Deblurring structural edges in variable thickness topology optimization via density-gradient-informed projection

TL;DR

This paper introduces a novel density-gradient-informed projection method to deblur structural edges in variable thickness topology optimization, effectively restoring sharpness without compromising structural performance.

Contribution

The main contribution is the development of the DGI projection, which enhances edge sharpness in VTTO by utilizing local density gradient information, addressing blurring artifacts.

Findings

DGI projection successfully restores sharp structural edges.

The method preserves internal structure and minimal impact on compliance.

Effectively suppresses low-thickness regions with combined penalization.

Abstract

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.