---
_id: '12801'
abstract:
- lang: eng
  text: The present contribution derives a theoretical framework for constructing
    novel geometrical constraints in the context of density-based topology optimization.
    Principally, the predefined geometrical dimensionality is enforced locally on
    the components of the optimized structures. These constraints are defined using
    the principal values (singular values) from a singular value decomposition of
    points clouds represented by elemental centroids and the corresponding relative
    density design variables. The proposed approach is numerically implemented for
    demonstrating the designing of lattice or membrane-like structures. Several numerical
    examples confirm the validity of the derived theoretical framework for geometric
    dimensionality control.
article_number: '160'
author:
- first_name: Nikolai
  full_name: Gerzen, Nikolai
  id: '76704'
  last_name: Gerzen
- first_name: Thorsten
  full_name: Mertins, Thorsten
  last_name: Mertins
- first_name: Claus B. W.
  full_name: Pedersen, Claus B. W.
  last_name: Pedersen
citation:
  ama: Gerzen N, Mertins T, Pedersen CBW. Geometric dimensionality control of structural
    components in topology optimization. <i>Structural and Multidisciplinary Optimization</i>.
    2022;65(5). doi:<a href="https://doi.org/10.1007/s00158-022-03252-7">10.1007/s00158-022-03252-7</a>
  apa: Gerzen, N., Mertins, T., &#38; Pedersen, C. B. W. (2022). Geometric dimensionality
    control of structural components in topology optimization. <i>Structural and Multidisciplinary
    Optimization</i>, <i>65</i>(5), Article 160. <a href="https://doi.org/10.1007/s00158-022-03252-7">https://doi.org/10.1007/s00158-022-03252-7</a>
  bjps: <b>Gerzen N, Mertins T and Pedersen CBW</b> (2022) Geometric Dimensionality
    Control of Structural Components in Topology Optimization. <i>Structural and Multidisciplinary
    Optimization</i> <b>65</b>.
  chicago: Gerzen, Nikolai, Thorsten Mertins, and Claus B. W. Pedersen. “Geometric
    Dimensionality Control of Structural Components in Topology Optimization.” <i>Structural
    and Multidisciplinary Optimization</i> 65, no. 5 (2022). <a href="https://doi.org/10.1007/s00158-022-03252-7">https://doi.org/10.1007/s00158-022-03252-7</a>.
  chicago-de: Gerzen, Nikolai, Thorsten Mertins und Claus B. W. Pedersen. 2022. Geometric
    dimensionality control of structural components in topology optimization. <i>Structural
    and Multidisciplinary Optimization</i> 65, Nr. 5. doi:<a href="https://doi.org/10.1007/s00158-022-03252-7">10.1007/s00158-022-03252-7</a>,
    .
  din1505-2-1: '<span style="font-variant:small-caps;">Gerzen, Nikolai</span> ; <span
    style="font-variant:small-caps;">Mertins, Thorsten</span> ; <span style="font-variant:small-caps;">Pedersen,
    Claus B. W.</span>: Geometric dimensionality control of structural components
    in topology optimization. In: <i>Structural and Multidisciplinary Optimization</i>
    Bd. 65. Berlin, Springer Science and Business Media LLC (2022), Nr. 5'
  havard: N. Gerzen, T. Mertins, C.B.W. Pedersen, Geometric dimensionality control
    of structural components in topology optimization, Structural and Multidisciplinary
    Optimization. 65 (2022).
  ieee: 'N. Gerzen, T. Mertins, and C. B. W. Pedersen, “Geometric dimensionality control
    of structural components in topology optimization,” <i>Structural and Multidisciplinary
    Optimization</i>, vol. 65, no. 5, Art. no. 160, 2022, doi: <a href="https://doi.org/10.1007/s00158-022-03252-7">10.1007/s00158-022-03252-7</a>.'
  mla: Gerzen, Nikolai, et al. “Geometric Dimensionality Control of Structural Components
    in Topology Optimization.” <i>Structural and Multidisciplinary Optimization</i>,
    vol. 65, no. 5, 160, 2022, <a href="https://doi.org/10.1007/s00158-022-03252-7">https://doi.org/10.1007/s00158-022-03252-7</a>.
  short: N. Gerzen, T. Mertins, C.B.W. Pedersen, Structural and Multidisciplinary
    Optimization 65 (2022).
  ufg: '<b>Gerzen, Nikolai/Mertins, Thorsten/Pedersen, Claus B.W.</b>: Geometric dimensionality
    control of structural components in topology optimization, in: <i>Structural and
    Multidisciplinary Optimization</i> 65 (2022), H. 5.'
  van: Gerzen N, Mertins T, Pedersen CBW. Geometric dimensionality control of structural
    components in topology optimization. Structural and Multidisciplinary Optimization.
    2022;65(5).
date_created: 2025-04-16T05:58:58Z
date_updated: 2025-06-26T13:39:04Z
department:
- _id: DEP3020
doi: 10.1007/s00158-022-03252-7
external_id:
  isi:
  - '000796069200001'
intvolume: '        65'
isi: '1'
issue: '5'
keyword:
- Manufacturing constraints
- Topology optimization
- Geometric constraints
- Gradient based structural optimization
- Lattice designing
- Additive manufacturing
language:
- iso: eng
place: Berlin
publication: Structural and Multidisciplinary Optimization
publication_identifier:
  eissn:
  - 1615-147X
  issn:
  - 1615-1488
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Geometric dimensionality control of structural components in topology optimization
type: scientific_journal_article
user_id: '83781'
volume: 65
year: '2022'
...