Minimum feature size control in level set topology optimization via density fields

Barrera, Jorge L.; Geiss, Markus J.; Maute, Kurt

doi:10.1007/s00158-021-03096-7

Title: Minimum feature size control in level set topology optimization via density fields

Journal Article · 21 February 2022 · Structural and Multidisciplinary Optimization

DOI: https://doi.org/10.1007/s00158-021-03096-7 · OSTI ID:1860910

^[1]; Geiss, Markus J. ^[2]; Maute, Kurt ^[3]

Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
OHB System AG, Wessling (Germany)
Univ. of Colorado, Boulder, CO (United States)

A level set topology optimization approach that uses an auxiliary density field to nucleate holes during the optimization process and achieves minimum feature size control in optimized designs is explored. The level set field determines the solid-void interface and the density field describes the distribution of a fictitious porous material using the solid isotropic material with penalization. These fields are governed by two sets of independent optimization variables which are initially coupled using a penalty for hole nucleation. The strength of the density field penalization and projection is gradually increased during the optimization process to promote a 0-1 density distribution. In addition, a second penalty regulates the evolution of the density field in the void phase. The treatment of the density field combined with the second penalty mitigate the appearance of small design features. The minimum feature size of optimized designs is controlled by the radius of the linear filter applied to the density optimization variables. The structural response is predicted by the extended finite element method, the sensitivities by the adjoint method, and the optimization variables are updated by a gradient-based optimization algorithm. Numerical examples investigate the robustness of this approach with respect to algorithmic parameters and mesh refinement. The results show the applicability of the combined density level set topology optimization approach for both optimal hole nucleation and for minimum feature size control in 2D and 3D. This comes, however, at the cost of a more complex problem formulation and additional computational cost due to an increased number of optimization variables.

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Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); National Science Foundation (NSF); Defense Advanced Research Projects Agency (DARPA)

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 1860910

Report Number(s):: LLNL-JRNL-820531; 1032110

Journal Information:: Structural and Multidisciplinary Optimization, Journal Name: Structural and Multidisciplinary Optimization Journal Issue: 3 Vol. 65; ISSN 1615-147X

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

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