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

TL;DR

This paper introduces a multi-level adaptive mesh refinement and coarsening strategy driven by configurational forces, based on Eshelby stress, to improve efficiency and accuracy in topology optimization, especially near design boundaries and stress-critical regions.

Contribution

It presents a novel adaptive refinement and coarsening method using configurational forces for efficient and precise topology optimization, reducing computational costs while maintaining high resolution.

Findings

Refinement along design boundaries and stress-critical regions improves structure accuracy.

Multilevel coarsening significantly reduces computational effort.

Configurational forces effectively guide adaptive mesh modifications.

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.