###### Abstract
Figure 2: Schematic diagram of the structure of a two-dimensional turntable in a satellite space. pivotal for lightweight design, encompasses size, shape, and topology optimization [8], as depicted in Figure 3.  
Topology optimization is a key technique in the design of lightweight structures, providing enhanced design flexibility and significant technical advantages, including material reduction and improved structural performance [9]. Owing to advancements in computer technology and finite element theory, its application in engineering projects has progressively increased. Within the aerospace sector, the spaceborne optoelectronic tracking and pointing rotary table is subjected to a complex mechanical environment during launch, characterized by sinusoidal vibration, random vibration, and impacts. This demands that the structure exhibits sufficient dynamic stiffness. Therefore, in light of lightweight design criteria, ensuring the structure's dynamic performance is crucial to prevent performance degradation (e.g., diminished measurement accuracy of optical devices), system or component failures, or damage due to flawed design [10] (pp. 156-162). [PERSON] et al. studied the method of improving the dynamic performance of satellite components through topology optimization and verified its effectiveness [11]. In recent years, many studies have focused on improving topology optimization methods for aerospace structures. [PERSON] et al. proposed advanced topology optimization techniques for the design and optimization of aerospace structures [12] (pp. 150-162). Also, extensive research has been conducted on U-frame topology optimization by numerous scholars. For example, [PERSON] [5] applied the variable density method for optimizing the topology of a carbon fiber matrix U-frame, with a focus on enhancing structural stiffness. This process resulted in an optimized internal reinforcement layout of the U-frame matrix, leading to a 30% reduction in weight. Modal analysis was subsequently performed to validate the optimization results. [PERSON] [7] (pp. 110-115) leveraged topology optimization theory, employing the variable density method and the SIMP model, to optimize the topology of a satellite's two-dimensional turntable U-frame. The outcome was a 4.3% weight reduction along with improvements in both dynamic and static mechanical properties. [PERSON] and [PERSON] also obtained similar results when performing structural optimization on satellite support frames, confirming the effectiveness of the optimization method [13] (pp. 975-990). [PERSON] [14] utilized the variable density method, integrating the SIMP material interpolation model to maximize structural stiffness, and introduced volume constraints for the topology optimization of a space-based two-dimensional tracking and pointing mechanism's U-frame. This approach facilitated a lightweight structure design, ensuring the turntable system's fundamental frequency met task index requirements and exhibited strong resistance to external interference. Prior studies have typically prioritized optimizing the static stiffness of the structure, with dynamic performance analysis following optimization. [PERSON] et al. proposed a multi-constraint optimization method in their study and demonstrated its potential for application in aerospace engineering [15] (pp. 827-844). In contrast, the proposed U-frame topology optimization method by TOSCA integrates dynamic performance analysis directly into the topology optimization process and imposes multiple constraints simultaneously, introducing new ideas and methods for lightweight U-frame structure design. Figure 3: Three ways of structural optimization. In this paper, the finite element analysis software Abaqus/CAE and the optimization design tool TOSCA are employed to investigate the topology optimization of the U-frame of a spaceborne optoelectronic tracking and pointing turntable, aiming for a lightweight design without compromising the static and dynamic performance of the structure.