Stress‐constrained topology optimization of structures subjected to nonproportional loading

• Published in: International journal for numerical methods in engineering Vol. 124; no. 12; pp. 2818 - 2836
• Main Authors: Granlund, Gunnar, Wallin, Mathias, Tortorelli, Daniel, Watts, Seth
• Format: Journal Article
• Language: English
• Published: Hoboken, USA John Wiley & Sons, Inc 30.06.2023; Wiley Subscription Services, Inc; Wiley Blackwell (John Wiley & Sons)
• Subjects: Applied Mechanics; Constraints; ENGINEERING; Engineering and Technology; hyperelasticity; Load history; Maskinteknik; Mechanical Engineering; Nonproportional loads; Stiffness; stiffness maximization; stress constraints; Teknik; Teknisk mekanik; Topology optimization
• ISSN: 0029-5981; 1097-0207; 1097-0207
• DOI: 10.1002/nme.7230

This work considers the topology optimization of hyperelastic structures for maximum stiffness (minimum compliance) subject to constraints on their volume and maximum stress. In contrast to almost all previous works, we subject the structures to nonproportional loading, wherein the maximum stress does not necessarily occur at the final load step. As such, the stress is constrained at each load step. The augmented Lagrangian method is used to formulate the optimization problem with its many constraints. In numerical examples, we investigate different load trajectories for the same terminal load and compare the optimized designs and their performances. The results show the importance of considering the entire load trajectory as the load history significantly influences the optimized designs.