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Title: Multiscale topology optimization using neural network surrogate models

Abstract

In this study, we are concerned with optimization of macroscale elastic structures that are designed utilizing spatially varying microscale metamaterials. The macroscale optimization is accomplished using gradient-based nonlinear topological optimization. But instead of using density as the optimization decision variable, the decision variables are the multiple parameters that define the local microscale metamaterial. This is accomplished using single layer feedforward Gaussian basis function networks as a surrogate models of the elastic response of the microscale metamaterial. The surrogate models are trained using highly resolved continuum finite element simulations of the microscale metamaterials and hence are significantly more accurate than analytical models e.g. classical beam theory. Because the derivative of the surrogate model is important for sensitivity analysis of the macroscale topology optimization, a neural network training procedure based on the Sobolev norm is described. Since the SIMP method is not appropriate for spatially varying lattices, an alternative method is developed to enable creation of void regions. Lastly, the efficacy of this approach is demonstrated via several examples in which the optimal graded metamaterial outperforms a traditional solid structure.

Authors:
 [1];  [1];  [1];  [1]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (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:
1557076
Report Number(s):
LLNL-JRNL-760619
Journal ID: ISSN 0045-7825; 948858
Grant/Contract Number:  
AC52-07NA27344
Resource Type:
Accepted Manuscript
Journal Name:
Computer Methods in Applied Mechanics and Engineering
Additional Journal Information:
Journal Volume: 346; Journal Issue: C; Journal ID: ISSN 0045-7825
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; 97 MATHEMATICS AND COMPUTING; Topology optimization; Multiscale analysis; Neural networks; Material models

Citation Formats

White, Daniel A., Arrighi, William J., Kudo, Jun, and Watts, Seth E. Multiscale topology optimization using neural network surrogate models. United States: N. p., 2018. Web. doi:10.1016/j.cma.2018.09.007.
White, Daniel A., Arrighi, William J., Kudo, Jun, & Watts, Seth E. Multiscale topology optimization using neural network surrogate models. United States. doi:10.1016/j.cma.2018.09.007.
White, Daniel A., Arrighi, William J., Kudo, Jun, and Watts, Seth E. Wed . "Multiscale topology optimization using neural network surrogate models". United States. doi:10.1016/j.cma.2018.09.007.
@article{osti_1557076,
title = {Multiscale topology optimization using neural network surrogate models},
author = {White, Daniel A. and Arrighi, William J. and Kudo, Jun and Watts, Seth E.},
abstractNote = {In this study, we are concerned with optimization of macroscale elastic structures that are designed utilizing spatially varying microscale metamaterials. The macroscale optimization is accomplished using gradient-based nonlinear topological optimization. But instead of using density as the optimization decision variable, the decision variables are the multiple parameters that define the local microscale metamaterial. This is accomplished using single layer feedforward Gaussian basis function networks as a surrogate models of the elastic response of the microscale metamaterial. The surrogate models are trained using highly resolved continuum finite element simulations of the microscale metamaterials and hence are significantly more accurate than analytical models e.g. classical beam theory. Because the derivative of the surrogate model is important for sensitivity analysis of the macroscale topology optimization, a neural network training procedure based on the Sobolev norm is described. Since the SIMP method is not appropriate for spatially varying lattices, an alternative method is developed to enable creation of void regions. Lastly, the efficacy of this approach is demonstrated via several examples in which the optimal graded metamaterial outperforms a traditional solid structure.},
doi = {10.1016/j.cma.2018.09.007},
journal = {Computer Methods in Applied Mechanics and Engineering},
number = C,
volume = 346,
place = {United States},
year = {2018},
month = {10}
}

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