Abstract 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.

中文翻译：

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移动可变形贴片，用于具有厚度控制的三维拓扑优化

摘要 提出了使用移动可变形补丁解决三维问题的厚度可控拓扑优化问题。三角形补片的几何特征被用作设计变量，以能够用少量设计组件表示壳状构件和​​梁或杆构件。通过将贴片厚度变量的下限设置为给定的最小值，可以简单地控制平均柔度最小化问题的最小厚度。关于最大厚度，控制接近最大厚度的贴片在它们的侧面连接或完美重叠，为此在每个贴片上引入空隙掩模，避免通过它们的面部分重叠。因此，构件的最大厚度作为由构件组成的补丁的厚度变量的最大值获得。因此，构件的最大厚度可以通过厚度变量的上限来控制。对每个补丁的材料体积施加约束，以防止与其他补丁部分重叠或不完整连接。通过展示具有最小、最大和均匀厚度控制的各种示例，验证了所提出的配方的有效性。