Three-dimensional manufacturing tolerant topology optimization with hundreds of millions of local stress constraints

Author(s)

da Silva, Gustavo Assis ^[1] ; Aage, Niels ^[1] ; Beck, Andre Teofilo ^[1] ; Sigmund, Ole ^[2]

Affiliation

^[1] Univ Sao Paulo, Sao Carlos Sch Engn, Dept Struct Engn, BR-13566590 Sao Carlos, SP - Brazil

^[2] Tech Univ Denmark, Dept Mech Engn, Solid Mech, Lyngby - Denmark

• Document type: Journal article
• Source: INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING; v. 122, n. 2, p. 548-578, JAN 30 2021.
• Web of Science Citations: 1

Abstract

In topology optimization, the treatment of stress constraints for very large scale problems (more than 100 million elements and more than 600 million stress constraints) has so far not been tractable due to the failure of robust agglomeration methods, that is, their inability to accurately handle the locality of the stress constraints. This article presents a three-dimensional design methodology that alleviates this shortcoming using both deterministic and robust problem formulations. The robust formulation, based on the three-field density projection approach, is extended and proved necessary to handle manufacturing uncertainty in three-dimensional stress-constrained problems. Several numerical examples are solved and further postprocessed with body-fitted meshes using commercial software. The numerical investigations demonstrate that: (1) the employed solution approach based on the augmented Lagrangian method is able to handle very large problems, with hundreds of millions of stress constraints; (2) three-dimensional stress-based results are extremely sensitive to slight manufacturing variations; (3) if appropriate interpolation parameters are adopted, voxel-based (fixed grid) models can be used to compute von Mises stresses with excellent accuracy; and (4) in order to ensure manufacturing tolerance in three-dimensional stress-constrained topology optimization, a combination of double filtering and more than three density field realizations may be required. (AU)

• FAPESP's process: 19/08654-6 - Topology optimization of three-dimensional structures considering manufacturing uncertainties and stress failure criterion
• Grantee: Gustavo Assis da Silva
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
• FAPESP's process: 18/16701-1 - Topology optimization of compliant mechanisms considering manufacturing uncertainties and stress failure criterion
• Grantee: Gustavo Assis da Silva
• Support Opportunities: Scholarships in Brazil - Post-Doctoral