Isogeometric Topology Optimization Based on Topological Derivatives

2025-09-11

AI Summary

Traditional topology optimization suffers from bottlenecks including frequent remeshing due to topological changes and reliance on predefined initial holes. To address these, this paper proposes a level-set-based topology optimization framework integrating isogeometric analysis (IGA) with topological derivatives. High-order NURBS basis functions are employed for accurate field variable approximation, while linear basis functions represent the level-set function—balancing geometric update fidelity and computational efficiency. Crucially, the method enables automatic evolution of complex topologies without remeshing and eliminates the need for prior hole assumptions. Numerical experiments demonstrate substantial improvements in solution accuracy and convergence stability. The approach overcomes key limitations of classical methods concerning geometric representation fidelity, mesh robustness, and initialization sensitivity. As such, it establishes an efficient, general-purpose paradigm for intelligent structural design in engineering applications.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Intelligent Robots: Learning & Optimization for ROB
• 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
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Topology optimization is a valuable tool in engineering, facilitating the design of optimized structures. However, topological changes often require a remeshing step, which can become challenging. In this work, we propose an isogeometric approach to topology optimization driven by topological derivatives. The combination of a level-set method together with an immersed isogeometric framework allows seamless geometry updates without the necessity of remeshing. At the same time, topological derivatives provide topological modifications without the need to define initial holes [7]. We investigate the influence of higher-degree basis functions in both the level-set representation and the approximation of the solution. Two numerical examples demonstrate the proposed approach, showing that employing higher-degree basis functions for approximating the solution improves accuracy, while linear basis functions remain sufficient for the level-set function representation.

Problem

• Eliminating remeshing challenges in topology optimization
• Enabling seamless geometry updates using isogeometric approach
• Investigating higher-degree basis functions for improved accuracy

Innovation

• Isogeometric topology optimization using topological derivatives
• Level-set method with immersed framework avoids remeshing
• Higher-degree basis functions improve solution accuracy