# Topology Optimization with Explicit Components Considering Stress Constraints
## 1 Introduction
The global stress strategy is based on the P-mean aggregation function, and extensive parameter studies were conducted for L-shaped design problems [18], with one of the results shown in Design D.  
Unlike the more mature developments in implicit topology optimization methods, explicit topology optimization methods considering stress constraints are still in their initial stages. Explicit topology optimization methods, characterized by geometric parametrization, allow for the explicit realization of structural boundaries with clear borders. This means that the problem of calculating stress in intermediate-density elements is avoided, offering significant potential to improve the accuracy of boundary stress calculations and reduce computational complexity. [PERSON] et al. were the first to include stress constraints in structural topology optimization involving discrete geometric parts. By projecting the explicit and analytical geometric description of components onto a continuously varying density field, they inherited the convenience and advantages of density-based topology optimization [19], as shown in Design E. [PERSON] et al. proposed a solution to the stress constraint problem based on the moving morphable voids method (MMV), achieving an optimized design with clear and explicitly parameterized boundaries using a limited number of finite-element analysis degrees of freedom and optimization variables [20], as seen in Design F. Design G was obtained by [PERSON] et al. They proposed a new component topology description function based on polar coordinates under the framework of the moving morphable components (MMC) method, which has a strong curve expression ability. Global and local volume constraints are introduced in the explicit topology optimization framework, which holds significant engineering relevance [21]. The primary focus of this paper is on addressing stress constraint issues using explicit topology optimization methods. Within the framework of the moving morphable components (MMC) method, a topology description function with robust deformation capability was developed, and the lower-bound Kreisselmeier-Steinhauser function was utilized to aggregate stress constraints. Compared to existing methods for topology optimization considering stress constraints, this paper avoids the issue of intermediate-density elements through the use of an explicit topology optimization method, resulting in more accurate stress calculations. Additionally, a new component topology description function with enhanced deformation capability is introduced to improve geometric representation. Furthermore, the ends of the components are curved to prevent issues such as sharp connections at straight ends, which can lead to stress concentration. The proposed method was proven effective in classical L-shaped and T-shaped beam case studies. The structure of the remainder of the paper is as follows. Section 2 elaborates on the basic concept of the MMC method and the proposed topology description function. The formulation of the topology optimization problem and the aggregation treatment of stress constraints are presented in Section 3. Sensitivity analysis is conducted in Section 4. Representative examples are provided in Section 5, demonstrating the effectiveness of the method. Finally, a summary is provided in Section 6.