We propose a topology optimization method for design of transversely isotropic elastic continua subject to high-cycle fatigue. The method is applicable to design of additive manufactured components, where transverse isotropy is often manifested in the form of a lower Young’s modulus but a higher fatigue strength in the build direction. The fatigue constraint is based on a continuous-time model in the form of ordinary differential equations governing the time evolution of fatigue damage at each point in the design domain. Such evolution occurs when the stress state lies outside a so-called endurance surface that moves in stress space depending on the current stress and a back-stress tensor. Pointwise bounds on the fatigue damage are approximated using a smooth aggregation function, and the fatigue sensitivities are determined by the adjoint method. Several problems where the objective is to minimize mass are solved numerically. The problems involve non-periodic proportional and non-proportional load histories. Two alloy steels, AISI-SAE 4340 and 34CrMo6, are treated and the respective as well as the combined impact of transversely isotropic elastic and fatigue properties on the design are compared.

我们提出了一种用于高周疲劳的横向各向同性弹性连续体设计的拓扑优化方法。该方法适用于增材制造零件的设计，其中横向各向同性通常表现为较低的杨氏模量，但在构造方向上具有较高的疲劳强度。疲劳约束基于连续时间模型，该模型以常微分方程的形式控制设计域中每个点的疲劳损伤的时间演变。当应力状态位于根据当前应力和背应力张量在应力空间中移动的所谓耐力表面之外时，会发生这种演变。使用光滑的聚集函数来近似疲劳损伤的点状边界，并通过伴随方法确定疲劳敏感性。以数字方式解决了以最小化质量为目标的几个问题。问题涉及非周期性的比例和非比例的载荷历史。处理了两种合金钢AISI-SAE 4340和34CrMo6，并比较了横观各向同性弹性和疲劳特性对设计的影响以及它们的组合影响。