Abstract This paper proposes a nested algorithm for truss topology optimization under plastic shakedown theory, which aims at maximizing the shakedown loading capacity. The nested algorithm consists of shakedown analysis and sensitivity-based optimization. Analytical sensitivity of shakedown load with respect to the design variables is derived in a concise form for the first time in conjunction with the adjoint variable scheme. A primal-dual shakedown algorithm is implemented for the determination of the shakedown load limit of structures and adjoint variables needed in the sensitivity analysis. The ground structure approach is applied to formulate the optimization problem for determining the optimized topology and cross-sections of the truss structure. Based on the analytical sensitivity above, the nested algorithm of truss structure topology optimization can be done efficiently by a gradient-based mathematical programming algorithm. Through independent shakedown analysis and optimization processes, the proposed approach facilitates the computation scale and efficiency for large-scale structure optimization design. Several numerical examples involving two- and three-dimensional truss illustrate the effectiveness of the proposed approach.

中文翻译：

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一种最大塑性安定承载能力的桁架拓扑优化嵌套算法

摘要 提出了一种基于塑性安定理论的桁架拓扑优化嵌套算法，旨在最大化安定承载能力。嵌套算法由安定分析和基于灵敏度的优化组成。结合伴随变量方案，首次以简明形式导出了安定载荷对设计变量的分析灵敏度。采用原始-双重安定算法来确定结构的安定载荷极限和灵敏度分析所需的伴随变量。采用地面结构方法来制定优化问题，以确定桁架结构的优化拓扑和横截面。基于上述分析灵敏度，桁架结构拓扑优化的嵌套算法可以通过基于梯度的数学规划算法有效地完成。通过独立的安定分析和优化过程，该方法有助于大规模结构优化设计的计算规模和效率。几个涉及二维和三维桁架的数值示例说明了所提出方法的有效性。