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Hollow structures can meet the demand of thickness control in manufacture, and achieve lightweight structures in design. However, topologically optimized results are generally solid structures, which are not easily transformed into hollow structures. Therefore, this paper proposes a three-dimensional moving morphable bar method to obtain hollow structures directly. The geometrical features of the three-dimensional solid moving morphable bars are projected onto a fixed grid, so the element density function can be obtained by a smooth Heaviside approximation of distance functions. Then the three-dimensional hollow moving morphable bars are further obtained by performing the Boolean subtraction of two solid bars. Also, the differentiable optimization model is established and the corresponding sensitivities are analytically derived. Numerical examples demonstrate that the proposed method can effectively achieve optimized designs of hollow structures. Besides, the Matlab code is provided to illustrate this method and facilitate further expansion.

Hollow structural topology optimization to improve manufacturability using three-dimensional moving morphable bars