###### Abstract
By using the Solid Isotropic Material with Penalization (SIMP) method, the penalty factor p is introduced to increase the cost of intermediate-density elements and reduce the number of intermediate-density elements to make the density of elements as close as possible to 0 or 1 [15; 16], which highlights the overall structure of the vehicle frame. In the design process, the initial density distribution is not necessarily uniform. Therefore, some methods need to be adopted in the design process to achieve a uniform distribution of density. Common homogenization methods include the volume fraction method, sensitivity analysis, and topological gradient method. These methods basically use some rules to balance the mass distribution of different units and achieve homogenization. Although density-based topology optimization has significant advantages in optimization time, material utilization, and reliability, its application still faces some challenges. For example, optimizing the nonlinear behavior of materials and special boundary conditions in complex regions can help solve these challenges. More importantly, in the solution module, the applicability of the variable density method is more extensive. There are also some modern CAD-compatible topology optimization methods, such as the method based on non-uniform rational basis spline entities [17]. This can generate high-precision three-dimensional models with high efficiency and excellent computational performance. The geometric projection method realizes the distribution of materials and the filling of voids by dividing the optimization domain into grids and projecting them onto geometry [18]. The topology optimization method with a completely missing movable deformable gap and movable deformable component [19] is a new topology optimization algorithm that can be used to deal with holes and inherent scaling problems in topology optimization. It can effectively eliminate the empty area while maintaining the strength and stiffness of the structure. It will be a major challenge to apply these methods to formula racing in the future. In terms of size optimization, the main issue is the large number of design variables. When optimizing dimensions, sensitivity analysis is added to select variables with larger influencing factors from numerous variables, and optimization design is carried out on these variables to improve the efficiency and effectiveness of size optimization. Design sensitivity is the partial derivative of the design response to the optimization variable. From the perspective of calculation, the numerical methods of sensitivity analysis mainly include the following: the finite difference method, the direct differential method, and the adjoint variable method [20]. The finite difference method is a method based on numerical derivation that converts small changes in design variables into small changes in function values to calculate the sensitivity of design variables. In this method, numerical differentiation based on fractional differences is a common derivative technique. In addition, the finite difference method is not only suitable for calculating the sensitivity of one-dimensional and multi-dimensional functions but also for numerical models based on continuous and discrete variables. This method is simple, intuitive, and easy to implement, but in most cases, it needs to deal with very complex gradient calculations. The direct differential method is a method based on differential calculation. It calculates the differential between the design parameters and the system response by directly solving the analytical expression of the problem. The direct differential method can calculate the derivatives of multivariate functions more accurately, which makes it more widely used in nonlinear and dynamic systems. However, this method is computationally expensive, especially when the number of variables increases [21]. Due to the large number of frame fittings, there are many variables, so this method is not applicable.