Kinematic hardening (KH) is a common characteristic displayed by numerous metallic materials when subjected to loading beyond their elastic limit. This property enhances yield strength and expands the shakedown load domain, offering an opportunity to fully utilize the material’s potential and achieve a lightweight design. In this study, we present a shakedown-oriented topology optimization algorithm specifically developed for bounded linear KH materials. Our proposed approach adopts a nested optimization framework, where the inner loop handles the shakedown analysis formulated as a second-order cone programming problem that incorporates KH effects, while the outer loop iteratively updates the design variables using the method of moving asymptotes. To enhance computational efficiency, the inequality constraints in the shakedown problem are transformed into Euclidean ball constraints, and slack variables are introduced to facilitate the sensitivity calculation. The effectiveness of the proposed algorithm is demonstrated through various 2D and 3D numerical examples. The results show significant improvements in structural payload capacities compared with previous optimization methods based solely on elastic–perfectly plastic material behavior. These findings highlight the considerable potential and practical application of the presented method for the design of advanced lightweight structures demanded in aerospace and other challenging engineering fields.
Huang et al. (Sun,) studied this question.