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

2026-03-10

AI Summary

This work addresses the challenges of manufacturability and ambiguous boundaries in variable-thickness topology optimization, particularly in low-thickness regions. To resolve these issues, the authors propose a Density Gradient-guided Interpolation (DGI) method that integrates SIMP material interpolation with regularized filtering. By intensifying projection in regions of high density gradient, DGI sharpens solid–void boundaries, while preserving internal structural features in low-gradient areas. The approach enables non-intrusive, locally adaptive regularization that significantly enhances edge clarity with negligible increase in structural compliance. Numerical experiments demonstrate that DGI effectively recovers crisp boundaries without compromising internal structural integrity, achieving near-zero compliance loss.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Machine Learning: Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

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.

Problem

• variable thickness topology optimization
• structural edge blurring
• low-thickness regions
• regularization artifacts
• solid-void transition

Innovation

• density-gradient-informed projection
• variable thickness topology optimization
• edge deblurring
• regularization
• SIMP penalization