Errors were identified in the article¹ subsequent to its publication.

Equations (12)–(14) were written incorrectly in the article,¹ the corresponding correct equations are

$${\tilde{\rho }}_i=\frac{{\sum }_{j=1}^{N_e}{v}_j{\rho }_{j}w({\mathbf{x}}_j)}{{\sum }_{j=1}^{N_e}{v}_{j}w({\mathbf{x}}_j)},$$ (12)

$$w({\mathbf{x}}_j)=\max \left(0,1-\frac{||{\mathbf{x}}_i-{\mathbf{x}}_j||}{R_{\text{fill}}}\right),$$ (13)

$$\frac{\partial {\tilde{\rho }}_i}{\partial {\rho }_j}=\frac{v_{j}w({\mathbf{x}}_j)}{{\sum }_{k=1}^{N_e}{v}_{k}w({\mathbf{x}}_k)}.$$ (14)

These corrections do not change any results, discussions, or conclusions as they were implemented correctly in the codes.

中文翻译：

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基于设计的压力加载三维结构和柔顺机构的拓扑优化

第¹条在发表后发现了错误。

文章中的方程（12）-（14）写错了，¹对应的正确方程是

$${\stackrel{～}{\rho }}_{\mathrm{一世}}=\frac{{\sum }_{j=1}^{N_{\mathrm{电子}}}{v}_j{\rho }_j瓦({\mathbf{X}}_j)}{{\sum }_{j=1}^{N_{\mathrm{电子}}}{v}_j瓦({\mathbf{X}}_j)},$$ (12)

$$瓦({\mathbf{X}}_j)=\mathrm{最大限度}\left(0,1-\frac{||{\mathbf{X}}_{\mathrm{一世}}-{\mathbf{X}}_j||}{{\mathrm{电阻}}_{\text{充满}}}\right),$$ (13)

$$\frac{\partial {\stackrel{～}{\rho }}_{\mathrm{一世}}}{\partial {\rho }_j}=\frac{v_j瓦({\mathbf{X}}_j)}{{\sum }_{克=1}^{N_{\mathrm{电子}}}{v}_{克}瓦({\mathbf{X}}_{克})}.$$ (14)

这些更正不会改变任何结果、讨论或结论，因为它们在代码中正确实施。