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

Many topological objectives and constraints can not easily be assessed by analyticalformulations. this paper introduces a number of graph theoretical operators, as suitable combinatorialtools, for discrete topology assessment. using such an approach, the load paths from their exertion pointsto the support joints can be guided topologically during the optimization process. eleven variants of theproposed method are developed for the inclusion of various constraints and/or objectives. the presentedalgorithms are then applied to the optimal bracing layout of multi-story frames under lateral loadingsfor minimal weight or static compliance. benchmark examples from literature are treated to validate theeciency and to compare the capability of the proposed algorithms. the bracing patterns obtained fromoptimization are graph theoretically categorized.