Topology optimization (TO) has significant potential for industrial applications and offers greater design freedom than size or shape optimization. However, currently the design result of topology optimization is difficult to be directly applied to industrial design and manufacturing. The reason is that, at present, the optimal topologies produced by the most popular topology optimization methods lack explicit and computer-aided design (CAD) friendly representation. The triangular mesh derived from the smoothed results of topology optimization by conventional post-processing exhibits a high density of patches with low quality, making them difficult to edit and lacking in parameter control. This paper presents a general framework and method for automatically and self-adaptively reconstructing CAD models from complex topology optimization results. Firstly, a routine surface smoothing on the topology optimization results is performed to generate a triangular mesh. Then the Instant-Meshes and the generalized motorcycle graphs method are introduced for surface quadrilateral processing of the triangular mesh and generation of the sparse quadrilateral layouts. The improved harmonic mapping and adaptive sampling methods are developed to deal with each quadrilateral layout to generate non-uniform rational B-spline (NURBS) expression, and finally result in a smooth, explicit, and easy to edit boundary representation (B-Rep) model. A multi-resolution control strategy is proposed to significantly reduce the number of control points of NURBS patches. A highly efficient parameter domain initialization approach for harmonic mapping is presented using geodesic distance. The proposed framework and methods have been modularized and implemented in Python. The Python code (PYTOCAD) and all the testing models are available for download on https://github.com/rhy-thu/AMRTO. Various 3D examples including metamaterial designs with complex topology optimization results are tested to verify the effectiveness and robustness of the method. The developed program based on the present method requires less manual operation, thus paving the way for the automatic connection between topology optimization and CAD. Compared with commercial software, our method significantly reduces the number of NURBS patches, control points, and model file size of CAD model generated.

中文翻译：

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AMRTO：拓扑优化结果的自动 CAD 模型重建


拓扑优化 （TO） 在工业应用中具有巨大的潜力，并且比尺寸或形状优化提供更大的设计自由度。然而，目前拓扑优化的设计结果难以直接应用于工业设计和制造。原因是，目前，由最流行的拓扑优化方法生成的最优拓扑缺乏显式且计算机辅助设计 （CAD） 友好的表示。通过常规后处理从拓扑优化的平滑结果中得出的三角形网格表现出高密度的补丁和低质量，使其难以编辑且缺乏参数控制。本文提出了一种从复杂拓扑优化结果中自动自适应地重建 CAD 模型的通用框架和方法。首先，对拓扑优化结果进行常规表面平滑，生成三角网格。然后，引入 Instant-Meshes 和广义摩托车图方法对三角网格进行表面四边形处理并生成稀疏四边形布局。开发了改进的谐波映射和自适应采样方法，以处理每个四边形布局以生成非均匀有理 B 样条曲线 （NURBS） 表达式，并最终产生平滑、显式且易于编辑的边界表示 （B-Rep） 模型。提出了一种多分辨率控制策略，以显著减少 NURBS 面片的控制点数量。提出了一种使用测地线距离进行谐波映射的高效参数域初始化方法。提出的框架和方法已模块化并在 Python 中实现。 Python 代码 （PYTOCAD） 和所有测试模型都可以在 https://github.com/rhy-thu/AMRTO 上下载。测试了各种 3D 示例，包括具有复杂拓扑优化结果的超材料设计，以验证该方法的有效性和稳健性。基于该方法开发的程序需要较少的人工操作，从而为拓扑优化与 CAD 之间的自动连接铺平了道路。与商业软件相比，我们的方法显着减少了 NURBS 补丁的数量、控制点和生成的 CAD 模型的模型文件大小。