## 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:

- 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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