Topology optimization considering contact and stress constraints

Abstract This work advances the field of stress-constrained topology optimization by addressing frictionless unilateral contact problems. The approach focuses on minimizing mass of a contact-constrained structure while enforcing stress-constraints using local or global stress measures. Various contact coupling techniques, i.e. node-to-surface and surface-to-surface formulations, are examined and implemented using Lagrange multipliers or penalty methods. The study emphasizes the importance of accurately modeling contact surface geometries as discretization errors at these surfaces can dominate computed stresses and adversely affect optimization outcomes. Blending functions are introduced to mitigate this issue by enabling exact consideration of contact surface geometry without incurring the prohibitive computational costs associated with very fine discretizations. The results demonstrate that surface-to-surface contact methods outperform node-to-segment approaches due to their superior convergence properties and ability to pass the patch test. Additionally, a detailed comparison of augmented Lagrangian and aggregation-based stress-constraint enforcement reveals the superiority of augmented Lagrangian methods for the contact problem. Finally, a weighted augmented Lagrangian approach is proposed to resolve convergence issues in challenging contact scenarios.