# Two-Dimensional Topology Optimization of Headtube in Electric Scooter Considering Multiple Loads
## 1 Introduction  
Electric scooters have become a hallmark of personal mobility and have been rapidly adopted globally. The popularity of electric scooters is driven by their user-friendly operation and the widespread availability of shared services, such as Lime and Alpaca, which considerably increase their accessibility. Additionally, electric scooters contribute to reducing traffic congestion in tourist hotspots. In cities like Paris and Barcelona, electric scooters account for 45-60% of personal mobility [1]. This growing demand has propelled the expansion of the personal mobility industry, including sharing services, at a rate of 10.3%, with market research forecasting significant growth in the future [2, 3]. However, their rapid proliferation has been accompanied by a substantial increase in accidents involving these scooters. In South Korea, accident rates have surged by 282%, whereas in the USA, injuries related to electric scooters have tripled from 4583 in 2014 to 14,641 in 2018 [4]. These accidents are often more severe than car accidents because of their direct impact on riders, highlighting the urgent need for improved safety measures. Efforts to mitigate accidents have focused on enhancing driving regulations and laws to reduce driver-induced accidents. However, these measures do not address accidents caused by scooter malfunctions. Safety concerns are often compromised by designs driven by cost-effectiveness and the desire for lightweight structures at the expense of rigorous safety standards. Despite being preventable, accidents owing to the quality defects ofelectric scooters persist. Previous studies have attempted to address this issue by improving the structural integrity of scooters through material and design modifications, such as adopting magnesium alloy frames [5,6] and ergonomic designs [7, 8, 9]. These innovations have improved rigidity and safety while managing lightweight structures. Despite these advancements, design improvements have primarily relied on engineering expertise and designer intuition rather than a systematic design framework. Design optimization offers a robust solution to the limitations of conventional design methods for electric scooters. Design optimization, known for its systematic, efficient, and automated approach across various engineering fields, surpasses empirical methods by minimizing objective functions (e.g., maximum equivalent stress) while satisfying constraints (e.g., weight limits), even when dealing with multiple design variables. The benefits of design optimization are widely recognized in the automotive [10, 11, 12, 13], maritime [14], healthcare [15, 16], robotics [17], construction [18, 19], aerospace [20, 21], and other fields [22, 23, 24, 25]. Specifically, existing studies in automotive engineering primarily focus on multi-material optimization, whereas robotic engineering research emphasizes the optimization of kinematic flexibility and dynamic stability [26, 27, 28]. Similarly, topology optimization has been widely applied in the design of automotive and robotic structures. However, research on its application to electric scooters remains limited owing to the unique structural and loading characteristics of personal mobility devices. Topology optimization is a powerful numerical method that optimizes the material distribution within a design space to maximize performance under specific loads, boundary conditions, and constraints [29]. By systematically removing nonessential material, lightweight and structurally robust designs are produced. However, the effectiveness of topology optimization is highly dependent on the load conditions [30]. For example, a vertical structure optimized for normal loads may struggle to maintain its structural integrity under lateral forces. This highlights the need to incorporate multiple loading scenarios into the optimization process, as most existing studies have focused on singular loading conditions [31], potentially overlooking the diverse forces encountered in real-world applications.