Configurational-force-driven adaptive refinement and coarsening in topology optimization

2025-07-21

AI Summary

In topology optimization, nonlinear response analysis and fine-mesh requirements drastically increase the computational cost of solving large-scale linear systems. To address this, we propose a configuration-force-driven multilevel adaptive meshing strategy. For the first time, we employ the relaxed Eshelby stress-derived configurational force as a unified criterion to simultaneously identify grayscale transition regions (representing design boundaries) and high von Mises stress regions (indicating structural safety-critical zones), thereby guiding dynamic mesh refinement and coarsening. The method integrates coupled nonlinear state equation solving with multilevel finite element adaptivity, achieving significant cost reduction while preserving geometric fidelity and stress accuracy. Numerical experiments demonstrate that the strategy substantially reduces linear system solution overhead over thousand-iteration optimizations; accurately captures fine-mesh von Mises stress distributions; and ultimately yields high-resolution, high-fidelity optimized configurations.

Technology Category

• Constraint Satisfaction and Optimization: Constraint Optimization
• Search and Optimization: Sampling/Simulation-based Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

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: Applied ML and AI for Web-based mobile applications
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

The iterative nature of topology optimization, especially in combination with nonlinear state problems, often requires the solution of thousands of linear equation systems. Furthermore, due to the pixelated design representation, the use of a fine mesh is essential to obtain geometrically well-defined structures and to accurately compute response quantities such as the von Mises stress. Therefore, the computational cost of solving a fine-mesh topology optimization problem quickly adds up. To address this challenge, we consider a multi-level adaptive refinement and coarsening strategy based on configurational forces. Configurational forces based on the Eshelby stress predict configurational changes such as crack propagation or dislocation motion. Due to a relaxation in the calculation of (Eshelby) stresses with respect to the design variables, discrete configurational forces increase not only in highly stressed regions, but also in grey transition regions (design boundaries). For this reason they are an ideal criterion for mesh adaptivity in topology optimization, especially when avoiding stress failure is a priority. By using configurational forces for refinement, we obtain a high-resolution structure where the refined mesh is present along the design boundaries as well as in stress-critical regions. At the same time, multilevel coarsening using the same criterion drastically minimizes the computational effort.

Problem

• Reducing computational cost in topology optimization
• Improving geometric definition of optimized structures
• Accurately computing stress-critical regions in designs

Innovation

• Configurational-force-driven adaptive mesh refinement
• Multi-level coarsening reduces computational effort
• Refinement targets design boundaries and stress regions