Optimal fail-safe truss structures: new solutions and uncommon characteristics

To investigate the characteristics of optimal fail-safe structures subjected to single and multi-member damage scenarios, we consider a pin-jointed cantilever truss with all members directly connected from the load point to the boundary. Two problem formulations are considered—minimizing the compliance with a volume constraint and minimizing the volume with stress constraints. Whilst these formulations produce equivalent structures for traditional truss design problems, we find that this is not always the case in the fail-safe setting. Analytical solutions are developed for a three-bar truss under both problem formulations. Damage is modelled as the complete removal of any one member, and a minmax problem is constructed to minimize the compliance or volume of the structure for the worst-case damage scenario. These new analytical solutions provide much needed benchmarks for numerical fail-safe methods. The problems are extended to n-bar systems with damage to multiple members. Results show that as the structural complexity (the number of members in a system) increases, the optimum fail-safe structure tends towards a variation of the nominal two-bar design with overlapping members. From these observations, we then approach the idea of full redundancy through the introduction of parallel substructures into a more complex truss design. We compare our fully redundant truss design with a benchmark fail-safe solution and show that the fully redundant design has significantly better performance and with fewer members. Practically, this suggests that fully redundant structural designs are highly efficient and have the additional benefit of only requiring the computation of the nominal solution.