The level set method can express smooth boundaries in structural topology optimization with the level set function’s zero-level contour. However, most applications still use rectangular/hexahedral mesh in finite element analysis, which results in zig-zag interfaces between the void and solid phases. We propose a reaction diffusion-based level set method using the adaptive triangular/tetrahedral mesh for structural topology optimization in this work. Besides genuinely expressing smooth boundaries, such a body-fitted mesh can increase finite element analysis accuracy. Unlike the traditional upwind algorithm, the proposed method breaks through the constraint of Courant–Friedrichs–Lewy stability condition with an updating scheme based on finite element analysis. Numerical examples for minimum mean compliance and maximum output displacement at specified positions, in both 2D and 3D, converge within dozens of iterations and present elegant structures.

水平集方法可以在结构拓扑优化中表达平滑边界带有电平设置功能的零电平轮廓。但是，大多数应用程序仍在有限元分析中使用矩形/六面体网格，这会导致空隙相与固相之间形成锯齿形界面。在这项工作中，我们提出了一种使用基于自适应三角/四面体网格的基于反应扩散的水平集方法来进行结构拓扑优化。除了真正表达平滑边界之外，这种贴身网格还可以提高有限元分析的准确性。与传统的迎风算法不同，该方法通过基于有限元分析的更新方案突破了库兰特-弗里德里希斯-路易​​稳定性条件的约束。在2D和3D中指定位置的最小平均柔度和最大输出位移的数值示例，