## 1 Introduction
That study aimed to analyze the placement of the stiffener plates using finite element analysis techniques to reduce the overall weight and enhance the stability of the machine tool structure, providing insights into the optimization of machine tool structures [16]. [PERSON] et al. (2023) introduced a new approach to address stress-based topology optimization problems by utilizing a binary structural topology optimization method. Design updates were performed using binary values (0 or 1), and a boundary identification scheme was employed to smooth the structural contours, avoiding artificial stress concentrations caused by the rugged nature of the topology optimization process. Due to boundary identification, re-meshing was required at each iteration. To minimize discontinuities in the moving domain during the iterative process, a two-domain technique, as presented by [PERSON] et al. 's TOBS (topology optimization of binary structures)--GT (geometric trimming) methodology was followed. Two distinct domains were defined: the first was an extension domain (referred to as the topology domain) that remains fixed and is meshed only at the beginning of the optimization process. The second was the trimmed domain with identified structure boundaries (referred to as the analysis domain), which needs to be meshed at each iteration for displacement and stress calculations using finite element methods. Within this mesh, a variable called pseudo-density is defined for each element, even though there are no void elements in the analysis domain. Spatial filtering techniques were applied to prevent numerical instability and extrapolate the void region. Numerical examples were provided to demonstrate the efficiency of this approach. The results indicated that the proposed trimming and remeshing domain method successfully addresses optimization problems where considering strength criteria can become troublesome, mitigating the rugged boundary transition between void and phase materials [17]. [PERSON] et al. (2022) employed first-order reliability method-based displacement and stress limit state functions for reliability analysis to quantify uncertainties in material properties, applied load and geometric parameters, and determined new optimized topologies through the proportional topology optimization (PTO) method. The innovation lies in incorporating the framework of reliability-based design optimization into topology optimization within a dual-loop scheme. Reliability analysis serves as the inner loop within the topology optimization outer loop. The PTO method was applied to analyze beams based on bidirectional evolutionary structural optimization. Moreover, a sensitivity analysis was conducted to assist in revealing the relative importance of uncertain variables in the final reliability within the design decisions of the topology optimized structures. Failure probabilities and corresponding reliability indices of the optimized geometries were obtained in numerical examples of a simply supported beam and a double-clamped beam. The results demonstrated the importance of considering reliability constraints in the final topology to ensure a safe and cost-effective design [18]. Many researchers have proposed various methods for structural design and numerical refinement analysis, which are highly beneficial and worth referencing for structural design improvement. However, this study adopted a practical approach based on machining characteristics, systematically conducting topology optimization analysis and structural stiffness enhancement design step-by-step. In this study, topology optimization based on machining characteristics was applied for structural design improvement of a machine tool. The machining characteristics, such as grinding vibrations, grinding forces, and surface roughness obtained from the ultrasonic-assisted grinding experiments of zirconia were utilized as the boundary conditions in static analysis.