###### Abstract
They were the first to introduce the concept of microstructure into structural optimization, describing the distribution of reinforcing ribs on the plate using a microstructural parameter (the number of ribs per unit length). This resulted in the optimal design of variable-thickness plates with ribs that allow for infinite density. In 1988, [PERSON] and [PERSON] [7] introduced the concept of material distribution within the design domain to describe structural topology, proposing the Homogenization Method for topology optimization. This method assumes that the design domain consists of cells with centered voids, where the voids have predefined geometric shapes (such as squares) and can be described by one or more size variables. By treating the size variables of the voids as design variables, the topology optimization problem is transformed into one of redistributing material within the design domain through size optimization. This work pioneered a new direction in continuum structural topology optimization. Evolutionary Structural Optimization (ESO) [8], the Level Set Method [9], and Solid Isotropic Material with Penalization (SIMP) [10; 11; 12] are also mainstream topology optimization methods. With its long development history and simple model, SIMP is considered a classic topology optimization method [13]. It serves as the theoretical foundation for mainstream commercial topology optimization software, including OptiStruct, which was used in this study. The most commonly used material interpolation method in density-based approaches is based on the power law form of orthotropic material density interpolation theory [14]. By introducing penalty factors to drive values toward zero or one, the intermediate density converges to these extremes, allowing for the addition or removal of intermediate-density elements, ultimately forming the topology structure. Additionally, other topology optimization methods include the Geometrical Projection Method (GPM) [15], the Moving Morphable Component (MMC) method [16], and the Moving Morphable Bar (MMB) method [17]. These methods describe topology optimization problems by defining components or bars, offering high computational efficiency, and yielding optimal structures that are simple and intuitive [18]. The application of structural topology optimization in lightweight and multifunctional design of aerospace structures is extensive, significantly enhancing the performance and design flexibility of aircraft and spacecraft. Aerospace structures demand high strength and low weight to withstand the complex loading conditions of extreme environments, such as high temperatures, high speeds, vibrations, and impacts. Traditional design methods often struggle to achieve the best balance between performance and weight, whereas topology optimization allows designers to optimize material distribution within the structure, significantly reducing material usage while maintaining strength and stiffness, thereby achieving lightweight structures. In aerospace structures, topology optimization is widely used in key components such as wings, fuselage frames, support structures, and engine parts. For example, wings and internal supports of the fuselage designed using topology optimization can effectively reduce weight while maintaining or even enhancing their bending and torsional stiffness. Additionally, topology optimization can generate porous or lattice structures based on different functional requirements. This multifunctional design not only reduces weight but also improves the structure's thermal management or optimizes its aerodynamic performance. Moreover, topology optimization combined with additive manufacturing (3D printing) plays a crucial role in realizing complex geometries. Traditional manufacturing processes often struggle with complex shapes, while additive manufacturing can directly produce complex structures generated by topology optimization, further expanding design freedom.