通过密度梯度感知投影在变厚度拓扑优化中去模糊结构边缘
Deblurring structural edges in variable thickness topology optimization via density-gradient-informed projection
AI总结：
本文提出密度梯度感知投影方法，用于解决变厚度拓扑优化中结构边缘模糊和低厚度区域问题，提升设计精度与刚度性能。
摘要：
变厚度拓扑优化（VTTO）是一种设计高性能、高刚度板状结构的有力方法。然而，这种方法经常面临两个主要挑战：1）形成不希望的低厚度区域，这带来了制造困难；2）结构边缘的模糊。这种模糊是为保证问题良态所必需的正则化滤波器的固有产物。本文提出了解决这两个挑战的解决方案。首先，为了减轻低厚度区域，我们引入了一种稳健的综合方法。该策略利用基于SIMP的惩罚和更新的投影方法，有效地抑制了几乎所有低厚度区域。其次，本文的主要贡献是提出了一种新的方法来去模糊结构边缘，称为密度梯度感知（DGI）投影。该投影利用局部密度梯度信息。它在高梯度区域（即结构边缘）选择性地应用强投影以恢复锐利度，而在结构内部的低梯度区域则影响较小。数值示例表明，DGI投影成功去模糊了结构边缘，恢复了明显的固-空转变，同时保持了内部形状。最重要的是，这种显著的边缘定义改进是在对最终结构刚度影响极小的情况下实现的。这使DGI投影成为一种非侵入且有效的正则化工具，用于增强VTTO设计。
英文摘要：
Variable thickness topology optimization (VTTO) is a potent methodology for designing high-performance, high-stiffness sheet structures. However, this method frequently encounters two primary challenges: 1) the formation of undesirable low-thickness regions, which present manufacturing difficulties, and 2) the blurring of structural edges. This blurring is an artifact inherent to the regularization filters required for well-posedness. This paper proposes solutions to address both challenges. First, to mitigate low-thickness regions, we introduce a robust, combined approach. This strategy utilizes a SIMP-based penalization and an updated projection method, which effectively suppresses nearly all low-thickness domains. Second, the main contribution of this work is a novel method to deblur structural edges, termed the density-gradient-informed (DGI) projection. This projection utilizes local density gradient information. It selectively applies a strong projection in high-gradient regions (i.e., structural edges) to restore sharpness, while minimally affecting low-gradient regions within the structure's interior. Numerical examples demonstrate that the DGI projection successfully deblurs the structural edges, restoring a distinct solid-void transition, while preserving the internal form. Most importantly, this significant improvement in edge definition is achieved with a negligible impact on the final structural compliance. This establishes the DGI projection as a non-invasive and effective regularization tool for enhancing VTTO designs.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
