Graph Theoretical Topology Control in Structural Optimization of Frames with Bracing Systems

Many topological objectives and constraints can not easily be assessed by analytical formulations. This paper introduces a number of graph theoretical operators, as suitable combinatorial tools, for discrete topology assessment. Using such an approach, the load paths from their exertion points to the support joints can be guided topologically during the optimization process. Eleven variants of the proposed method are developed for the inclusion of various constraints and/or objectives. The presented algorithms are then applied to the optimal bracing layout of multi-story frames under lateral loadings for minimal weight or static compliance. Benchmark examples from literature are treated to validate the e ciency and to compare the capability of the proposed algorithms. The bracing patterns obtained from optimization are graph theoretically categorized.