An alloy wheel is generally a symmetrically shaped part integral to a vehicle because its weight and strength can improve driving performance. Therefore, alloy wheel design is essential, and a novel design method should be considered. Currently, the Multi-Additional Sampling Efficient Global Optimization (MAs-EGO) has been proposed and widely implemented in various fields of engineering design. This study employed a surrogate model to maximize Expected Hypervolume Improvement (EHVI) for multi-objectives by increasing multi-sampling per iteration to update a surrogate model and evaluate an optimal point for alloy wheel design. Latin Hypercube Sampling (LHS) was used to generate an initial design of an alloy wheel, including the thickness and width of the spoke wheel. The maximum principal stress according to the dynamic cornering fatigue simulation was then evaluated for risk of failure using Finite Element (FE) analysis. The objectives were to minimize both the principal stress and weight of the symmetric alloy wheel. The Kriging method was used to construct a surrogate model, including a Genetic Algorithm (GA), which was performed to maximize hypervolume improvement to explore the next additional sampling point, and that point was also an optimal point for the process when computation had converged. Finally, FE results were validated through a designed apparatus to confirm the numerical solution. The results exhibit thatMulti-Additional Sampling Efficient Global Optimization can achieve an optimal alloy shape. The maximum principal stress distribution occurs in the spoke area and exhibits a symmetrical pattern around the axis following the cyclic bending load. The optimal design point of the alloy wheel can reduce 20.181% and 3.176% of principal stress and weight, respectively, compared to the initial design. The experimental results are consistent trend in the same direction as FEA results.

The multiple additional sampling point method has become popular for use in Efficient Global Optimization (EGO) to obtain aerodynamically shaped designs in recent years. It is a challenging task to study the influence of adding multi-sampling points, especially when multi-objective and multi-fidelity requirements are applied in the EGO process, because its factors have not been revealed yet in the research. In this study, the addition of two (multi-) sampling points (2-MAs) and four (multi-) sampling points (4-MAs) in each iteration are used to study the proposed techniques and compare them against results obtained from a single additional sampling point (1-SA); this is the approach that is conventionally used for updating the hybrid surrogate model. The multi-fidelity multi-objective method is included in EGO. The performance of the system, the computational convergence rate, and the model accuracy of the hybrid surrogate are the main elements for comparison. Each technique is verified by mathematical test functions and is applied to the airfoil design. Class Shape Function Transformation is used to create the airfoil shapes. The design objectives are to minimize drag and to maximize lift at designated conditions for a Reynolds number of one million. Computational Fluid Dynamics is used for ensuring high fidelity, whereas the panel method is employed when ensuring low fidelity. The Kriging method and the Radial Basis Function were utilized to construct high-fidelity and low-fidelity functions, respectively. The Genetic Algorithm was employed to maximize the Expected Hypervolume Improvement. Similar results were observed from the proposed techniques with a slight reduction in drag and a significant rise in lift compared to the initial design. Among the different techniques, the 4-MAs were found to converge at the greatest rate, with the best accuracy. Moreover, all multiple additional sampling point techniques are shown to improve the model accuracy of the hybrid surrogate and increase the diversity of the data compared to the single additional point technique. Hence, the addition of four sampling points can enhance the overall performance of multi-fidelity, multi-objective EGO and can be utilized in highly sophisticated aerodynamic design problems.

This study presents a finite element analysis (FEA) of an external fixator rod incorporating a carbon fiber-reinforced epoxy resin composites (CFREs) to evaluate its mechanical performance. A detailed three-dimensional CAD model of the rod was developed, and the material properties of each component were defined using composite stacking techniques within the FEA framework. The external fixator rods were subjected to various loading conditions, including axial compression, torsion, and bending. The simulation results demonstrate that 18 mm CFREs rods exhibit superior resistance to compressive, torsional, and bending loads compared to conventional stainless-steel rods. These findings highlight the potential of composite materials to enhance the structural performance of external fixators in orthopedic applications. In addition, four carbon fiber ply orientation cases were investigated to identify the optimal configuration for load-bearing capacity. The [60°, 0°, −60°, 0°] ply orientation was found to provide the best performance under axial compression, offering improved load resistance and reducing deformation between fractured bone segments, thereby minimizing the risk of bone collision.