Automatic member grouping in optimization of truss systems with k-means algorithm

The main subject of structural optimization is to determine an optimal system that can carry the given loads with the minimum possible structural material. Optimization types in truss systems are topology, shape, and size optimization. Topology optimization aims to find the optimal configuration by adding/removing bar elements to the truss system. Shape optimization aims to obtain the optimal shape of the truss system. In size optimization, the main idea is to reach the optimal cross-sectional areas of the bar elements. These three optimization types can be applied simultaneously to find the best (optimal) possible truss design. In real-world truss system optimization problems, both manufacturing and structural constraints must be considered. Since there can be too many members, it is necessary to group the elements so that a reasonable number of section types are used; and this is one of the most important manufacturing constraints. As the number of different sections increases, the design becomes nearly impossible to build due to labor and purchasing difficulties. To satisfy this constraint, the bar elements should be grouped. The cross-section type selected for the grouped bar elements is the same. However, it is necessary to decide which group a member will be assigned to. This decision can lead to non-economic solutions, especially for complex truss designs. On the other hand, the inclusion of element grouping in the optimization process with common methods increases the computational effort. This study tested a method presented as a solution to the element grouping problem on popular truss optimization problems (117 bar space truss, 72 bar space truss, 25 bar space truss, and 10 bar planar truss) and analysis results presented.