構造物の設計において「想定外」の外乱に対して十分な安全性を確保することは難しい。とりわけ「進行性崩壊」と呼ばれる、ある事象(部材消失等)を起点として部分的な崩壊が引き金となり、構造物全体へと崩壊が広がる現象の危険性が懸念される。%The Truss Topology Design (TTD) problem deals with the selection of optimal configuration for pin-jointed trusses, in particular, optimization of the connectivity of the nodes by the members, in which volume and/or compliance are minimized. In general, it is known that such truss structures are statically determinate and not redundantly rigid, that is, if just one member is damaged or lost, the entire structure cannot support loads. Therefore, it is important to take redundancy of structures into consideration in the TTD. In this paper, we present a new practical design method for finding a redundant TTD based on combinatorial rigidity theory. We define, as redundancy, the margin of the number of members until the collapse of the entire structure when some components are damaged or lost. A truss structure is said to be a "2-edge-rigid truss" if we need to remove at least two members from the truss structure so that the structure becomes non-rigid. We can find a 2-edge-rigid TTD by using a method based on combinatorial rigidity theory. The present method enables us to find an approximately optimal TTD with low computational cost. In the numerical examples, we obtain redundantly rigid truss structures, in which the objective value of the solution is about one percent greater than that of the lower bound solution. Therefore, we can conclude that the method is effective to design an optimal redundant truss structure.
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