In engineering applications, plenty of components are subjected to variable-amplitude cyclic loading, resulting in fatigue damage, which is one of the main forms of structural damage. While the linear damage rule has long served as a fundamental approach, its limitations necessitate advancements for more accurate fatigue life predictions. Hence, this paper introduces a pioneering method termed nonlinear fatigue damage constrained topology optimization (NFDCTO). This method integrates several key components: the rainflow counting method to evaluate the non-proportional cyclic load levels, Basquin's equation to describe the S-N curve, and Morrow's plastic work interaction rule to calculate the nonlinear cumulative damage of the structure. Consequently, we establish a mathematical model for the NFDCTO method based on these components. The incorporation of penalized damage aggregation with the P-Normal function is used to address significant constraints and singularity challenges. Furthermore, by employing the adjoint method, we derive sensitivity equations for both the objective function and fatigue constraint function concerning the design variables. Subsequently, the superiority of the NFDCTO method over traditional linear fatigue damage method were verified applying 2D -shaped beam and simply supported structures as examples. Concurrently, bridge structures were employed to investigate the effect of the sensitivity index of the material to the history of variable amplitude stresses on the optimization results. In addition, the influence of the fatigue penalty factor on the topology optimization results was assessed using a 2D cantilever beam. Finaly, we verify the effectiveness and feasibility of the NFDCTO method in addressing fatigue optimization challenges for 3D structures utilizing two 3D examples.

中文翻译：

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非线性疲劳损伤约束拓扑优化


在工程应用中，大量构件受到变幅循环载荷的作用，产生疲劳损伤，是结构损伤的主要形式之一。虽然线性损伤规则长期以来一直是一种基本方法，但其局限性使得需要改进以实现更准确的疲劳寿命预测。因此，本文介绍了一种称为非线性疲劳损伤约束拓扑优化（NFDCTO）的开创性方法。该方法集成了几个关键部分：用于评估非比例循环荷载水平的雨流计数法、用于描述S-N曲线的Basquin方程以及用于计算结构非线性累积损伤的Morrow塑性功相互作用规则。因此，我们基于这些组件建立了 NFDCTO 方法的数学模型。将惩罚损伤聚合与 P-Normal 函数相结合，用于解决重大约束和奇点挑战。此外，通过采用伴随方法，我们推导了涉及设计变量的目标函数和疲劳约束函数的灵敏度方程。随后，以二维形梁和简支结构为例，验证了NFDCTO方法相对于传统线性疲劳损伤方法的优越性。同时，采用桥梁结构来研究材料对变幅应力历史的敏感性指数对优化结果的影响。此外，还使用二维悬臂梁评估了疲劳惩罚因子对拓扑优化结果的影响。 最后，我们利用两个 3D 示例验证了 NFDCTO 方法在解决 3D 结构疲劳优化挑战方面的有效性和可行性。