This paper presents a novel post-processing methodology for extracting high-quality geometries from density-based topology optimization results. Current post-processing approaches often struggle to simultaneously achieve smooth boundaries, preserve volume fraction, and maintain topological features. We propose a robust method based on a signed distance function (SDF) that addresses these challenges through a two-stage process: first, an SDF representation of density isocontours is constructed, which is followed by geometry refinement using radial basis functions (RBFs). The method generates smooth boundary representations that appear to originate from much finer discretizations while maintaining the computational efficiency of coarse mesh optimization. Through comprehensive validation, our approach demonstrates a 18% reduction in maximum equivalent stress values compared to conventional methods, achieved through continuous geometric transitions at boundaries. The resulting implicit boundary representation facilitates seamless export to standard manufacturing formats without intermediate reconstruction steps, providing a robust foundation for practical engineering applications where high-quality geometric representations are essential.

翻译：本文提出了一种新颖的后处理方法，用于从基于密度的拓扑优化结果中提取高质量几何模型。当前的后处理方法往往难以同时实现光滑边界、保持体积分数并保留拓扑特征。我们提出了一种基于符号距离函数的稳健方法，通过两阶段流程应对这些挑战：首先构建密度等值面的SDF表示，随后利用径向基函数进行几何细化。该方法生成的光滑边界表示看似源于更精细的离散化，同时保持了粗网格优化的计算效率。通过全面验证，与传统方法相比，我们的方法实现了最大等效应力值降低18%，这得益于边界处连续的几何过渡。所得隐式边界表示可直接导出为标准制造格式而无需中间重建步骤，为实际工程应用中高质量几何表示的需求提供了稳健基础。