## 1 Introduction  
With the increasing demand for lightweight structure and performance improvement in automotive, marine, aerospace, and other fields, structural optimization technology has been widely used in the past two decades. Topology optimization can lead to better performance designs in the conceptual design stage; so, many scholars and designers use this technique widely. In the traditional topology optimization field, the research mainly focuses on the minimization of structural flexibility [1, 2, 3]. Structural stiffness is increased by optimizing the material distribution. The topology optimization design technology based on structural flexibility minimization is mature, but topology optimization based on dynamic stress correlation is still in the development stage. At the same time, the stress of the structure under a static load and the stress under a dynamic load are very different, and the important criteria for measuring the strength failure of the structure are also different. Therefore, stress-constrained topology optimization is a hot spot in current research, but most of the current research focuses on static stress, and this paper mainly focuses on topology optimization under dynamic stress. Compared with the minimum flexibility design, there are three challenging problems in the stress-constrained topological optimization problem [4], namely the singular phenomenon of stress, the localization of the stress constraint, and the highly nonlinear nature of stress behavior. Firstly, the stress singular phenomenon mainly appears in the method based on variable density, because the stress value of the low-density element always behaves as a high stress value; so, it cannot be completely eliminated by the optimization algorithm. [PERSON] [5] proposed a smooth boundary function, namely the K-S (Kresselmeier Steinhauser) function. The smooth boundary function is used to relax the stress constraint to solve the stress singular value problem. [PERSON] et al. [6] proposed an \(\varepsilon\)-relaxation method that can effectively search the global optimal solution in the feasible design domain. [PERSON] et al. [7; 8] proposed a stress relaxation method based on the \(\varepsilon\)-relaxation method to deal with the stress singular value problem. [PERSON] et al. [9] applied the \(\varepsilon\)-relaxation method to the topology optimization problem with local stress constraints. Secondly, in the process of topology optimization, the position of maximum stress may shift due to the change in structural configuration in the different iterations. To constrain the maximum stress of the structure, the stress of each element must be constrained, and the optimization process needs to calculate the sensitivity of each constraint with respect to the density of the element, which causes a huge amount of calculation. To solve this problem, we can use a condensation function method, such as the P-norm method and the K-S function method. This method condenses multiple local stress constraints into a global stress function and only needs to constrain the global stress function to constrain the stress of the whole structure. [PERSON] [10; 11] used the K-S condensation function method to deal with the topology optimization problem of local stress constraints, condensing multiple local stress constraints into an overall stress function; then, it was only necessary to constrain this overall stress function to constrain the stress of the entire structure. This algorithm solves the topology optimization to minimize the volume of the structure under stress constraints. [PERSON] [12] established a topology optimization method for a continuum structure with stress gradient constraints, solved the problem of stress concentration, and proposed a topology optimization algorithm through P-norm and Lagrange multipliers. [PERSON] [13] and others proposed the following. Using the BESO method [14; 15], they adopted the global stress measure based on P-norm to deal with the flexibility minimization problem under volume and stress constraints.