Three-dimensional adaptive mesh refinement in stress-constrained topology optimization

• Published in: Structural and multidisciplinary optimization Vol. 62; no. 5; pp. 2467 - 2479
• Main Authors: Salazar de Troya, Miguel A., Tortorelli, Daniel A.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2020; Springer Nature B.V
• Subjects: Algorithms; Computational Mathematics and Numerical Analysis; Constraints; Engineering; Engineering Design; Finite element method; Grid refinement (mathematics); Iterative methods; Optimization; Regularization; Regularization methods; Research Paper; Software engineering; Theoretical and Applied Mechanics; Topology optimization; Topology optimization; Stress constrained; Adaptive mesh refinement; Large-scale design
• ISSN: 1615-147X; 1615-1488
• DOI: 10.1007/s00158-020-02618-z

Structural optimization software that can produce high-resolution designs optimized for arbitrary cost and constraint functions is essential to solve real-world engineering problems. Such requirements are not easily met due to the large-scale simulations and software engineering they entail. In this paper, we present a large-scale topology optimization framework with adaptive mesh refinement (AMR) applied to stress-constrained problems. AMR allows us to save computational resources by refining regions of the domain to increase the design resolution and simulation accuracy, leaving void regions coarse. We discuss the challenges necessary to resolve such large-scale problems with AMR, namely, the need for a regularization method that works across different mesh resolutions in a parallel environment and efficient iterative solvers. Furthermore, the optimization algorithm needs to be implemented with the same discretization that is used to represent the design field. To show the efficacy and versatility of our framework, we minimize the mass of a three-dimensional L-bracket subject to a maximum stress constraint and maximize the efficiency of a three-dimensional compliant mechanism subject to a maximum stress constraint.