## 1 Introduction  
In the last decade, researchers related to topology optimization (TO) for 3D elastic analysis using Matlab code have addressed evolutionary optimization methods, such as solid isotropic microstructure with penalization (SIMP), including extensions for various load cases, continuation strategy, the synthesis of compatible mechanisms, and heat conduction problems considering a compliance minimization problem, as presented by [PERSON] and [PERSON] [1], and bi-directional evolutionary structural optimization (BESO) by [PERSON] [2]. In addition, the 3D methodologies proposed by [PERSON] and [PERSON] [3, 4] for the soil structure and the TOPslicer tool, respectively, both developed in Matlab, generate suitable results for additive manufacturing. In their study, [PERSON] and [PERSON] [5] provided a mathematical model of stress-based topology optimization for three-dimensional optimization problems using SIMP. In the approach proposed in [6], the large-scale topology optimization for 3D elastic problem parallel computation is used in combination with domain decomposition. The equilibrium equations are solved by a preconditioned conjugate gradient algorithm, and the optimization is then performed using sequential convex programming. The TO procedure proposed in [7] presents 100-line Python code for general 3D topology optimization. It was developed for compliance minimization with a volume constraint using the bi-directional evolutionary structural optimization (BESO) method. The TO formulation presented in [8] includes simplified additive manufacturing (AM). The author demonstrated the procedure involving compliance minimization, self-frequency maximization, and flexible mechanism design. In the search for achieving a structure's best performance, parametric or topological optimization can be applied by using the deterministic or heuristic procedure. In the sense of the first case, several works have been proposed recently, such as Refs. [9; 10; 11; 12] which proposed novel methodologies for parameter optimization of antennas. In the case of the heuristic sense, evolutionary structural optimization (ESO) is a well-known procedure that seeks, by removing or adding material in the structure domain, to satisfy the design constraints. Thus, the search for stable, lightweight structures with low production costs and high performance becomes an important task for the industry that seeks technological competitiveness with little environmental impact due to the scarcity of material resources. Therefore, structural designs present uncertain variables, such as Young's modulus, yield stress, allowable stress, external loads, geometry, manufacturing error, etc. Deterministic topology optimization (DTO) cannot evaluate these uncertainties during the iterative procedure. To achieve these conditions, reliability-based topology optimization (RBTO) arises, which seeks the optimal topology under probabilistic constraints and has the ability to incorporate these variables during the optimization procedure to achieve a level of structural reliability. Researchers of Refs. [13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23] addressed RBTO using the first-order reliability method (FORM) with two more traditional approaches, the reliability index approach (RIA) and performance measure approach (PMA), over different methodologies, in general using a double-loop, single-loop or hybrid procedure. The work of [9] applied the reliability analysis for the optimization of antenna systems with the classical Monte Carlo procedure. [PERSON]. [16] initiated the hybrid approach, and it consists of a sequence of reliability and deterministic optimization analyses. Initially, the chosen random variables are modified as deterministic quantities according to the most probable point (MPP) obtained from the reliability index and the sensitivity analysis for the objective function (OF) regarding the random variables, which are used in the deterministic optimization procedure to obtain the optimal topology.