Means and Effects оf Constraining the Number of Used Cross-Sections in Truss Sizing Optimization

Abstract

This paper looks at sizing optimization results, and attempts to show the practical implications of using a novel constraint. Most truss structural optimization problems, which consider sizing in order to minimize weight, do not consider the number of different crosssections that the optimal solution can have. It was observed that all, or almost all, crosssections were different when conducting the sizing optimization. In practice, truss structures have a small, manageable number of different cross-sections. The constraint of the number of different cross-sections, proposed here, drastically increases the complexity of solving the problem. In this paper, the number of different cross-sections is limited, and optimization is done for four different sizing optimization problems. This is done for every number of different cross-section profiles which is smaller than the number of cross-sections in the optimal solution, and for a few numbers greater than that number. All examples are optimized using dynamic constraints for Euler buckling and discrete sets of cross-section variables. Results are compared to the optimal solution without a constrained number of different crosssections and to an optimal model with just a single cross-section for all elements. The results show a small difference between optimal solutions and the optimal solutions with a limited number of different profiles which are more readily applicable in practice.

Sizing and shape optimization material use in 10 bar trusses

“…The analytical solution has the advantage of being simplified in the sense that it uses the same cross-section for all bars making it easy to produce. This solution was compared to optimization results with the same three cross-section diameters for three different cases: the initial sizing optimized (sizing) [16], shape optimized from the initial model (shape), and simultaneous sizing and shape optimized (sizing shape). The masses of these models are presented in Fig.…”

“…The model is limited to a maximal displacement of ±0.0508m of all nodes in all directions, axial stress of ±172.3689MPa and Euler buckling constraints for all bars. The example analysed in this paper will use the results from [16] for the 10 bar truss load case 1 optimization where the number of different cross-sections was limited to 3 bars as the initial model configuration. This example is analysed since in practice the number of different cross-sections which are used for this type of problem in practice is 3 bars at most.…”

“…This example is analysed since in practice the number of different cross-sections which are used for this type of problem in practice is 3 bars at most. This solution presented in [16] uses only cross-section diameters of 240, 200 and 100mm, these cross-sections will be the only ones used. This model has been optimized for shape to find the best positions for nodes (1) and (3) for this configuration as well as sizing and shape just using the three optimal cross-sections as sizing variables.…”

“…This model has been optimized for shape to find the best positions for nodes (1) and (3) for this configuration as well as sizing and shape just using the three optimal cross-sections as sizing variables. The analytical solution for this problem if only one cross-section is used uses 240mm cross-sections [16].…”

“…Authors of [16] have gone a step further in using truss optimization to design trusses which have a specific number of different cross-sections. This method simulates real design practice with the use of only a few different cross-sections in order to minimize the complexity of the structure as well as costs in unused stock.…”