# A smooth boundary extraction technique for topology optimization with binary design variables and a geometry trimming procedure

## Palavras-chave:

Topology optimization, Integer Linear Programming, Body-fitted mesh, Three-dimensional analysis## Resumo

One important step for topology optimization methods is to obtain representative smooth boundaries of the design. This is a step mostly used as a post-processing tool to facilitate manufacturing. However, smooth boundaries become also relevant during optimization in problems where the information at the boundaries is crucial, e.g., in stress-based design or fluid-structure interaction problems. This work investigates a boundary smoothing procedure to be used at every iteration of the topology optimization procedure. The present technique is proposed for binary-based topology optimization methods, such as the BESO (Bi-directional Evolutionary Structural Optimization) or the TOBS (Topology Optimization of Binary Structures) algorithms. In this context, a nodal numerical filter is applied to the binary design, and a smooth level set boundary is extracted from the design. The idea is further discussed in the context of the TOBS-GT (TOBS with geometry trimming) method, where the optimization and finite element meshes are separated. In this method, the void regions are trimmed out of the analysis domain and a new finite element mesh is generated at every optimization step. In this procedure, smooth boundaries are fundamental to guarantee a reasonably cheap and convergent finite element mesh. The smoothing procedure has the potential to improve the performance of the resulting structural surface as well as its appearance. 3D Numerical examples are investigated to evaluate the smoother robustness.