A design method for optimal truss structures with redundancy based on combinatorial rigidity theory

Abstract

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.