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

Area of Science:

• Computational Engineering
• Materials Science
• Mechanical Engineering

Background:

• Topology optimization is computationally intensive, especially with nonlinear problems requiring many linear system solutions.
• Fine meshes are crucial for accurate structural definition and stress calculation (e.g., von Mises stress) in topology optimization.
• The computational cost escalates significantly with fine-mesh requirements in topology optimization.

Purpose of the Study:

• To develop an efficient computational strategy for topology optimization.
• To reduce the computational burden associated with fine-mesh requirements in topology optimization.
• To enhance the accuracy and efficiency of topology optimization for stress-critical structures.

Main Methods:

• A multi-level adaptive mesh refinement and coarsening strategy was developed.
• The strategy is based on configurational forces derived from Eshelby stress.
• Configurational forces were used to identify regions needing mesh refinement (stress concentrations and design boundaries).

Main Results:

• Configurational forces effectively identify both highly stressed regions and gray transition zones (design boundaries).
• Adaptive refinement using configurational forces creates high-resolution meshes in critical areas.
• Multi-level coarsening significantly reduces overall computational effort.

Conclusions:

• Configurational forces provide an ideal criterion for mesh adaptivity in topology optimization, particularly for avoiding stress failure.
• The proposed strategy balances the need for high-resolution meshes in critical areas with computational efficiency.
• This approach offers a promising solution for computationally demanding topology optimization problems.