A fatigue-resistance topology optimization formulation for continua subject to general loads using rainflow counting

• Published in: Structural and multidisciplinary optimization Vol. 66; no. 9; p. 210
• Main Authors: Chen, Zhuo, Long, Kai, Zhang, Chengwan, Yang, Xiaoyu, Lu, Feiyu, Wang, Rixin, Zhu, Benliang, Zhang, Xianmin
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2023; Springer Nature B.V
• Subjects: Asymptotes; Computational Mathematics and Numerical Analysis; Constraints; Damage assessment; Engineering; Engineering Design; Fatigue failure; Fatigue strength; Nonlinearity; Optimization; Research Paper; Robustness (mathematics); Structural damage; Theoretical and Applied Mechanics; Topology optimization; Wind turbines; Topology optimization; Fatigue resistance; Augmented lagrangian; General loads
• DOI: 10.1007/s00158-023-03658-x
• ISSN: 1615-147X

Currently, fatigue-resistance topology optimization has received ever increasing attention, in which most of the literature considers this issue as a simple extension of stress-based topology optimization. However, previous approaches may not be applicable when considering general loads, as the conventional uniaxial rainflow counting method, commonly employed in prior studies, can result in significant errors. Furthermore, the inclusion of general loads introduces additional nonlinearity to fatigue-resistant topology optimization, posing challenges in identifying the optimal solution. To this end, a novel methodology for fatigue-resistance topology optimization considering general loads is proposed in this paper. The independent rainflow counting method is utilized during the process of structural damage estimation. The damage penalization model is subsequently adopted to reduce the nonlinearity by scaling the value of fatigue damage. To illustrate the necessity of an independent rainflow counting method, an example of a double L -shaped structure subjected to general loads is presented. The augmented Lagrangian (AL) approach is introduced to transform numerous damage constraint equations into the objective function, generating a sequence of box-constrained optimization sub-problems. After employing the typical SIMP technique, the relative sensitivities of the AL function regarding design variables are derived, which facilitates the efficient solution using the method of moving asymptotes (MMA). Through 2D and 3D numerical tests, the effectiveness of the proposed method is validated in comparison to the traditional method. Further investigation is conducted into the influences of general loads, damage penalization model, and manufacturing error robustness. In addition, the fatigue-resistance performance of a bearing support of a wind turbine is improved by the suggested approach, and its overall weight is decreased by 25.40%. The proposed method addresses the nonlinear and localized nature of fatigue-resistant topology optimization more efficiently. The results indicate that the proposed method can develop a lightweight design for structures under general loads.