## 1 Introduction
\begin{table}
\begin{tabular}{c c c c c} Reference & \multicolumn{1}{c}{Scope of the Reference} & Author & Algorithm & \\ \hline  & [PERSON] and [PERSON] [31] & Interior point method & \(\bullet\) & \\ \hline [PERSON] et al. [52] & MMA & \(\bullet\) & \\ \hline [PERSON] et al. [53] & MMA & \(\bullet\) & \\ \hline [PERSON] et al. [54] & SLP MMA, and OC & \(\bullet\) & \\ \hline [PERSON] et al. [55] & SLP and steeper descent & \(\bullet\) & \\ \hline [PERSON] and [PERSON] [56] & Level-set method & \(\bullet\) & \\ \hline [PERSON] et al. [57] & MMA & \(\bullet\) & \\ \hline [PERSON] et al. [58] & Commercial software (black box) & \(\bullet\) & \(\bullet\) \\ \hline [PERSON] et al. [59] & MMA & \(\bullet\) & \\ \hline [PERSON] and [PERSON] [60] & MMA & \(\bullet\) & \\ \hline [PERSON] et al. [51] & MMA & \(\bullet\) & \\ \hline [PERSON] et al. [62] & Level-set method & \(\bullet\) & \\ \hline [PERSON] et al. [63] & MMA & \(\bullet\) & \\ \hline [PERSON] et al. [64] & MMA & \(\bullet\) & \\ \hline [PERSON] and & Level-set method & \(\bullet\) & \\ \hline [PERSON] et al. [66] & MMA & \(\bullet\) & \\ \hline [PERSON] and [PERSON] [67] & MMA & \(\bullet\) & \\ \hline \end{tabular}
\begin{tabular}{c} Stress-constrained mass minimization \\ \hline [PERSON] et al. [68] & MMA & \(\bullet\) \\ \hline [PERSON] et al. [69] & SUPER & \(\bullet\) \\ \hline \end{tabular}
\end{table} 
Table 1: Cont. Table 1 includes several publications with open access implementations of topology optimization methods suitable for compliance-minimization problems [6; 7; 14; 17; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 34]. However, only four publications provide implementations of topology optimization methods compatible with stress-constrained compliance-minimization problems [36; 46; 47; 64]. Regarding these three publications, [PERSON] et al. [46] proposed a non-sensitivity method and [PERSON] [47] proposed a method based on inexact sensitivities, leaving the MATLAB implementations proposed by [PERSON] and [PERSON] [36] and by [PERSON] et al. [64] as the only publications providing a non-approximated solution to the stress-constrained compliance-minimization problem. On top of the reduced number of publications providing open access solutions with non-approximated methods to this problem statement, there are additional points of improvement that could be addressed to promote the research and application of topology optimization methods in the industry: including the compatibility with complex design spaces and geometries, as well as the interaction with commercially available and validated solvers. Finally, it is also relevant to consider that the topology optimization methods available in commercial software, such as ABAQUS(r) 2023 and ANSYS(r) 2023, operate on an opaque black-box system, limiting the access to relevant information and hindering their extension to a new feature of interest, such as reliability-based topology optimization [90; 91; 92] and robust topology optimization considering uncertainties [93]. To address this issue, the present article contributes with a methodology capable of solving non-self-adjoint problems in commercial software, including stress-constrained compliance minimization and stress-minimization problem statements, defined in a complex geometrical space. This methodology has been validated, evaluating the sensitivity analysis with finite differences and solving two benchmark problems with the following optimizers: Optimality Criteria, Method of Moving Asymptotes, Sequential Least-Squares Quadratic Programming, and Trust-constr optimization algorithms. In compliance-minimization problems and stress-constrained compliance-minimization problems, the methodology herein implemented achieved a performance equal to ABAQUS(r) in terms of the objective function. In stress-minimization problems, the methodology herein implemented allowed a stress reduction 35% superior to the one obtained with ABAQUS(r). To allow straightforward use even in an industrial field, a Python implementation is provided as Supplementary Material.