long span stadium roof truss problem that involves several shape variables and several hundred sizing variables. This industry case study is intended to test the scalability of the proposed method in terms of stability and computational time.

1

G. Vanderplaats, F. Moses, "Automated design of trusses for optimum geometry", Journal of the Structural Division, 98(3), 671-690, 1972.

2

P. Pedersen, "On the minimum mass layout of trusses", 1970.

3

P. Kripakaran, A. Gupta, J.W.J. Baugh, "A novel optimization approach for minimum cost design of trusses", Computers & Structures, 85(23-24), 1782-1794, 2007. doi:10.1016/j.compstruc.2007.04.006

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