Topology optimization of buckling-induced multistable structures for energy absorption

The multistable structure, which consists of an array of buckling-induced bistable elements, serves as an energy-absorbing system knowned for its reusability. However, its energy absorption efficiency remains comparatively low, thereby limiting its practical application. To address this limitation, this study examines the mechanical characteristics of buckling-induced multistable structures and introduces a topology optimization method designed to maximize their theoretical energy absorption capacity. To ensure stable and accurate finite element simulations and sensitivity analysis, we propose a method that alternates between the Newton and arc-length methods for solving nonlinear equations, and switches between force and displacement loading modes during the simulation. Utilizing this topology optimization approach, we perform optimizations on traditional cosine-shaped two-dimensional curved shells as well as on cosine-shaped domes, resulting in two distinct optimized structures. These optimized structures are subsequently benchmarked against similar bistable structures documented in existing literatures in terms of mechanical performance. The results demonstrate significant enhancements in theoretical maximum energy absorption capacities for the optimized structures, thereby validating the effectiveness of the presented method.