摘要：To investigate the characteristics of optimal fail-safe structures subjected to single and multi-member damage scenarios,we con-sider a pin-jointed cantilever truss with all members directly connected from the load point to the *** problem formu-lations are considered—minimizing the compliance with a volume constraint and minimizing the volume with stress *** these formulations produce equivalent structures for traditional truss design problems,we find that this is not always the case in the fail-safe *** solutions are developed for a three-bar truss under both problem *** 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 *** new analytical solutions provide much needed benchmarks for numerical fail-safe *** problems are extended to n-bar systems with damage to multiple *** 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 *** these observations,we then approach the idea of full redundancy through the introduction of parallel substructures into a more complex truss *** 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 ***,this suggests that fully redundant structural designs are highly efficient and have the additional benefit of only requiring the computation of the nominal solution.