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Title: A computational study of symmetry and well-posedness of structural topology optimization

Abstract

We report on computational topological optimization of elastic structures, in particular minimization of compliance subject to a constraint on the mass. Through computational experiments, it is discovered that even very simple optimization problems can exhibit complex behavior such as critical points and bifurcation. In the vicinity of significant points, structural topology optimization problems are not well-posed since infinitesimally small perturbations lead to distinct topologies.

Authors:
ORCiD logo [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:
1557061
Report Number(s):
LLNL-JRNL-761457
Journal ID: ISSN 1615-147X; 949598
Grant/Contract Number:  
AC52-07NA27344
Resource Type:
Accepted Manuscript
Journal Name:
Structural and Multidisciplinary Optimization
Additional Journal Information:
Journal Volume: 59; Journal Issue: 3; Journal ID: ISSN 1615-147X
Publisher:
Springer
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; 97 MATHEMATICS AND COMPUTING; Structures; Topology; Optimization; Bifurcation; Well-posed

Citation Formats

White, Daniel A., and Voronin, Alexey. A computational study of symmetry and well-posedness of structural topology optimization. United States: N. p., 2018. Web. doi:10.1007/s00158-018-2098-9.
White, Daniel A., & Voronin, Alexey. A computational study of symmetry and well-posedness of structural topology optimization. United States. doi:10.1007/s00158-018-2098-9.
White, Daniel A., and Voronin, Alexey. Thu . "A computational study of symmetry and well-posedness of structural topology optimization". United States. doi:10.1007/s00158-018-2098-9. https://www.osti.gov/servlets/purl/1557061.
@article{osti_1557061,
title = {A computational study of symmetry and well-posedness of structural topology optimization},
author = {White, Daniel A. and Voronin, Alexey},
abstractNote = {We report on computational topological optimization of elastic structures, in particular minimization of compliance subject to a constraint on the mass. Through computational experiments, it is discovered that even very simple optimization problems can exhibit complex behavior such as critical points and bifurcation. In the vicinity of significant points, structural topology optimization problems are not well-posed since infinitesimally small perturbations lead to distinct topologies.},
doi = {10.1007/s00158-018-2098-9},
journal = {Structural and Multidisciplinary Optimization},
number = 3,
volume = 59,
place = {United States},
year = {2018},
month = {10}
}

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Cited by: 3 works
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Figures / Tables:

Fig. 1 Fig. 1: A Two-Dimensional Cantilever Beam Problem

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Works referenced in this record:

Ill-posed problems in structural optimization and their practical consequences
journal, April 1994


Discussion on symmetry of optimum topology design
journal, July 2011

  • Cheng, Gengdong; Liu, Xiaofeng
  • Structural and Multidisciplinary Optimization, Vol. 44, Issue 5
  • DOI: 10.1007/s00158-011-0686-z

Some symmetry results for optimal solutions in structural optimization
journal, April 2012

  • Guo, Xu; Ni, Changhui; Cheng, Gengdong
  • Structural and Multidisciplinary Optimization, Vol. 46, Issue 5
  • DOI: 10.1007/s00158-012-0802-8

A symmetry reduction method for continuum structural topology optimization
journal, January 1999


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

Symmetry and asymmetry of solutions in discrete variable structural optimization
journal, January 2013

  • Richardson, James N.; Adriaenssens, Sigrid; Bouillard, Philippe
  • Structural and Multidisciplinary Optimization, Vol. 47, Issue 5
  • DOI: 10.1007/s00158-012-0871-8

Exact analytical solutions for some popular benchmark problems in topology optimization
journal, February 1998


On symmetry and non-uniqueness in exact topology optimization
journal, September 2010


A 99 line topology optimization code written in Matlab
journal, April 2001


On some fundamental properties of structural topology optimization problems
journal, January 2010


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


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    journal, January 2020

    • Zhao, Junpeng; Yoon, Heonjun; Youn, Byeng D.
    • Structural and Multidisciplinary Optimization, Vol. 61, Issue 3
    • DOI: 10.1007/s00158-019-02457-7