A cliff-guided algorithm for optimizing energy-absorbing designs

A major engineering problem is the design of lightweight structures and components that are capable of absorbing a given amount of energy under external loading, e.g. in crash-worthiness or impacts. Load and displacements are unknown and the problem is nonlinear and non-conservative. Dissipation and resistance requirements render the optimization task complex and non-intuitive. A simple packet-based sizing optimization algorithm for lightweight hierarchical energy-absorbing truss-based structures is presented. The approach starts from a quasi-empty layout with connectivity background and thickens the member whose strain is highest at first failure. As a history-dependent gradient-free heuristic that tracks a specific structural failure trajectory, the algorithm converges to a path-dependent local optimum. A reduced-gradient analysis shows that this simple rule is a steepest-ascent step in a frozen-multiplier sub-space, guaranteeing a positive first-order gain in absorbed work. Numerical tests on 2D cantilever and simply-supported-beam (SSB) examples demonstrate weight savings of 88%–94% relative to fully solid baselines while meeting the energy target. The method shows robustness from an oscillatory “cliff-guided” dynamic, and requires only one nonlinear FE solve per packet.