Search Menu
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information
Search Scholarly Publications

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]
+ Show Author Affiliations
  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
Alternate Identifier(s):
OSTI ID: 1636038
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.
Copy to clipboard
White, Daniel A., Arrighi, William J., Kudo, Jun, & Watts, Seth E. Multiscale topology optimization using neural network surrogate models. United States. https://doi.org/10.1016/j.cma.2018.09.007
Copy to clipboard
White, Daniel A., Arrighi, William J., Kudo, Jun, and Watts, Seth E. Wed . "Multiscale topology optimization using neural network surrogate models". United States. https://doi.org/10.1016/j.cma.2018.09.007. https://www.osti.gov/servlets/purl/1557076.
Copy to clipboard
@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 = {Wed Oct 10 00:00:00 EDT 2018},
month = {Wed Oct 10 00:00:00 EDT 2018}
}
Copy to clipboard
Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1016/j.cma.2018.09.007
Copyright Statement
Other availability
Search WorldCat Search WorldCat to find libraries that may hold this journal
Citation Metrics:
Cited by: 81 works
Citation information provided by
Web of Science

Figures / Tables:

Figure 1 Figure 1: Illustration of metamaterial unit cells.
All figures and tables (17 total)
Save / Share:
Export Metadata
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.

Works referenced in this record:

Optimal shape design as a material distribution problem
journal, December 1989

Aims, scope, methods, history and unified terminology of computer-aided topology optimization in structural mechanics
journal, April 2001

  • Rozvany, G. I. N.
  • Structural and Multidisciplinary Optimization, Vol. 21, Issue 2
  • DOI: 10.1007/s001580050174

Sufficiency of a finite exponent in SIMP (power law) methods
journal, April 2001

Topology optimization of non-linear elastic structures and compliant mechanisms
journal, March 2001

  • Bruns, Tyler E.; Tortorelli, Daniel A.
  • Computer Methods in Applied Mechanics and Engineering, Vol. 190, Issue 26-27
  • DOI: 10.1016/S0045-7825(00)00278-4

An element removal and reintroduction strategy for the topology optimization of structures and compliant mechanisms
journal, January 2003

  • Bruns, T. E.; Tortorelli, D. A.
  • International Journal for Numerical Methods in Engineering, Vol. 57, Issue 10
  • DOI: 10.1002/nme.783

Filters in topology optimization based on Helmholtz-type differential equations
journal, December 2010

  • Lazarov, B. S.; Sigmund, O.
  • International Journal for Numerical Methods in Engineering, Vol. 86, Issue 6
  • DOI: 10.1002/nme.3072

Free material optimization via mathematical programming
journal, October 1997

  • Zowe, Jochem; Kočvara, Michal; Bendsøe, Martin P.
  • Mathematical Programming, Vol. 79, Issue 1-3
  • DOI: 10.1007/BF02614328

Free material optimization: recent progress†
journal, February 2008

Shape optimization by the homogenization method
journal, March 1997

  • Allaire, Grégoire; Bonnetier, Eric; Francfort, Gilles
  • Numerische Mathematik, Vol. 76, Issue 1
  • DOI: 10.1007/s002110050253

A geometric projection method for designing three-dimensional open lattices with inverse homogenization: A geometric projection method
journal, July 2017

  • Watts, Seth; Tortorelli, Daniel A.
  • International Journal for Numerical Methods in Engineering, Vol. 112, Issue 11
  • DOI: 10.1002/nme.5569

Error estimates and condition numbers for radial basis function interpolation
journal, April 1995

  • Schaback, Robert
  • Advances in Computational Mathematics, Vol. 3, Issue 3
  • DOI: 10.1007/BF02432002

Universal Approximation Using Radial-Basis-Function Networks
journal, June 1991

Multilayer feedforward networks are universal approximators
journal, January 1989

Interpolation and rates of convergence for a class of neural networks
journal, March 2009

Approximation capability of interpolation neural networks
journal, December 2010

On learning the derivatives of an unknown mapping with multilayer feedforward networks
journal, January 1992

Neural networks as material models within a multiscale approach
journal, October 2009

Accurate cyclic plastic analysis using a neural network material model
journal, March 2004

Artificial Neural Networks in numerical modelling of composites
journal, May 2009

  • Lefik, M.; Boso, D. P.; Schrefler, B. A.
  • Computer Methods in Applied Mechanics and Engineering, Vol. 198, Issue 21-26
  • DOI: 10.1016/j.cma.2008.12.036

Neural network constitutive modelling for non-linear characterization of anisotropic materials
journal, August 2010

  • Man, H.; Furukawa, T.
  • International Journal for Numerical Methods in Engineering, Vol. 85, Issue 8
  • DOI: 10.1002/nme.2999

Neural network based constitutive model for elastomeric foams
journal, July 2008

A neural network-based surrogate model for carbon nanotubes with geometric nonlinearities
journal, January 2018

  • Papadopoulos, V.; Soimiris, G.; Giovanis, D. G.
  • Computer Methods in Applied Mechanics and Engineering, Vol. 328
  • DOI: 10.1016/j.cma.2017.09.010

On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming
journal, April 2005

Optimal lattice-structured materials
journal, November 2016

Approximation of a function and its derivative with a neural network
journal, January 1992

Approximation of function and its derivatives using radial basis function networks
journal, March 2003

On the limited memory BFGS method for large scale optimization
journal, August 1989

  • Liu, Dong C.; Nocedal, Jorge
  • Mathematical Programming, Vol. 45, Issue 1-3
  • DOI: 10.1007/BF01589116

Data dimensionality estimation methods: a survey
journal, December 2003

Polynomial Bounds for VC Dimension of Sigmoidal and General Pfaffian Neural Networks
journal, February 1997

  • Karpinski, Marek; Macintyre, Angus
  • Journal of Computer and System Sciences, Vol. 54, Issue 1
  • DOI: 10.1006/jcss.1997.1477

Almost Linear VC-Dimension Bounds for Piecewise Polynomial Networks
journal, November 1998

    Sort by:
    [ × clear filter / sort ]

    Works referencing / citing this record:

    Simple, accurate surrogate models of the elastic response of three-dimensional open truss micro-architectures with applications to multiscale topology design
    journal, May 2019

    • Watts, Seth; Arrighi, William; Kudo, Jun
    • Structural and Multidisciplinary Optimization, Vol. 60, Issue 5
    • DOI: 10.1007/s00158-019-02297-5
      Sort by:
      [ × clear filter / sort ]

      Figures / Tables found in this record:

      Figure 1 (p. 13)figure
      Figure 2 (p. 15)figure
      Table 1 (p. 20)table
      Table 2 (p. 20)table
      Figure 3 (p. 21)figure
      Figure 4 (p. 22)figure
      Figure 5 (p. 23)figure
      Figure 6 (p. 24)figure
      Figure 7 (p. 25)figure
      Figure 8 (p. 26)figure
      Table 3 (p. 27)table
      Figure 9 (p. 28)figure
      Figure 10 (p. 29)figure
      Figure 11 (p. 30)figure
      Figure 12 (p. 31)figure
      Figure 13 (p. 31)figure
      Table 4 (p. 31)table
        [ × clear filter / sort ]
        Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.

        Similar Records in DOE PAGES and OSTI.GOV collections: