Truss fail-safe optimization - Concerning dynamic response and different material models

Fail-safe optimization balances the dual demands of maximising material efficiency and ensuring robust resistance against progressive collapse. However, existing frameworks heavily rely on simplified static and elastic assumptions, neglecting the complex transient and non-linear responses triggered by rapid structural damage. Before embedding computationally intensive analysis routines directly into first-order optimization frameworks, it is critical to isolate how individual response features alter the properties of the optimization problem. This study evaluates five distinct structural analysis methodologies—comprising three static and two dynamic formulations—applied to a diagnostic four-bar cantilever example. Using an exhaustive grid search to map the optimization landscape, the comparative analysis illuminates the pivotal role of material plasticity in non-linear dynamic problems. Notably, expanding the strain limit to eight times the yield strain allows plastic work to absorb transient kinetic energy, driving the non-linear dynamic optimum to within 2% of the rigid-plastic lower bound. Based on these findings, we recommend prioritising the development of rigid-plastic optimization formulations that provide computationally efficient approximations of non-linear dynamic behaviour while bypassing elastic singularity issues. Additionally, linear-elastic dynamic analysis should be advanced to establish upper-bound designs when material plasticity cannot be leveraged.