Shakedown Strength-Based Elastoplastic Topology Optimization and Its Application in Mechanical Exoskeleton Design

Traditional structural lightweight optimization based on the elastic limit rule often leads to weight or strength redundancy, highlighting the necessity of considering elastoplastic properties for material savings. However, in typical elastoplastic topology optimization, the actual stress state of the structure must be provided, which is closely related to the loading history. In practical engineering applications, accurately describing the loading history in advance is often challenging, and only the range of load variations is typically known. Consequently, incremental elastoplastic topology optimization is impractical for real-world engineering applications. This study integrates shakedown analysis via the Direct Method with elastoplastic topology optimization. Shakedown analysis identifies a load range beyond the elastic limit but below the plastic limit, independent of loading history. The proposed method innovatively accounts for self-equilibrium residual stress at the element level, thus redefining effective and ineffective elements by replacing elastic equivalent stress with shakedown total stress. Following adjoint sensitivity analysis, the proposed method was applied to the lightweight design of a three-dimensional L-shaped bracket. This study also explores the application of this method in the design of a mechanical exoskeleton. The two cases demonstrate that our approach effectively balances the trade-off between shakedown strength and structural stiffness. These findings underscore the potential of the method and the advantage of redefining effective and ineffective elements using shakedown stress in topology optimization.