# Optimization Method for Stiffened-Plate Layout in Box Structures Based on Load Paths
## 1 Introduction  
Large-box structures are widely used in heavy equipment such as machine tools and cranes, often serving as primary load-bearing structures. Their stiffness, strength, and weight directly influence the mechanical performance and processing quality of the equipment. Currently, the design of box structures primarily relies on empirical analogies, lacking scientific guidance. As a result, excessive design margins are often left, leading to structural bulkiness and impacting the structural mechanical performances. Therefore, large box structures with high stiffness, high strength, and low weight are pursued by the equipment design industry. The box structure is composed of outer skin and internal stiffening plates. The outer skin is sometimes limited by equipment design criteria, therefore, the essence of lightweight design is usually to optimize the layout and dimensional parameters of the internal-stiffening plates [1]. Research on the layout optimization of 2D stiffened panels has garnered widespread attention from numerous scholars [2; 3; 4], while studies on large 3D box structures are relatively scarce. As the empirically based stiffened plate layout is more initial, the researchers will also optimize the stiffened plate dimensions based on the static analysis of the box structure. [PERSON] et al. [5] conducted size optimization for the beam of a high-speed vertical machining center that utilizes a gantry structure to obtain better structural performance. [PERSON] et al. [6] carried out finite element analysis and optimized the design of the structure of the gantry beam of a guideway grinding machine, which resulted in a significant reduction of the maximum stress and displacement of the gantry beam. [PERSON] et al. [7] addressed the issueof the bulky structure and high material consumption in the gantry-milling machine bed within the current mechanical industry, through the static analysis of the bed along with stress-strain profiles and optimizing its dimensions while meeting stiffness and strength requirements, they achieved a lightweight design of the bed. [PERSON] et al. [8] derived a modal analysis method for variable cross-section beams based on Euler beam theory and the transfer matrix method for gantry machine tool beam structures, which provides a reference for the design of machine tool beam structures. [PERSON] et al. [9] proposed a bilevel accelerated microbial genetic algorithm for lightweight optimization design of sliding pillow block thickness, successfully achieving a weight reduction of 11.51%. However, such designs are limited to empirical approaches and are unable to offer the optimal stiffener layout. Topology optimization, as a method for optimizing material distribution within a continuous domain towards various objectives, has been widely applied in structural lightweight design. And, some scholars have carried out the optimization of 3D stiffenedplate layouts by topology optimization method. [PERSON] et al. [10] carried out a topology optimization design for medical devices with semi-gantry structures and reduced the weight by 30% with the same accuracy. [PERSON] et al. [11] proposed a two-level approximation method for multi-objective optimization of composite material stiffened panels. They introduced the concept of base structure in the reinforcement layout and laminate stacking sequence, formulated the design problem using a combination of discrete and continuous variables, and sought to minimize structural weight and maximize the fundamental frequency under given displacement constraints and manufacturing limitations. However, researchers gradually discovered during the research process that classical topology optimization methods face challenges in effectively identifying the stiffener layout within 3D box structures [12]. Moreover, the material distribution patterns provided may be overly complex and difficult to manufacture, making it challenging to effectively guide the optimization and improvement of the stiffener layout [13; 14].