Stress-constrained topology optimization considering uniform manufacturing uncertainties

• Published in: Computer methods in applied mechanics and engineering Vol. 344; pp. 512 - 537
• Main Authors: da Silva, Gustavo Assis, Beck, André Teófilo, Sigmund, Ole
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.02.2019; Elsevier BV
• Subjects: Finite element method; Interpolation; Manufacturing uncertainties; Post-processing; Robust design; Sharpness; Stiffness; Stress constraints; Stresses; Topology optimization; Uncertainty; Topology optimization; Stress constraints; Robust design; Manufacturing uncertainties
• ISSN: 0045-7825; 1879-2138; 1879-2138
• DOI: 10.1016/j.cma.2018.10.020

This paper proposes a robust design approach, based on eroded, intermediate and dilated projections, to handle uniform manufacturing uncertainties in stress-constrained topology optimization. In addition, a simple scheme is proposed to increase accuracy of stress evaluation at jagged edges, based on limiting sharpness of the projections to intentionally allow a thin layer of intermediate material between solid and void phases. A reference problem is analyzed through voxel-based finite element models, demonstrating that, in association with a proper choice of stiffness and stress interpolation functions, the proposed scheme can ensure consistent stress magnitude and smooth stress behavior for uniform boundary variation. Optimization problems are solved and post-processing with body-fitted meshes is performed over optimized solutions, demonstrating that: (1) stresses evaluated with voxel-based meshes containing thin soft transition boundaries are consistent with stresses evaluated with body-fitted meshes; and (2) optimized structures are robust with respect to uniform boundary variations.