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


1 Department of Civil Engineering,Iran University of Science and Technology

2 Department of Engineering,Building and Housing Research Center


Abstract. 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
eciency and to compare the capability of the proposed algorithms. The bracing patterns obtained from
optimization are graph theoretically categorized.