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.

翻译：可变厚度拓扑优化（VTTO）是一种设计高性能、高刚度薄板结构的有效方法。然而，该方法经常面临两个主要挑战：1）产生不期望的低厚度区域，这带来了制造上的困难；2）结构边缘的模糊化。这种模糊化是保证问题适定性所需的正则化滤波器所固有的伪影。本文提出了应对这两项挑战的解决方案。首先，为减少低厚度区域，我们引入了一种鲁棒的组合方法。该策略利用基于SIMP的惩罚和一种改进的投影方法，能有效抑制几乎所有的低厚度区域。其次，本研究的主要贡献在于提出了一种新颖的结构边缘去模糊化方法，称为密度梯度信息（DGI）投影。该投影利用了局部密度梯度信息。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度，同时对结构内部的低梯度区域影响最小。数值算例表明，DGI投影成功地对结构边缘进行了去模糊化，恢复了清晰的实体-空隙过渡，同时保持了内部形态。最重要的是，这种边缘清晰度的显著提升，对最终的结构柔度影响微乎其微。这确立了DGI投影作为一种非侵入且有效的正则化工具，可用于增强VTTO设计。