## 1 Introduction  
Additive manufacturing technology such as 3D-printing provides a new way of manufacturing complex components by printing structures layer by layer with materials [1]. Topology optimization is a structural optimization design method to distribute materials reasonably and to determine the optimal force transmitting path according to the specified load conditions, performance indicators, and constraints [2]. On comparison with size optimization and shape optimization, topology optimization does not depend on the choice of the initial configuration and offers a wider design space. Therefore, it is an effective design method for seeking high performance, lightweight, and multiple innovative structures, and has been applied extensively in aerospace [3, 4] heat transfer systems [5], and architectural design [6]. For example, the European Aeronautic Defence and Space company (EADS) Innovation Works optimized the Airbus A320 cabin hinge bracket by topology optimization and manufactured the topology optimization results using additive manufacturing. The new structure has a 60% weight reduction compared to the original structure design while meeting the strength requirements [7]. Thales Alenia Space (France) and Poly-shape (a 3D printing service company), designed and printed the antenna mount structure for the new Korean communication satellites Koreaast-5A and Koreaast-7 with 22% weight reduction compared to the conventional structure [8]. The combination of topology optimization and additive manufacturing provides a reliable path to compactness, integrated layout, and lightweight structure design [9]. The continuum topology optimization method has been fruitfully undergoing development over the last several decades [2; 10; 11; 12]. After many years of research and development, there are three major approaches in the field of topology optimization, which are the Solid Isotropic Material with Penalization (SIMP) method, the Evolutionary Structural Optimization (ESO)/Bidirectional Evolutionary Structural Optimization (BESO) method, and the level set method. Respectively, each of these methods has its own characteristics: the SIMP method is simple and convenient to implement numerically; the ESO/BESO method optimizes the results without intermediate density region; the level set method can clearly describe the boundary of the optimization results. In this article, the SIMP method is used because it is convenient to implement. Under periodic cyclic loading, most components are vulnerable to fatigue failure, which makes the service life of the components much shorter. There has been some work on fatigue-resistant design using topology optimization methods. [PERSON], et al. [13] proposed the simulation of the stress state at the joint using a combined element and introduced the fatigue criterion as a constraint to the topology optimization design, while the p-norm equation was also used to improve the computational efficiency, which was aimed at fatigue performance of multi riveted joint structures. However, the author did not elaborate further on the accuracy of simulated stresses using combined elements. [PERSON], et al. [14] investigated the topology optimization problem considering fatigue properties under asymmetric loading and described the complete time course of asymmetric loading action as a linear superposition of a series of unit static loads to ease the computationally burdensome problem of topology optimization under asymmetric loading. In paper [14], there is a 3D industrial example with a large grayscale result, which indicates that there is still potential to improve the convergence of the algorithm. [PERSON] and [PERSON] [15] studied the topology optimization of structures at low periodic cycle, where the fatigue of the material was strongly influenced by the plasticity of the material, and by introducing the Lemaitre material damage criterion, the fatigue life of the structure was optimized to the greatest extent. [PERSON], et al.