고품질 형상 추출을 위한 밀도 기반 토폴로지 최적화 후처리 기법

📝 Abstract

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.

💡 Analysis

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.

📄 Content

With the increasing availability of additive manufacturing and other modern manufacturing methods, topology optimization (TO) has become an invaluable tool for structural design, enabling engineers to discover novel geometries. This approach to computational design determines the optimal material distribution within a design space to achieve specified performance objectives while satisfying given constraints [34,1]. The field has rapidly evolved from academic research into practical engineering applications across aerospace [40], automotive [32], and biomedical industries [38]. Among various TO methods, density-based approaches like the Solid Isotropic Material with Penalization (SIMP) method have become predominant due to their mathematical simplicity and robust convergence properties [25,19]. However, the raw results from density-based TO typically exhibit two significant limitations: jagged boundaries due to the underlying finite element discretization and regions of intermediate density values that do not represent physically meaningful material states [35,30].

These limitations present significant challenges in translating optimized designs into practical applications. Consequently, the development of effective post-processing methods has become a critical area of research [30]. Several key factors must be considered in the development of such methods:

1. Geometric fidelity: The post-processed geometry must preserve the fundamental structural features and topological characteristics of the optimized solution while eliminating artificial artifacts.

The specified material volume fraction from the original optimization must be maintained to ensure design feasibility and performance requirements remain satisfied.

The extracted geometry should exhibit smooth boundaries to reduce stress concentrations and improve manufacturability.

The geometry extraction procedure should be applicable across various discretization schemes used in topology optimization, including regular and irregular meshes, elements of different polynomial orders, and geometrically diverse element types.

The resulting geometry must be compatible with downstream engineering processes, such as computer-aided design (CAD) systems, finite element analysis (FEA) software, or manufacturing processes.

Recent research efforts have explored various approaches to address the challenges arising from considering the abovelisted factors. First, image processing techniques employ thresholding operations followed by boundary smoothing using control points and spline interpolation [20]. While computationally efficient, these methods often struggle to simultaneously preserve volume fractions and critical geometric features. Next, model reconstruction approaches attempt to fit geometric primitives or spline surfaces to the optimized topology [33], offering improved boundary smoothness but frequently introducing significant computational complexity and potential loss of topological features.

More recent developments have shown promising advances in addressing multiple requirements simultaneously. Li et al. [18] introduced a boundary density evolution method that combines density-based optimization with levelset smoothing to produce manufacturable designs without penalty factors. While the method generates smooth boundaries suitable for 3D printing, its implementation is limited by its computational complexity and restriction to structured meshes.

In parallel, iso-density contour methods have demonstrated significant potential for balanced post-processing solutions. Li et al. [19] developed a novel lookup tablebased smoothing method for topology optimization results that achieves both computational efficiency and volumetric preservation. Their method shows particular strength in feature preservation and processing speed, though additional steps including internal surface removal and remeshing algorithms are required for three-dimensional structures.

Despite these advances, several limitations persist in current post-processing approaches. First, many methods struggle to simultaneously achieve boundary smoothness and precise volume preservation, particularly for complex geometries. Second, the computational efficiency of existing approaches often deteriorates with increasing mesh refinement or geometric complexity. Third, while some methods work well for regular meshes, their performance on irregular discretizations or higher-order elements remains inconsistent. Finally, the generation of CAD-compatible geometries, especially for three-dimensional problems, continues to pose significant challenges [30].

This paper builds upon principles established in [35] and extends the work of [31], which introduced an effective method for extracting geometries from SIMP-based results while preserving critical geometric features, maintaining precise volume fractions, and generating smooth boundaries through subsequent level-set shape optimization. This work exten

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