Reducing the number of different members in truss layout optimization

Despite the long history of the truss layout optimization approach, its practical applications have been limited, partly due to high manufacturing costs associated with complex optimized structures consisting of members with different cross-sectional areas and member lengths. To address this issue, this study considers optimizing truss structures comprising limited types of members. On this topic, two distinct problems are considered, wherein the first problem, members of the same type share the same cross-sectional area (i.e., section-type problem); and in the second problem, members of the same type share the same cross-sectional area and length (i.e., member-type problem). A novel post-processing approach is proposed to tackle the target problems. In this approach, the optimized structures from the traditional layout and geometry optimization approaches are used as the starting points, members of which are then separated into groups by the k-means clustering approach. Subsequently, the clustered structures are geometrically optimized to reduce the area and length deviations (i.e., the differences between member area/length values and the corresponding cluster means). Several 2D and 3D examples are presented to demonstrate the capability of the proposed approaches. For the section-type problem, the area deviations can be reduced to near 0 for any given cluster number. The member-type problem is relatively more complex, but by providing more clusters, the maximum length deviation can be reduced below the target thresholds. Through the proposed clustering approach, the number of different members in the optimized trusses can be substantially decreased, thereby significantly reducing manufacturing costs.