This paper proposes a new methodology for continuum topology optimization that is capable of fatigue-resistance design. Firstly, penalized stress is adopted to circumvent the singularity issue. Secondly, another additional penalization formulation of the elemental fatigue damage is proposed. The quasi-static finite element method is performed to calculate structural responses efficiently according to the principle of linear superposition. To cope with large scale constraints, the p-norm function is adopted to aggregate all constraints into sole constraint. The density filter SIMP method is developed while the sensitivity expressions of proposed indices with respect to design variables are derived. The established optimization problem is solved by the method of moving asymptotes. Influences of varying damage penalization parameters mean stress, proportional and non-proportional loads on final designs are investigated through 2D and 3D numerical tests. It is revealed that the larger value of the fatigue penalty factor results in lighter weight while fatigue damages in the majority of solid material approach to the threshold. The results demonstrate that the proposed approach can achieve lightweight design by simultaneously restricting the maximum fatigue damage.

本文提出了一种能够进行抗疲劳设计的连续体拓扑优化的新方法。首先，采用惩罚性压力来规避奇点问题。其次，提出了元素疲劳损伤的另一种附加惩罚公式。根据线性叠加原理，采用准静态有限元方法有效地计算结构响应。为了应对大规模的限制，p-norm函数用于将所有约束聚合为唯一约束。开发了密度滤波器SIMP方法，同时导出了针对设计变量的拟议指标的灵敏度表达式。通过移动渐近线的方法解决了已建立的优化问题。通过2D和3D数值测试，研究了变化的损伤惩罚参数平均应力，比例和非比例载荷对最终设计的影响。结果表明，较大的疲劳惩罚因子值导致重量更轻，而大多数固体材料的疲劳损伤接近阈值。结果表明，所提出的方法可以通过同时限制最大的疲劳损伤来实现轻量化设计。