ABSTRACT The traditional approach to structural lightweight optimization design, which is based on the elastic limit rule, often results in a structure that exhibits either weight redundancy or strength redundancy to some extent. This study introduces a novel integration of shakedown analysis with structural topology optimization, departing from the conventional elastic limit rule. Shakedown analysis identifies a non‐failure external load region beyond the elastic limit but below the plastic limit, independent of loading history. The proposed method, for the first time, accounts for the influence of self‐equilibrium residual stress at the element level, redefining effective and ineffective elements in topology optimization. Shakedown total stress replaces elastic equivalent stress, offering a comprehensive measure. Utilizing Melan's lower bound theorem, a gradient‐based topology optimization framework for shakedown analysis is developed, ensuring structures stay within the elastic–plastic range, preventing excessive plastic deformation. The approach, employing the moving asymptotes method after adjoint sensitivity analysis of shakedown total stress, is applied to a three‐dimensional L‐shaped bracket. Even with a remarkable 50% reduction in weight, the maximum total shakedown stress of the bracket reveals that it only increases by a modest 17.20% from its initial value. Moreover, compared to traditional topology optimization methods based on either elastic stress or stiffness, the proposed method based on total shakedown stress leads to a higher shakedown limit. Specifically, the configuration designed using the total shakedown stress exhibited increases of 2.01% and 9.82% in the shakedown limit compared to those obtained using stiffness and equivalent elastic stress, respectively. This suggests that the proposed method can effectively balance the trade‐off between shakedown strength and structural stiffness, achieving a 2.01% rise in shakedown strength with only a 2.24% compromise in structural stiffness. These findings highlight the method's effectiveness and potential, emphasizing the benefit of redefining effective and ineffective elements using shakedown stress in topology optimization.

Songhua Huang

Lele Zhang

Geng Chen

Yugong Xu

Min Chen

Zhiyuan Liu

Eng Gee Lim

International Journal for Numerical Methods in Engineering

《国际工程数值方法杂志》发表了原创论文，描述了适用于工程问题的数值方法的重大、新颖的发展。该杂志以欢迎在计算工程广泛领域的贡献而闻名，包括模型简化中的计算问题，不确定性量化、验证和确认、逆分析和随机方法、优化、元素技术、求解技术和并行计算、损伤和断裂、微观和纳米尺度力学、低速流体动力学、流固耦合、电磁学、耦合扩散现象，以及误差估计和网格生成。需要强调的是，这绝不是一份详尽的清单，尤其欢迎有关多尺度、多物理或多学科问题以及新兴主题的论文。

The International Journal for Numerical Methods in Engineering publishes original papers that describe significant and novel developments in numerical methods applicable to engineering problems. The journal is known for welcoming contributions across a wide range of computational engineering fields, including computational issues in model simplification, uncertainty quantification, validation and verification, inverse analysis and stochastic methods, optimization, element techniques, solution techniques and parallel computing, damage and fracture, micromechanics and nanomechanics, low-speed fluid dynamics, fluid-structure interaction, electromagnetics, coupled diffusion phenomena, as well as error estimation and mesh generation. It is important to emphasize that this is by no means an exhaustive list, and papers on multiscale, multiphysics, or interdisciplinary issues, as well as emerging topics, are especially encouraged.

《International Journal for Numerical Methods in Engineering》发表原创论文，介绍适用于工程问题的数值方法的重大和新颖发展。该杂志以欢迎计算工程广泛领域的贡献而闻名，包括模型简化中的计算问题、不确定性量化、验证与确认、逆分析和随机方法、优化、元素技术、求解技术与并行计算、损伤与断裂、微观和纳米尺度力学、低速流体动力学、流固耦合、电磁学、耦合扩散现象，以及误差估计和网格生成。需要强调的是，这并不是一份详尽的清单，尤其欢迎有关多尺度、多物理或多学科问题以及新兴主题的论文。

Category	Quartile
工程技术	3
工程技术, 工程综合	3
工程技术, 数学跨学科应用	3

Topology Optimization of Elastoplastic Structure Based on Shakedown Strength

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Category	Quartile
MATHEMATICS, INTERDISCIPLINARY APPLICATIONS	1