Interactive structural topology optimization via skeleton control

Authors: Zhi Li, Haochen Liu, Yi Min Xie
Time: Mar 2026
Journal: Computer-Aided Geometric Design
DOI: https://doi.org/10.1016/j.cagd.2026.102538 Software: https://apps.apple.com/au/app/touchbeso/id6743680067

Abstract

Innovative load-bearing designs depend on a careful balance between creative shape and structural performance. While existing preference-based topology optimization methods let designers add subjective preference, they pose high design experience barriers and suffer from inefficient interactions due to reliance on skilled manual sketching. In this study, we propose the bidirectional evolutionary structural optimization with skeleton control (SC-BESO) method. This method begins with extracting the skeleton graph of an existing design, where users can subjectively drag its skeletal nodes to deform the design. The deformed design is then used to guide the generation of its optimized structural design. A design parameter allows users to adjust the optimized result toward either performance-driven or preference-driven outcomes. Based on the proposed method, a cross-platform digital design tool, TouchBESO, is developed for 2D structural designs. Parametric studies show that, even after user interaction that results in stiffness reduction, the SC-BESO method can regain most of the lost performance with only small shape changes. Furthermore, a 3D cantilever example illustrates the scalability of the method, and two potential integrations with drawing systems and the similarity constraint are discussed for future interactive design frameworks.

Keywords: structural design, skeleton graph, topology optimization, subjective preference, skinning algorithm, innovative structure

Citation

Paper：

Z. Li, H. Liu, Y. M. Xie, "[Interactive structural topology optimization via skeleton control](https://doi.org/10.1016/j.cagd.2026.102538)," Computer-Aided Geometric Design, vol.126, 102538, 2026.

BibTex

@article{Li2026,
title = {Interactive structural topology optimization via skeleton control},
journal = {Computer-Aided Geometric Design},
pages = {102538},
volume = {126},
year = {2026},
doi = {https://doi.org/10.1016/j.cagd.2026.102538},
author = {Zhi Li and Haochen Liu and Yi Min Xie},
}