A maximum-rectifier-function approach to stress-constrained topology optimization

• Published in: Structural and multidisciplinary optimization Vol. 65; no. 10
• Main Authors: Norato, Julián A., Smith, Hollis A., Deaton, Joshua D., Kolonay, Raymond M.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2022; Springer Nature B.V
• Subjects: 14th World Congress of Structural and Multidisciplinary Optimization; Agglomeration; Approximation; Computational Mathematics and Numerical Analysis; Constraints; Engineering; Engineering Design; Lagrange multiplier; Methods; Optimization; Parameter sensitivity; Rectifiers; Research Paper; Theoretical and Applied Mechanics; Topology optimization; Aggregation functions; Constraint scaling; Stress constraints
• ISSN: 1615-147X; 1615-1488
• DOI: 10.1007/s00158-022-03357-z

This paper introduces a novel method for stress-constrained topology optimization in which the stress constraint is a differentiable approximation of the maximum element stress violation in the structure. The element stress violation is given by a differentiable rectifier function. A key feature of the proposed method is its ability to render designs that satisfy the stress limit without renormalization of the constraint, as in some existing aggregation approaches. Numerical experiments demonstrate that the proposed technique exhibits better convergence and is less sensitive to the aggregation parameter than aggregation methods that employ renormalization. The effectiveness of the proposed method is demonstrated by several examples.