Moving morphable patches for three-dimensional topology optimization with thickness control

Thickness-controllable topology optimization is presented for three-dimensional problems using moving morphable patches. Geometric features of triangular patches were employed as design variables to enable the representation of shell-like members and beam or bar members with a small number of design components. The minimum thickness for mean compliance minimization problems can be controlled simply by setting the lower bound of thickness variables of the patches as the given minimum. Regarding the maximum thickness, the patches with close-to-maximum thicknesses were controlled to be connected on their sides or perfectly overlapped, for which a void mask is introduced on each patch, avoiding partial overlapping through their faces. Thus, the maximum thickness of a member was obtained as the maximum value of thickness variables of the patches consisting of the member. Therefore, the maximum thickness of members can be controlled by the upper bound of thickness variables. A constraint was imposed on the material volume of each patch to prevent partial overlapping or incomplete connection with other patches. The effectiveness of the proposed formulation was verified by showing various examples with minimum, maximum, and uniform thickness controls. (C) 2020 Elsevier B.V. All rights reserved.