Novel implementation of extrusion constraint in topology optimization by Helmholtz-type anisotropic filter

In this paper, a novel implementation of extrusion constraint in topology optimization is proposed based on Helmholtz-type anisotropic filter approach. The main idea is to set a far larger filter feature size along the extrusion direction than other directions, and thus, the density field is kept constant along the extrusion direction. The Helmholtz-type anisotropic filter can be easily implemented by adding a few more parameters to the isotropic one. Three illustrative examples, including 3D cantilever, spherical frame, and S-shape curved shell, are carried out to verify the effectiveness and robustness of the proposed method. Example results corroborate that the proposed method is suitable for both regular and irregular meshes regardless of geometrical complexity. Compared with the traditional variable mapping method, the proposed method needs less manual setup in the preprocessing of the analysis model for implementing extrusion constraint in topology optimization, which can be easily integrated into the solid isotropic materials with penalization (SIMP) topology optimization or commercial topology optimization software.