Fatigue-constrained topology optimization (FCTO) is a currently research hotspot, and its fatigue constraints have material property dependency, highly nonlinear, and local features, which lead to challenges for the algorithm stability, computational efficiency, and different material application of FCTO. This research provides a FCTO method for structures subjected to variable-amplitude fatigue loading, incorporating the potential orthotropic behavior of materials. Firstly, a fatigue failure function derived from the constitutive model of orthotropic materials and the polynomial form in the Tsai-Hill criterion is proposed to predict multiaxial fatigue failure with a given loading spectrum. Secondly, a FCTO model minimizing structural weight is established based on the independent continuous mapping (ICM) method and constrained by a filtered, scaled, and aggregated fatigue failure function to enhance stability and convergence speed. Thirdly, the sensitivities of objective and constraint in the FCTO model are analyzed, and the optimal model is solved using convolutional filters and the globally convergent method of moving asymptotes (GCMMA) to generate manufacturable design. Finally, numerical examples demonstrate the feasibility of the method for 2D and 3D structures with varying material properties, load spectrums, and design domains. The developed method aims to facilitate the creation of lightweight designs capable of withstanding fatigue loads and to provide a framework and references for the advancement of integrated material-structure-performance designs.

中文翻译：

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基于扩展 Tsai-Hill 准则的正交各向异性材料疲劳约束拓扑优化方法


疲劳约束拓扑优化 （FCTO） 是目前的研究热点，其疲劳约束具有材料属性依赖性、高度非线性和局部性特征，这对 FCTO 的算法稳定性、计算效率和不同材料应用提出了挑战。本研究为承受可变振幅疲劳载荷的结构提供了一种 FCTO 方法，结合了材料的潜在正交各向异性行为。首先，提出了一个由正交各向异性材料本构模型和 Tsai-Hill 准则中的多项式衍生的疲劳失效函数，用于预测给定载荷谱下的多轴疲劳失效。其次，基于独立连续映射 （ICM） 方法建立最小化结构重量的 FCTO 模型，并受过滤、缩放和聚合疲劳失效函数的约束，以提高稳定性和收敛速度。然后，分析了 FCTO 模型中目标和约束的敏感性，并使用卷积滤波器和移动渐近线的全局收敛方法 （GCMMA） 求解最优模型以生成可制造设计。最后，数值实例证明了该方法适用于具有不同材料属性、载荷谱和设计域的 2D 和 3D 结构的可行性。开发的方法旨在促进创建能够承受疲劳载荷的轻量化设计，并为推进集成材料-结构-性能设计提供框架和参考。