###### Abstract  
To analyze the impact of different objective functions and additive manufacturing (AM) constraints on structural topology optimization, it is necessary to perform an in-depth comparative study. This analysis should consider specific structural design factors, such as compliance, volume, or stress minimization, and assess their effects on the topology optimization for AM. In addition, the inclusion of AM constraints can have a significant influence on various aspects, including optimal part geometry, part volume, support structure volume, and structural performance. Thus, it is essential to investigate and compare these factors to determine the optimal part design for AM. This study focuses on comparing topology optimization results obtained using compliance, stress, or multi-objective minimization, with and without AM constraints. A comparative analysis was conducted in the study, utilizing three structural design examples: cantilever beam, bridge-shaped structure, and L-shaped beam. The comparison results provide insights into the effects of build orientation, AM constraints such as overhang, and different design objectives on the structural topology optimization for AM.  
additive manufacturing; topology optimization; design objectives; additive manufacturing constraint +
Footnote †: journal: _Applied Sciences_  
height, and material properties. Small features may be inaccurately printed or fail to form properly. Designers should adhere to minimum feature sizes, understand the resolution limitations of the chosen AM technology, and avoid designing features that are smaller than what the process can accurately reproduce [9; 10; 11; 12].  
Topology optimization that incorporates AM constraints and builds orientation enables the optimization of part designs that not only meet structural requirements but also take into account the limitations and capabilities of AM processes. By considering the build direction, the optimization process ensures that the design can be manufactured with minimal support structures and reduces the need for additional post-processing steps [13]. Several studies have been conducted to topologically optimize designs using AM constraints to reduce the need for post-processing [9; 14; 15]. To impose layer-wise overhang constraints and achieve specific overhang thresholds of 45 degrees, voxel-based topology optimization frameworks were employed [15]. An image-based computational approach was utilized to control the optimized maximum or minimum lengths within the design [16]. Furthermore, optimization techniques such as combining compliance and overhang as objectives, applying overhang constraints with hanging features, and setting arbitrary thresholds based on voxel aspect ratios have been adopted, and the modified moving asymptotes process and the bi-directional evolutionary structural optimization (BESO) approaches have also been utilized in the literature [15; 16; 17; 18]. The use of ANSYS APDL to reduce compliance and ensure the absence of overhanging surfaces also showed the impact of incorporating AM constraints [19; 20].  
Despite the significant progress in the field of design for AM, there is a lack of comprehensive studies that investigate the impact of AM constraints and different design objectives on topology optimization for AM. This study aims to fill this gap by analyzing the effects of AM constraints, such as overhang and member size, and different design objectives (e.g., compliance, stress, or multi-objectives) on structural topology optimization. It also focuses on providing a deeper understanding of how to formulate design problems for AM and to balance the trade-offs between design objectives, total volume, and manufacturing feasibility with respect to support structures.