Weighted graph form of structures and its application in robustness analysis

Structural robustness is the concept to evaluate whether local damages to the structure will cause disproportional consequences. It is one of the most important indexes to keep the structural safety, especially to consider a special loading named as “human active damage”. In the present paper, the loaded structure is analyzed by a weighted graph. The joints and members of the structure correspond to the vertexes and edges of the graph, and the ratio of the most dangerous stress state to the material strength of each member is treated as the weight of each edge. Based on the quantitative description of the structural topology, the structure graph is expressed as a hierarchical model which is built by a set of vertex-connected units. The local damage can be expressed as the deterioration of the unit(s), while the final possible failure mode of the structure can be obtained by a specific assignment of its weighted graph. In this way, the relationship between the structural behavior and the combined damages of the subordinate units in each hierarchy can be formed as an envelope diagram. This diagram exactly shows the contribution of each subordinate unit to the robustness of the whole structure. Furthermore, the most vulnerable part, as well as the topologic difference between the subordinates, can be found visually.