Here, this paper presents for the first time an adaptive immersed approach for level-set topology optimization using higher-order truncated hierarchical B-spline discretizations for design and state variable fields. Boundaries and interfaces are represented implicitly by the iso-contour of one or multiple level-set functions. An immersed finite element method, the eXtended IsoGeometric Analysis, is used to predict the physical response. The proposed optimization framework affords different adaptively refined higher-order B-spline discretizations for individual design and state variable fields. The increased continuity of higher-order B-spline discretizations together with local refinement enables direct control over the accuracy of the representation of each field while simultaneously reducing computational cost compared to uniformly refined discretizations. A flexible mesh adaptation strategy enables local refinement based on geometric measures or physics-based error indicators. These adaptive discretization and analysis approaches are integrated into gradient-based optimization schemes, evaluating the design sensitivities using the adjoint method. Numerical studies illustrate the features of the proposed framework with static, linear elastic, multi-material, two- and three-dimensional problems. The examples provide insight into the effect of refining the design variable field on the optimization result and the convergence rate of the optimization process. Using coarse higher-order B-spline discretizations for level-set fields promotes the development of smooth designs and suppresses the emergence of small features. Moreover, adaptive mesh refinement for state variable fields results in a reduction of overall computational cost. Higher-order B-spline discretizations are especially interesting when evaluating gradients of state variable fields due to their higher inter-element continuity.
@article{osti_2522862,
author = {Schmidt, Mathias R. and Noël, Lise and Wunsch, Nils and Doble, Keenan and Evans, John A. and Maute, Kurt},
title = {Adaptive immersed isogeometric level-set topology optimization},
annote = {Here, this paper presents for the first time an adaptive immersed approach for level-set topology optimization using higher-order truncated hierarchical B-spline discretizations for design and state variable fields. Boundaries and interfaces are represented implicitly by the iso-contour of one or multiple level-set functions. An immersed finite element method, the eXtended IsoGeometric Analysis, is used to predict the physical response. The proposed optimization framework affords different adaptively refined higher-order B-spline discretizations for individual design and state variable fields. The increased continuity of higher-order B-spline discretizations together with local refinement enables direct control over the accuracy of the representation of each field while simultaneously reducing computational cost compared to uniformly refined discretizations. A flexible mesh adaptation strategy enables local refinement based on geometric measures or physics-based error indicators. These adaptive discretization and analysis approaches are integrated into gradient-based optimization schemes, evaluating the design sensitivities using the adjoint method. Numerical studies illustrate the features of the proposed framework with static, linear elastic, multi-material, two- and three-dimensional problems. The examples provide insight into the effect of refining the design variable field on the optimization result and the convergence rate of the optimization process. Using coarse higher-order B-spline discretizations for level-set fields promotes the development of smooth designs and suppresses the emergence of small features. Moreover, adaptive mesh refinement for state variable fields results in a reduction of overall computational cost. Higher-order B-spline discretizations are especially interesting when evaluating gradients of state variable fields due to their higher inter-element continuity.},
doi = {10.1007/s00158-024-03921-9},
url = {https://www.osti.gov/biblio/2522862},
journal = {Structural and Multidisciplinary Optimization},
issn = {ISSN 1615-147X},
number = {1},
volume = {68},
place = {United States},
publisher = {Springer},
year = {2024},
month = {12}}
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA); US Air Force Office of Scientific Research (AFOSR); Defense Advanced Research Projects Agency (DARPA); National Science Foundation (NSF)
Grant/Contract Number:
AC52-07NA27344
OSTI ID:
2522862
Report Number(s):
LLNL--JRNL-866238; 1099747
Journal Information:
Structural and Multidisciplinary Optimization, Journal Name: Structural and Multidisciplinary Optimization Journal Issue: 1 Vol. 68; ISSN 1615-147X