COLLABORATIVE OPTIMIZATION OF TOPOLOGY AND CROSS-SECTIONAL SHAPE FOR SPACE FRAME STRUCTURES

Frame structures are commonly used in architecture, civil engineering and other fields, and their design often necessitates a balance between weight reduction and the enhancement of mechanical properties. To achieve these design objectives, structural optimization methods are widely used to solve the shape and topology optimization problems of frame structures. The ground structure method is a fundamental approach for optimizing discrete truss or frame structures. The traditional ground structure method employs a set of nodes with fixed positions and achieves structural topology optimization by modifying the connectivity of members between the nodes. The introduction of the node-moving ground structure method has effectively expanded the design space of the traditional methods. However, current research on the node-moving ground structure method mostly is based on circular beam cross-sections, without considering the optimization of cross-sectional shapes or the principal direction design problems arising from irregular cross-sectional shapes. This limitation restricts the design space of existing optimization methods. Therefore, this paper proposes a collaborative optimization method for topology and cross-sectional shape of space frame structures, based on Rodrigues’ rotation rule and discrete cross-sectional shape optimization. This method addresses the issue of adaptive updating of the principal direction of beam cross-sections caused by node movement. By utilizing Rodrigues’ rotation, it establishes a unique correspondence between the principal direction of the initial structure and that of the structure after node movement. On this basis, the design variable of cross-sectional rotation angle is introduced, effectively expanding the design framework of the node-moving ground structure method. The method also takes into account the differences in bending and torsional resistance among beams with different cross-sectional shapes, enabling the automatic selection of various beam cross-sectional shapes to ensure efficient material utilization under complex conditions. Numerical examples demonstrate that through the collaborative optimization of structural topology and cross-sectional shape, frame configurations in three-dimensional space with superior performance can be obtained.