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Title: Adaptive mesh refinement in stress-constrained topology optimization

Abstract

We present a topology structural optimization framework with adaptive mesh refinement and stress-constraints. Finite element approximation and geometry representation benefit from such refinement by enabling more accurate stress field predictions and greater resolution of the optimal structural boundaries. We combine a volume fraction filter to impose a minimum design feature size, the RAMP penalization to generate “black-and-white designs” and a RAMP-like stress definition to resolve the “stress singularity problem.” Regions with stress concentrations dominate the optimized design. As such, rigorous simulations are required to accurately approximate the stress field. To achieve this goal, we invoke a threshold operation and mesh refinement during the optimization. We do so in an optimal fashion, by applying adaptive mesh refinement techniques that use error indicators to refine and coarsen the mesh as needed. In this way, we obtain more accurate simulations and greater resolution of the design domain. We present results in two dimensions to demonstrate the efficiency of our method.

Authors:
ORCiD logo [1];  [1]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Univ. of Illinois, Urbana-Champaign, IL (United States)
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1481053
Report Number(s):
LLNL-JRNL-748566
Journal ID: ISSN 1615-147X; 933663
Grant/Contract Number:  
AC52-07NA27344
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Structural and Multidisciplinary Optimization
Additional Journal Information:
Journal Name: Structural and Multidisciplinary Optimization; Journal ID: ISSN 1615-147X
Publisher:
Springer
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING

Citation Formats

Salazar de Troya, Miguel A., and Tortorelli, Daniel A. Adaptive mesh refinement in stress-constrained topology optimization. United States: N. p., 2018. Web. doi:10.1007/s00158-018-2084-2.
Salazar de Troya, Miguel A., & Tortorelli, Daniel A. Adaptive mesh refinement in stress-constrained topology optimization. United States. doi:10.1007/s00158-018-2084-2.
Salazar de Troya, Miguel A., and Tortorelli, Daniel A. Fri . "Adaptive mesh refinement in stress-constrained topology optimization". United States. doi:10.1007/s00158-018-2084-2.
@article{osti_1481053,
title = {Adaptive mesh refinement in stress-constrained topology optimization},
author = {Salazar de Troya, Miguel A. and Tortorelli, Daniel A.},
abstractNote = {We present a topology structural optimization framework with adaptive mesh refinement and stress-constraints. Finite element approximation and geometry representation benefit from such refinement by enabling more accurate stress field predictions and greater resolution of the optimal structural boundaries. We combine a volume fraction filter to impose a minimum design feature size, the RAMP penalization to generate “black-and-white designs” and a RAMP-like stress definition to resolve the “stress singularity problem.” Regions with stress concentrations dominate the optimized design. As such, rigorous simulations are required to accurately approximate the stress field. To achieve this goal, we invoke a threshold operation and mesh refinement during the optimization. We do so in an optimal fashion, by applying adaptive mesh refinement techniques that use error indicators to refine and coarsen the mesh as needed. In this way, we obtain more accurate simulations and greater resolution of the design domain. We present results in two dimensions to demonstrate the efficiency of our method.},
doi = {10.1007/s00158-018-2084-2},
journal = {Structural and Multidisciplinary Optimization},
issn = {1615-147X},
number = ,
volume = ,
place = {United States},
year = {2018},
month = {10}
}

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on October 26, 2019
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